{"id":61296,"date":"2025-06-23T21:44:28","date_gmt":"2025-06-23T13:44:28","guid":{"rendered":"https:\/\/swarma.org\/?p=61296"},"modified":"2025-06-23T21:44:28","modified_gmt":"2025-06-23T13:44:28","slug":"%e4%bb%80%e4%b9%88%e6%a0%b7%e7%9a%84%e9%a9%ac%e5%b0%94%e7%a7%91%e5%a4%ab%e9%93%be%e5%8f%af%e4%bb%a5%e8%a2%ab%e6%97%a0%e6%8d%9f%e5%9c%b0%e7%b2%97%e7%b2%92%e5%8c%96%ef%bc%9f%ef%bd%9c%e9%9b%86%e6%99%ba","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=61296","title":{"rendered":"\u4ec0\u4e48\u6837\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u53ef\u4ee5\u88ab\u65e0\u635f\u5730\u7c97\u7c92\u5316\uff1f\uff5c\u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u5bfc\u8bed<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n

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\u6210\u5757\u6027\uff08Lumpability\uff09\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7c97\u7c92\u5316\u7406\u8bba\u4e2d\u4e00\u79cd\u63cf\u8ff0\u662f\u5426\u53ef\u805a\u7c7b\u6216\u53ef\u7c97\u7c92\u5316\u7684\u6982\u5ff5\uff0c\u6700\u65e9\u7531Kemeny\u548cSnell\u5728\u51761969\u5e74\u7684\u8457\u4f5cFinite Markov Chains[1]\u4e2d\u63d0\u51fa\u3002Lump\u4e00\u8bcd\u6709\u2018\u5757\u2019\u7684\u610f\u601d\u3002\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u662f\u5426\u53ef\u6210\u5757\uff08lumpable\uff09\uff0c\u5c31\u662f\u8981\u5224\u5b9a\u662f\u5426\u5b58\u5728\u4e00\u79cd\u72b6\u6001\u5212\u5206\u65b9\u5f0f\uff0c\u80fd\u591f\u5c06\u539f\u59cb\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u538b\u7f29\u4e3a\u4e00\u4e2a\u4fdd\u7559\u5176\u4e3b\u8981\u52a8\u529b\u5b66\u7279\u5f81\u7684\u7b80\u5316\u94fe\u3002<\/span><\/span><\/span><\/strong><\/p>\n


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\u7b80\u800c\u8a00\u4e4b\uff0c\u6210\u5757\u6027\u8981\u6c42\u88ab\u805a\u7c7b\u6210\u4e00\u4e2a\u5757\u4e2d\u7684\u72b6\u6001\u8f6c\u79fb\u5230\u5176\u4ed6\u5757\u7684\u6982\u7387\u5728\u7c97\u7c92\u5316\u524d\u540e\uff08\u5373\u72b6\u6001\u88ab\u5f52\u5e76\uff0c\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u88ab\u7ea6\u7b80\u524d\u540e\uff09\u8981\u4fdd\u6301\u4e00\u81f4\u3002\u8fd9\u79cd\u5212\u5206\u867d\u7136\u62b9\u9664\u4e86\u5206\u7ec4\u5185\u90e8\u72b6\u6001\u7684\u5fae\u89c2\u5dee\u5f02\uff0c\u4f46\u80fd\u7cbe\u786e\u4fdd\u6301\u5757\u95f4\u7684\u8f6c\u79fb\u673a\u5236\uff0c\u5e76\u4e3a\u72b6\u6001\u7a7a\u95f4\u7684\u5408\u7406\u5212\u5206\u63d0\u4f9b\u4e86\u4e25\u683c\u7684\u6570\u5b66\u5224\u636e\uff0c\u4ece\u800c\u4f7f\u5f97\u5728\u72b6\u6001\u7a7a\u95f4\u4e0a\u5b9a\u4e49\u7684\u5206\u7ec4\u65b9\u6848\u81ea\u7136\u8574\u542b\u4e86\u4e00\u4e2a\u5408\u7406\u7684\u5b8f\u89c2\u7684\u52a8\u529b\u5b66\uff0c\u5373\u5b8f\u89c2\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u3002<\/span><\/span><\/span><\/strong><\/p>\n


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\u7b26\u5408\u6210\u5757\u6027\u7684\u7c97\u7c92\u5316\u65b9\u6848\u901a\u5e38\u6ee1\u8db3\u5f88\u597d\u7684\u6027\u8d28\uff0c\u5982\u5b83\u80fd\u4fdd\u8bc1\u5bf9\u5b8f\u89c2\u5c42\u9762\u4e0a\u7684\u6700\u5927\u9884\u6d4b\u6027\u3001\u5fae\u89c2\u4e0e\u5b8f\u89c2\u8fc7\u7a0b\u7684\u4e00\u81f4\u6027\u7b49\u3002\u8fd9\u4f7f\u5f97\u6210\u5757\u6027\u6210\u4e3a\u9a6c\u5c14\u79d1\u592b\u94fe\u7ef4\u5ea6\u7ea6\u7b80\u7814\u7a76\u4e2d\u6700\u5e38\u7528\u7684\u6807\u51c6\u4e4b\u4e00\u3002<\/span><\/span><\/span><\/strong><\/p>\n


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\u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u56e0\u679c\u6d8c\u73b0\u7cfb\u5217\u8bfb\u4e66\u4f1a\uff0c\u76ee\u524d\u5df2\u7ecf\u6301\u7eed\u5230\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u5982\u679c\u4f60\u5bf9\u8fd9\u4e00\u8bdd\u9898\u611f\u5174\u8da3\uff0c\u975e\u5e38\u63a8\u8350\u4f60\u52a0\u5165\u793e\u533a\uff01<\/span><\/span><\/strong><\/p>\n


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\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff0c\u6587\u672b\u53ef\u4ee5\u626b\u7801\u62a5\u540d\u52a0\u5165\u767e\u79d1\u5fd7\u613f\u8005\uff01<\/span><\/strong><\/span><\/strong><\/p>\n


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\u2191\u2191\u2191\u626b\u7801\u76f4\u8fbe\u767e\u79d1\u8bcd\u6761<\/span><\/p>\n

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\u5173\u952e\u8bcd\uff1a\u56e0\u679c\u6d8c\u73b0\uff0c\u6709\u6548\u4fe1\u606f<\/span><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
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\u5f20\u6c5f\u3001\u6881\u4eac\u660a <\/span><\/span><\/span>| \u4f5c\u8005<\/span><\/span><\/p>\n

\u5f20\u6c5f\u3001\u8881\u51b0\u3001\u5218\u51ef\u5a01\u3001\u6768\u660e\u54f2\u3001\u738b\u5fd7\u9e4f <\/span><\/span><\/span>| \u6574\u7406&\u5ba1\u6821<\/span><\/span><\/section>\n


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\u76ee\u5f55<\/span><\/strong><\/p>\n

1. \u6210\u5757\u6027\u4e3a\u4ec0\u4e48\u91cd\u8981\uff1f<\/span><\/span><\/p>\n

2. \u6700\u521d\u5b9a\u4e49<\/span><\/span><\/p>\n

2.1\t\u57fa\u672c\u6982\u5ff5\u5b9a\u4e49<\/span><\/span><\/p>\n

2.2\t\u7b80\u5316\u8fc7\u7a0b\u5b9a\u4e49<\/span><\/span><\/p>\n

2.3\t\u6210\u5757\u7684\u5212\u5206<\/span><\/span><\/p>\n

2.4\t\u4e3e\u4f8b<\/span><\/span><\/p>\n

3. \u6210\u5757\u6027\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6<\/span><\/span><\/p>\n

3.1\t\u5b9a\u4e49\u4e09\u79cd\u6982\u7387<\/span><\/span><\/p>\n

3.2\t\u6210\u5757\u6027\u5145\u8981\u6761\u4ef6\u5b9a\u7406<\/span><\/span><\/p>\n

3.3\t\u6210\u5757\u6027\u7684\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/span><\/p>\n

3.4\t\u5b9a\u74061\u7684\u8bc1\u660e<\/span><\/span><\/p>\n

3.5\t\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027<\/span><\/span><\/p>\n

4. \u6210\u5757\u6027\u7684\u6b63\u4f8b\u548c\u53cd\u4f8b<\/span><\/span><\/p>\n

4.1\t\u6b63\u4f8b<\/span><\/span><\/p>\n

4.2\t\u53cd\u4f8b<\/span><\/span><\/p>\n

4.3\t\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u6b63\u4f8b<\/span><\/span><\/p>\n

5. \u6210\u5757\u6027\u6ee1\u8db3\u7684\u6027\u8d28<\/span><\/span><\/p>\n

5.1\t\u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027<\/span><\/span><\/p>\n

5.2\t\u6210\u5757\u5212\u5206\u548c\u7c97\u7c92\u5316\u7684\u53ef\u4ea4\u6362\u6027<\/span><\/span><\/p>\n

5.3\t\u4e00\u81f4\u6027<\/span><\/span><\/p>\n

6. \u6210\u5757\u6027\u6982\u5ff5\u7684\u53d8\u79cd<\/span><\/span><\/p>\n

6.1\t\u5f3a\u6210\u5757\u6027 Strong\/Ordinary Lumpability<\/span><\/span><\/p>\n

6.2\t\u5f31\u6210\u5757\u6027 Weak Lumpability<\/span><\/span><\/p>\n

6.3\t\u7cbe\u786e\u6210\u5757\u6027 Exact Lumpability<\/span><\/span><\/p>\n

6.4\t\u4e25\u683c\u6210\u5757\u6027 Strict Lumpability<\/span><\/span><\/p>\n

6.5\t\u51c6\u6210\u5757\u6027 Quasi Lumpability<\/span><\/span><\/p>\n

6.6\t\u6bd4\u4f8b\u6210\u5757\u6027 Proportional Lumpability<\/span><\/span><\/p>\n

7. \u6210\u5757\u6027\u548c\u7c97\u7c92\u5316<\/span><\/span><\/p>\n

7.1\t\u57fa\u4e8e\u6210\u5757\u6027\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\uff08\u672a\u7ed9\u5b9a\u6210\u5757\u7684\u5212\u5206\u7684\u60c5\u51b5\uff09<\/span><\/span><\/p>\n

8. \u6210\u5757\u6027\u7684\u76f8\u5173\u6982\u5ff5<\/span><\/span><\/p>\n

8.1\t\u56e0\u679c\u6001<\/span><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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1. \u6210\u5757\u6027\u4e3a\u4ec0\u4e48\u91cd\u8981\uff1f<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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\u4e3a\u7406\u89e3\u6210\u5757\u6027 (lumpability) \u7684\u91cd\u8981\u6027\uff0c\u6211\u4eec\u5148\u901a\u8fc7\u4e00\u4e2a\u53cd\u4f8b\u6765\u63ed\u793a\u4e0d\u6ee1\u8db3\u6210\u5757\u6027\u7684\u7c97\u7c92\u5316\u65b9\u6848\u7684\u7f3a\u9677\uff0c\u4ece\u800c\u8ba9\u8bfb\u8005\u611f\u53d7\u5230\u5f15\u51fa\u6210\u5757\u6027\u6982\u5ff5\u7684\u5fc5\u8981\u6027\u3002\u7ed9\u5b9a\u5982\u4e0b\u56fe\u6240\u793a\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u5047\u8bbe\u6211\u4eec\u5c1d\u8bd5\u8fdb\u884c\u5982\u4e0b\u7684\u7c97\u7c92\u5316\u64cd\u4f5c\uff0c\u5373\u5c06\u72b6\u6001{1,2}\u5408\u5e76\u4e3a\u5b8f\u89c2\u6001<\/span><\/span>A<\/span><\/span><\/span>\uff0c{3,4}\u5408\u5e76\u4e3a<\/span><\/span>B<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u56fe1\uff1a\u4e0d\u6ee1\u8db3\u4e00\u81f4\u6027\u7c97\u7c92\u5316\u793a\u4f8b<\/span><\/span><\/p>\n

\u5f53\u6211\u4eec\u6784\u5efa\u7c97\u7c92\u5316\u540e\u7684\u5c3a\u5bf8\u4e3a<\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span>2<\/span><\/span><\/span>\u7684\u5b8f\u89c2\u9a6c\u5c14\u79d1\u592b\u94fe<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u65f6\uff0c\u5206\u7ec4A\u5230\u5206\u7ec4B\u7684\u6982\u7387\u5e94\u6ee1\u8db3\uff1a<\/span><\/span>\u4ece<\/span><\/span>A<\/span><\/span>\u6216<\/span><\/span>B<\/span><\/span>\u7684\u4e2d\u4efb\u4e00\u5fae\u89c2\u6001\u51fa\u53d1\uff0c\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>\u6216<\/span><\/span>B<\/span><\/span>\u4e2d\u5404\u4e2a\u72b6\u6001\u7684\u603b\u6982\u7387\u5fc5\u987b\u76f8\u540c<\/span><\/span><\/b>\uff0c\u8fd9\u662f\u6839\u636e\u6761\u4ef6\u6982\u7387\u7684\u52a0\u6cd5\u516c\u7406\u800c\u81ea\u7136\u5bfc\u51fa\u7684\u8981\u6c42\u3002<\/span><\/span><\/p>\n

\u4f8b\u5982\uff0c\u56fe\u4e2d\u7684<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u5de6\u4e0a\u89d2\u7684\u5143\u7d20\uff08\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u5230\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u7684\u6982\u7387\uff09\u7b49\u4e8e\u5fae\u89c2\u60011\u6216\u5fae\u89c2\u60012\u8f6c\u79fb\u5230A\u7684\u6982\u7387\uff0c\u90fd\u7b49\u4e8e0.6\u3002\u540c\u7406\uff0c\u53f3\u4e0a\u89d2\u7684\u5143\u7d20\uff08\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u5230\u7ec4<\/span><\/span>B<\/span><\/span><\/span>\u7684\u6982\u7387\uff09\u7b49\u4e8e0.4\u3002<\/span><\/span><\/p>\n

\u7136\u800c\uff0c\u5f53\u6211\u4eec\u8ba1\u7b97\u5de6\u4e0b\u89d2\u7684\uff08\u5373\u7ec4<\/span><\/span>B<\/span><\/span><\/span>\u5230\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u7684\u6982\u7387\uff09\u7684\u6982\u7387\u65f6\u53d1\u73b0\uff1a\u4ece\u5fae\u89c2\u60013\u8f6c\u79fb\u5230\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u7684\u6982\u7387\u4e3a0.3+0.3=0.6\uff0c\u4ece\u5fae\u89c2\u60014\u8f6c\u79fb\u5230\u7ec4<\/span><\/span>A<\/span><\/span><\/span>\u7684\u6982\u7387\u4e3a0.1+0.1=0.2\u3002\u8fd9\u79cd\u7ec4\u5185\u8f6c\u79fb\u6982\u7387\u7684\u51b2\u7a81\u5bfc\u81f4\u6211\u4eec\u65e0\u6cd5\u5b9a\u4e49\u552f\u4e00\u7684<\/span><\/span>B<\/span><\/span>\u2192<\/span><\/span>A<\/span><\/span><\/span>\u7684\u5b8f\u89c2\u8f6c\u79fb\u6982\u7387\u3002<\/span><\/span><\/p>\n

\u4e3a\u4e86\u5f97\u5230\u4e00\u7ec4\u5408\u7406\u7684\u5b8f\u89c2\u8f6c\u79fb\u6982\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5\u5982\u4e0b\u4e09\u79cd\u53d6\u503c\u65b9\u6848\uff1a\u8bbe\u4ece\u5fae\u89c2\u60013\u5230A\u7684\u6982\u7387=0.6\uff1b\u8bbe\u4ece\u5fae\u89c2\u60014\u5230A\u7684\u6982\u7387=0.2\uff1b\u7136\u540e\u628a0.6\u548c0.2\u53d6\u5e73\u5747\uff0c\u4ece\u800c\u5f97\u5230\u4e00\u4e2a\u8f6c\u79fb\u6982\u7387\uff1a0.4\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u79cd\u65b9\u6848\u5f3a\u884c\u6784\u9020\u4e86\u4e00\u4e2a\u5b8f\u89c2\u7684\u8f6c\u79fb\u77e9\u9635\u3002\u8fd9\u79cd\u5f3a\u5236\u5b9a\u4e49\u7684\u8f6c\u79fb\u6982\u7387\u7c97\u7c92\u5316\u65b9\u6848\u770b\u4f3c\u5408\u7406\uff0c\u4f46\u662f\u5374\u6697\u85cf\u7740\u77db\u76fe\u3002<\/span><\/span><\/p>\n

\u6bd4\u5982\u8bbe\u5de6\u4e0b\u89d2\u7684\u6240\u6709\u5143\u7d20\u7684\u6982\u7387=0.6\uff0c\u53f3\u4e0b\u89d2\u7684\u6240\u6709\u5143\u7d20\u6982\u7387=0.4\uff0c\u5219\u6211\u4eec\u53ef\u5f3a\u884c\u5f97\u5230\u4e00\u4e2a\u5b8f\u89c2\u8f6c\u79fb\u6982\u7387\u77e9\u9635\uff08TPM\uff09\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u867d\u7136\u8be5TPM\u6ee1\u8db3\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684\u6240\u6709\u6761\u4ef6\uff0c\u4f46\u5c06\u5b83\u4e0e\u5fae\u89c2\u6001\u5206\u5e03\u4ee5\u53ca\u7c97\u7c92\u5316\u64cd\u4f5c\u5408\u5728\u4e00\u8d77\u4ee5\u540e\uff0c\u5c31\u53ef\u80fd\u5bfc\u81f4\u4e0d\u5408\u7406\u6027\u3002<\/span><\/span><\/p>\n

\u4f8b\u5982\uff0c\u6211\u4eec\u5047\u8bbe\u7cfb\u7edf\u7684\u5fae\u89c2\u521d\u59cb\u72b6\u6001\u5206\u5e03\u4e3a\uff1a(1, 0, 0, 0)\uff0c\u5219\u6839\u636e\u6211\u4eec\u7684\u7c97\u7c92\u5316\u65b9\u6848\uff0c\u7cfb\u7edf\u7684\u5b8f\u89c2\u521d\u59cb\u72b6\u6001\u5206\u5e03\u5219\u4f1a\u662f(1, 0)\u3002\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5b8f\u89c2\u548c\u5fae\u89c2\u5404\u6f14\u53162\u6b65\u540e\u7684\u6982\u7387\uff1a\u5fae\u89c2\u4e3a(0.28, 0.28, 0.28, 0.16)\uff0c\u5b8f\u89c2\u4e3a(0.6, 0.4)\u3002\u6211\u4eec\u53d1\u73b0\uff0c\u628a\u4e24\u6b65\u6f14\u5316\u540e\u5f97\u5230\u7684\u5fae\u89c2\u7684\u72b6\u6001\u5206\u5e03\u6620\u5c04\u5230\u5b8f\u89c2\u540e\u4fbf\u4f1a\u5f97\u5230\u4e00\u4e2a\u5b8f\u89c2\u6001\u5206\u5e03\uff1a(0.56, 0.44)\uff0c\u8fd9\u4e0e\u524d\u8ff0\u7531\u4e24\u6b65\u5b8f\u89c2\u52a8\u529b\u5b66\u6f14\u5316\u5f97\u5230\u7684\u72b6\u6001\u5206\u5e03(0.6, 0.4)\u4e0d\u4e00\u6837\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c<\/span><\/span>\u5b8f\u89c2\u548c\u5fae\u89c2\u7684\u6f14\u5316\u7ed3\u679c\u4e0d\u4e00\u81f4\uff0c\u8fd9\u6837\u7684\u7c97\u7c92\u5316\u65b9\u6848\u88ab\u79f0\u4e3a\u4e0d\u6ee1\u8db3\u4e00\u81f4\u6027\u3002\u5b83\u6784\u5efa\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u65e0\u6cd5\u51c6\u786e\u5730\u53cd\u6620\u7cfb\u7edf\u7684\u6f14\u5316\uff0c\u4e0e\u672c\u6765\u7684\u5fae\u89c2\u52a8\u529b\u5b66\u5b58\u5728\u504f\u5dee\u3002<\/span><\/span><\/b><\/p>\n

\u6240\u4ee5\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u80fd\u4fdd\u8bc1\u4e00\u81f4\u6027\u7684\u72b6\u6001\u5212\u5206\u4ee5\u53ca\u7c97\u7c92\u5316\u65b9\u6848\uff0c\u5e76\u6839\u636e\u8be5\u5212\u5206\u5b9a\u4e49\u5bf9\u5e94\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u6765\u51c6\u786e\u53cd\u6620\u5fae\u89c2\u52a8\u529b\u5b66\u5728\u5b8f\u89c2\u4e0a\u7684\u6620\u5c04\u3002\u800c\u6210\u5757\u6027\u662f\u4e00\u79cd\u9488\u5bf9\u72b6\u6001\u5212\u5206\u65b9\u6848\u7684\u6307\u6807\u3002\u5f53\u4e00\u4e2a\u72b6\u6001\u5212\u5206\u6ee1\u8db3\u6210\u5757\u6027\u65f6\uff0c\u5b83\u4e00\u5b9a\u80fd\u4fdd\u8bc1\u5b8f\u89c2\u548c\u5fae\u89c2\u52a8\u529b\u5b66\u7684\u4e00\u81f4\u6027\u3002\u800c\u4e14\uff0c\u5b83\u8fd8\u80fd\u4fdd\u8bc1\u52a8\u529b\u5b66\u7b97\u5b50\u548c\u7c97\u7c92\u5316\u7b97\u5b50\u7684\u53ef\u4ea4\u6362\u6027\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u65e0\u8bba\u6211\u4eec\u662f\u5148\u505a\u7c97\u7c92\u5316\u518d\u7ecf\u5386\u52a8\u529b\u5b66\u6f14\u5316\uff08\u5b8f\u89c2\u52a8\u529b\u5b66\u6f14\u5316\uff09\uff0c\u8fd8\u662f\u6211\u4eec\u5148\u7ecf\u5386\u52a8\u529b\u5b66\u6f14\u5316\uff08\u5fae\u89c2\u52a8\u529b\u5b66\u6f14\u5316\uff09\u518d\u8fdb\u884c\u7c97\u7c92\u5316\uff0c\u8fd9\u4e24\u6761\u8def\u5f84\uff0c\u5982\u56fe1\u6240\u793a\uff0c\u6700\u7ec8\u5f97\u5230\u7684\u7ed3\u679c\u90fd\u662f\u4e00\u6837\u7684\u3002<\/span><\/span><\/p>\n

<\/span>
<\/span><\/span><\/h2>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

2. \u6700\u521d\u5b9a\u4e49<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u4e3a\u4e86\u4e25\u8c28\u5730\u4ecb\u7ecd\u6210\u5757\u6027\u8fd9\u4e00\u5b9a\u4e49\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u7ffb\u8bd1\u6587\u7ae0<\/span><\/span>[1]<\/span><\/span><\/span>\u4e2d\u7684\u90e8\u5206\u5185\u5bb9\u3002<\/span><\/span>\u8bfb\u8005\u4e5f\u53ef\u76f4\u63a5\u8df3\u5230\u66f4\u7b80\u6d01\u76f4\u89c2\u7684\u2018\u6210\u5757\u6027\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6’\u7684\u90e8\u5206\u3002<\/span><\/span><\/b><\/p>\n

<\/span>2.1 \u57fa\u672c\u6982\u5ff5\u5b9a\u4e49<\/span><\/span><\/span><\/h3>\n

\u9996\u5148\uff0c\u6211\u4eec\u5f62\u5f0f\u5316\u5730\u5b9a\u4e49\u5fae\u89c2\u5c3a\u5ea6\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u4e3a\uff1a\u8bbe\u5fae\u89c2\u72b6\u6001\u7a7a\u95f4\u4e3a\u6709\u9650\u96c6<\/span><\/span>S<\/span><\/span>=<\/span><\/span>{<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/sub>}<\/span><\/span><\/span>\uff0c\u7cfb\u7edf\u5728<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u7684\u72b6\u6001\u5206\u5e03\u5411\u91cf<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>[<\/span><\/span>P<\/span><\/span>r<\/span><\/span>(<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>)<\/span><\/span>,<\/span><\/span>P<\/span><\/span>r<\/span><\/span>(<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>)<\/span><\/span>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>P<\/span><\/span>r<\/span><\/span>(<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>]<\/span><\/span><\/span>\u4e3a\u7cfb\u7edf\u5904\u4e8e\u5404\u4e2a\u5fae\u89c2\u72b6\u6001\u7684\u6982\u7387\uff0c\u5176\u4e2d<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>\u8868\u793a\u7cfb\u7edf\u5728\u7b2ct\u65f6\u523b\u7684\u72b6\u6001\u53d8\u91cf\u3002<\/span><\/span><\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u5fae\u89c2\u72b6\u6001\u7a7a\u95f4\u7684\u5212\u5206\uff08state partition\uff09\uff1a <\/span><\/span>A<\/span><\/span>=<\/span><\/span>{<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>A<\/span><\/span>r<\/span><\/span><\/sub>}<\/span><\/span><\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u89c6\u4e3a\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001\u7a7a\u95f4\uff0c\u5176\u4e2d<\/span><\/span>A<\/span><\/span>k<\/span><\/span><\/sub>\u4e3a\u7b2ck\u4e2a\u5b8f\u89c2\u6001\u3002<\/span><\/span><\/p>\n

\u56e0\u6b64\uff0c\u5fae\u89c2\u72b6\u6001\u7a7a\u95f4<\/span><\/span>S<\/span><\/span><\/span>\u548c\u5b8f\u89c2\u72b6\u6001\u7a7a\u95f4<\/span><\/span>A<\/span><\/span><\/span> \u4e4b\u95f4\u5b58\u5728\u786c\u6027\u5212\u5206\u6620\u5c04\u5173\u7cfb<\/span><\/span>\u03a6<\/span><\/span>:<\/span><\/span>S<\/span><\/span>\u2192<\/span><\/span>A<\/span><\/span><\/span>\uff0c\u5e76\u4e14\u6ee1\u8db3<\/span><\/span><\/p>\n

<\/section>\n

\u5373\uff1a1. <\/span><\/span>A<\/span><\/span><\/span>\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u90fd\u5305\u62ec\u82e5\u5e72\u4e2a<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\uff1b2. <\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e4b\u95f4\u6ca1\u6709\u4ea4\u96c6\uff0c\u5373\u6bcf\u4e2a<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u53ea\u80fd\u5c5e\u4e8e\u4e00\u4e2a<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\uff1b3. <\/span><\/span>S<\/span><\/span><\/span>\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u90fd\u5fc5\u987b\u5c5e\u4e8e\u67d0\u4e2a<\/span><\/span>A<\/span><\/span><\/span>\u7684\u5143\u7d20\uff0c\u5373<\/span><\/span>A<\/span><\/span><\/span>\u8986\u76d6\u4e86<\/span><\/span>S<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

<\/span>2.2 \u7b80\u5316\u8fc7\u7a0b\u5b9a\u4e49<\/span><\/span><\/span><\/h3>\n

\u6211\u4eec\u8003\u8651\u9a6c\u5c14\u79d1\u592b\u8fc7\u7a0b\u7684\u7ebf\u6027\u6295\u5f71\uff0c\u56e0\u6b64<\/span><\/span>\u03a6<\/span><\/span><\/span>\u662f\u4e00\u4e2a<\/span><\/span>{<\/span><\/span>0<\/span><\/span>,<\/span><\/span>1<\/span><\/span>}<\/span><\/span>n<\/span><\/span><\/sup>\u00d7<\/span><\/span><\/sup>r<\/span><\/span><\/sup><\/span>\u7684\u6295\u5f71\u77e9\u9635\u3002\u5bf9\u4e8e\u4efb\u610f <\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a<\/span><\/span>\u7b80\u5316\u8fc7\u7a0b\uff08lumped process\uff09<\/span><\/span><\/b>\uff0c<\/span><\/span>{<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>:<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>\u03a6<\/span><\/span>}<\/span><\/span><\/span>\uff0c\u5373\u901a\u8fc7\u6295\u5f71\u77e9\u9635<\/span><\/span>\u03a6<\/span><\/span><\/span>\u5c06\u5fae\u89c2\u7684\u52a8\u529b\u5b66\u8f68\u8ff9<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u6295\u5f71\u5230\u5b8f\u89c2\u72b6\u6001\u7a7a\u95f4<\/span><\/span>A<\/span><\/span><\/span>\u4e0a\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u56fe2\uff1a\u77e9\u9635\u7c97\u7c92\u5316\u793a\u4f8b<\/span><\/span><\/p>\n

\u4f8b\u5982\u56fe2\u6240\u793a\u76844\u72b6\u6001\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u9009\u62e9\u6295\u5f71\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\u65f6\uff0c\u5fae\u89c2\u72b6\u6001\u5e8f\u5217<\/span><\/span>(<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub>)<\/span><\/span>\u5728\u88ab\u5206\u7ec4\u540e\u7684\u72b6\u6001\u4e0a\u5c31\u8868\u73b0\u4e3a\u5e8f\u5217\uff1a<\/span><\/span>(<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub>)<\/span><\/span>\uff0c\u8fd9\u4e2a\u5e8f\u5217\u5b9e\u9645\u4e0a\u4fbf\u81ea\u7136\u5b9a\u4e49\u4e86\u4e00\u4e2a\u65b0\u7684\u968f\u673a\u8fc7\u7a0b\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u7b80\u5316\u8fc7\u7a0b\uff08lumped process\uff09\u3002<\/span><\/span>
<\/span><\/p>\n

\u6b63\u5f0f\u5730\uff0c\u6211\u4eec\u6709\u5b9a\u4e49\uff1a<\/span><\/span><\/p>\n

\u5b9a\u4e491<\/span><\/span><\/b><\/i>\uff1a<\/span><\/span>\u7b80\u5316\u8fc7\u7a0b\uff08lumped process\uff09\u53ca\u5176\u91cd\u8981\u6982\u7387<\/span><\/span><\/b><\/p>\n

\u7b80\u5316\u8fc7\u7a0b\uff08lumped process\uff09\uff0c\u662f\u5fae\u89c2\u8f68\u8ff9\u5728\u805a\u7c7b\u540e\u7684\u72b6\u6001\u7a7a\u95f4\u4e0a\u7684\u6295\u5f71\u3002<\/span><\/span><\/b><\/p>\n

\u5bf9\u4e8e\u6295\u5f71\u540e\u7684\u8f68\u8ff9<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e09\u79cd\u4e0d\u540c\u6982\u7387\uff1a<\/span><\/span><\/b><\/p>\n

<\/section>\n

\u5176\u4e2d\uff0c<\/span><\/span>\u03c0<\/span><\/span>\u4e3a\u521d\u59cb\u5fae\u89c2\u72b6\u6001\u5206\u5e03\u3002<\/span><\/span><\/b><\/p>\n

\u8fd9\u4e9b\u516c\u5f0f\u5206\u522b\u63cf\u8ff0\u4e86\uff1a<\/span><\/span><\/p>\n

1. \u5f0f\u5b50<\/span><\/span>1.1<\/span><\/span><\/b>\uff1a\u521d\u59cb\u5b8f\u89c2\u72b6\u6001\u5206\u5e03\uff1a\u7cfb\u7edf\u5728<\/span><\/span>t<\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span>\uff0c\u5728\u5fae\u89c2\u72b6\u6001\u5206\u5e03\u4e3a<\/span><\/span>\u03c0<\/span><\/span><\/span>\u7684\u6761\u4ef6\u4e0b\uff0c\u4efb\u610f\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>0<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5c5e\u4e8e\u67d0\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\uff1b<\/span><\/span><\/p>\n

2. \u5f0f\u5b50<\/span><\/span>1.2<\/span><\/span><\/b>\uff1a\u5355\u6b65\u8f6c\u79fb\u6982\u7387\uff1a\u5df2\u77e5\u5fae\u89c2\u72b6\u6001\u5206\u5e03\u4e3a<\/span><\/span>\u03c0<\/span><\/span><\/span>\uff0c\u5e76\u4e14\u7cfb\u7edf\u5728<\/span><\/span>t<\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span>\u7684\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>0<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5c5e\u4e8e\u67d0\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u7684\u6761\u4ef6\u4e0b\uff0c\u90a3\u4e48\u5728\u65f6\u95f4<\/span><\/span>t<\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span>\u65f6\u523b\uff0c\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5c5e\u4e8e\u67d0\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\uff1b<\/span><\/span><\/p>\n

3. \u5f0f\u5b50<\/span><\/span>1.3<\/span><\/span><\/b>\uff1a\u5386\u53f2\u4f9d\u8d56\u8f6c\u79fb\u6982\u7387\uff1a\u5df2\u77e5\u5fae\u89c2\u72b6\u6001\u5206\u5e03\u4e3a<\/span><\/span>\u03c0<\/span><\/span><\/span>\uff0c\u5e76\u4e14\u5df2\u77e5\u7cfb\u7edf\u7684\u5386\u53f2\u5fae\u89c2\u72b6\u6001<\/span><\/span>{<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>0<\/span><\/span><\/sup>)<\/span><\/span><\/sup>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>}<\/span><\/span><\/span>\u5206\u522b\u5bf9\u5e94\u67d0\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>{<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>A<\/span><\/span>k<\/span><\/span><\/sub>}<\/span><\/span><\/span>\uff0c\u90a3\u4e48\u7cfb\u7edf\u5728\u65f6\u95f4<\/span><\/span>t<\/span><\/span><\/span>\uff0c\u5b83\u7684\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5c5e\u4e8e\u67d0\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>m<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\uff1b<\/span><\/span><\/p>\n


<\/span>\u5f0f\u5b50<\/span><\/span>1.1<\/span><\/span><\/b>, <\/span><\/span>1.2<\/span><\/span><\/b>, <\/span><\/span>1.3<\/span><\/span><\/b>\u63cf\u8ff0\u7684\u7b80\u5316\u8fc7\u7a0b\uff0c\u662f\u6211\u4eec\u4ece\u4efb\u610f\u4e00\u4e2a\u521d\u59cb\u72b6\u6001\u5206\u5e03<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>0<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>\u03c0<\/span><\/span><\/span>\u5f00\u59cb\uff0c\u8d70\u4e86<\/span><\/span>t<\/span><\/span><\/span>\u6b65\u7684\u5fae\u89c2\u52a8\u529b\u5b66\uff0c\u7136\u540e\u5728\u6bcf\u4e00\u6b65<\/span><\/span>t<\/span><\/span><\/span>\u505a\u7c97\u7c92\u5316\u5f97\u5230<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u7684\u8fc7\u7a0b\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u5f3a\u8c03\u5bf9\u521d\u59cb\u72b6\u6001\u5206\u5e03<\/span><\/span>\u03c0<\/span><\/span><\/span>\u7684\u4f9d\u8d56\uff0c\u662f\u56e0\u4e3a\u8fd9\u4e09\u4e2a\u6982\u7387\u7684\u53d6\u503c\u6709\u53ef\u80fd\u4f1a\u968f\u7740\u4e0d\u540c\u7684<\/span><\/span>\u03c0<\/span><\/span><\/span>\u800c\u53d8\u5316\u3002<\/span><\/span><\/p>\n

\u56e0\u4e3a\u7b80\u5316\u8fc7\u7a0b\u662f\u4ece<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5148\u7ecf\u5386\u5fae\u89c2\u52a8\u529b\u5b66\u6f14\u5316\u518d\u7c97\u7c92\u5316\u5230\u8fbe<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u6240\u4ee5\u8d70\u7684\u662f\u56fe2\u4e2d”\u5fae\u89c2\u72b6\u6001->\u5fae\u89c2\u52a8\u529b\u5b66->\u7c97\u7c92\u5316->\u5b8f\u89c2\u72b6\u6001”\u7684\u8fd9\u6761\u8def\u5f84\uff08\u7ec6\u5fc3\u7684\u8bfb\u8005\u53ef\u80fd\u4f1a\u53d1\u73b0\u5728\u56fe\u4e2d\u8fd8\u6709\u53e6\u4e00\u6761\u8def\u5f84\uff0c\u6211\u4eec\u4f1a\u5728\u540e\u9762\u8ba8\u8bba\uff09\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u867d\u7136\u6211\u4eec\u80fd\u5bf9\u4efb\u610f\u4e00\u4e2a\u72b6\u6001\u5212\u5206<\/span><\/span>\u03a6<\/span><\/span><\/span>\u5b9a\u4e49\u8fd9\u6837\u7684\u7b80\u5316\u8fc7\u7a0b\uff0c\u4f46\u662f\u8fd9\u4e9b\u7b80\u5316\u8fc7\u7a0b\u4e0d\u4e00\u5b9a\u4f1a\u62e5\u6709\u9a6c\u5c14\u79d1\u592b\u6027\u3002<\/span><\/span><\/p>\n

\u56e0\u4e3a\u6709\u4e9b\u7b80\u5316\u8fc7\u7a0b\u7684\u6982\u7387\u4f1a\u53d7\u5230\u521d\u59cb\u72b6\u6001<\/span><\/span>\u03c0<\/span><\/span><\/span>\u7684\u5f71\u54cd\uff0c\u6216\u8005\u5b83\u4eec\u4e0d\u7b26\u5408\u9a6c\u5c14\u79d1\u592b\u6027\u3002\u5982\u56fe1\u7684\u4f8b\u5b50\u6240\u793a\uff0c\u6211\u4eec\u65e0\u6cd5\u7528\u8fd9\u79cd\u2018\u5931\u8d25\u2019\u7684\u7b80\u5316\u8fc7\u7a0b\u6765\u63cf\u8ff0\u4e00\u4e2a\u548c\u5fae\u89c2\u8fc7\u7a0b\u4fdd\u6301\u4e00\u81f4\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u4f1a\u7528<\/span><\/span>\u6210\u5757\u6027<\/span><\/span><\/b>\u8fd9\u4e00\u65b0\u6982\u5ff5\u6765\u5b9a\u4e49\u6240\u8c13\u7684<\/span><\/span>\u2018<\/span><\/span>\u6210\u529f<\/span><\/span>\u2019<\/span><\/span>\u7684\u52a8\u529b\u5b66\uff0c\u5373\u6211\u4eec\u4f1a\u628a\u2018\u6210\u529f\u2019\u7684\u60c5\u51b5\u5b9a\u4e49\u4e3a\u6210\u5757\u7684\u5212\u5206\uff0c\u800c\u2018\u5931\u8d25\u2019\u7684\u60c5\u51b5\u5219\u662f\u4e0d\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

<\/span>2.3 \u6210\u5757\u7684\u5212\u5206<\/span><\/span><\/span><\/h3>\n

\u5b9a\u4e492<\/span><\/span><\/b><\/i>\uff1a<\/span><\/span>\u6210\u5757\u7684\u5212\u5206 lumpable partition<\/span><\/span><\/b><\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u72b6\u6001\u5212\u5206 <\/span><\/span>\u03a6<\/span><\/span>\uff0c\u5f53\u4e0b\u5217\u4e24\u4e2a\u6761\u4ef6\u540c\u65f6\u6ee1\u8db3\u65f6\uff0c<\/span><\/span>\u03a6<\/span><\/span>\u662f\u4e00\u4e2a\u6210\u5757\u7684\u5212\u5206\uff08lumpable partition\uff09\u3002<\/span><\/span><\/b><\/p>\n

1. \u5b9a\u4e491\u4e2d\u5f0f\u5b50<\/span><\/span><\/b>1.3<\/span><\/span>\u6240\u63cf\u8ff0\u7684\u7b80\u5316\u8fc7\u7a0b\u5177\u6709\u9a6c\u5c14\u79d1\u592b\u6027\uff0c\u5373\u5f0f\u5b50<\/span><\/span><\/b>1.3<\/span><\/span>\u53ef\u5199\u6210\u5f0f\u5b50<\/span><\/span><\/b>1.2<\/span><\/span>\u7684\u5f62\u5f0f<\/span><\/span><\/b><\/p>\n

<\/section>\n

2. \u8f6c\u79fb\u6982\u7387(transition probability)\uff0c\u5373\u5f0f\u5b50<\/span><\/span><\/b>1.3<\/span><\/span>\u6216\u5f0f\u5b50<\/span><\/span><\/b>2<\/span><\/span>\uff0c\u5bf9\u4efb\u4f55\u5fae\u89c2\u521d\u59cb\u72b6\u6001(starting vector) <\/span><\/span>\u03c0<\/span><\/span> \u90fd\u4fdd\u6301\u4e00\u81f4\uff0c\u4ece\u800c\u6211\u4eec\u80fd\u591f\u5f97\u51fa\u5b8f\u89c2\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub><\/b><\/p>\n

\u5176\u4e2d\uff0c\u56e0\u4e3a\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c<\/span><\/span>\u03a6<\/span><\/span><\/span>\u4e0d\u662f\u65b9\u9635\uff0c\u6240\u4ee5\u6211\u4eec\u5b9a\u4e49<\/span><\/span>\u03a6<\/span><\/span>\u2020<\/span><\/span><\/sup><\/span>\u4e3a<\/span><\/span>\u03a6<\/span><\/span><\/span>\u7684\u4f2a\u9006\u77e9\u9635\uff0c\u6ee1\u8db3<\/span><\/span>\u03a6<\/span><\/span>\u03a6<\/span><\/span>\u2020<\/span><\/span><\/sup>\u03a6<\/span><\/span>=<\/span><\/span>\u03a6<\/span><\/span><\/span>\u3002\u53e6\u5916\uff0c<\/span><\/span>\u03a6<\/span><\/span>T<\/span><\/span><\/sup>\u03a6<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u5bf9\u89d2\u9635\uff0c\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u4e3a\u6bcf\u4e2a<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u5305\u62ec\u4e86\u591a\u5c11\u4e2a\u5fae\u89c2\u72b6\u6001\u7684\u8ba1\u6570\uff0c\u800c\u5b83\u7684\u9006\u77e9\u9635\u5c31\u662f\u628a\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u90e8\u53d6\u5012\u6570\u3002<\/span><\/span><\/p>\n

\u4e0d\u6ee1\u8db3\u4e0a\u8ff0\u4e24\u4e2a\u6761\u4ef6\u7684\uff0c\u90fd\u4e0d\u88ab\u5b9a\u4e49\u4e3a\u6210\u5757\u7684\u5212\u5206\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e0d\u662f\u6240\u6709\u7684\u7b80\u5316\u8fc7\u7a0b\u90fd\u662f\u6210\u5757\u7684\uff0c\u5373\u4f7f\u4ed6\u4eec\u7684\u547d\u540d\u65b9\u5f0f\uff08lumped process\u548clumpable process\uff09\u76f8\u4f3c\u3002<\/span><\/span><\/p>\n

<\/span>2.4 \u4e3e\u4f8b<\/span><\/span><\/span><\/h3>\n

\u4e0b\u56fe\u7ed9\u51fa\u4e24\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u548c\u5bf9\u5e94\u5206\u7ec4\uff08\u5206\u7ec4\u65b9\u5f0f\u90fd\u662f\u5c06\u524d\u4e24\u4e2a\u72b6\u6001\u5206\u4e3a\u4e00\u7ec4\uff0c\u540e\u4e24\u4e2a\u72b6\u6001\u5206\u4e3a\u4e00\u7ec4\uff09\u7684\u4f8b\u5b50\uff0c\u4e00\u4e2a\u662f\u6210\u5757\u7684\uff0c\u4e00\u4e2a\u662f\u4e0d\u6210\u5757\u7684\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u56fe3\uff1a\u5bf9\u6210\u5757\u7684\u548c\u4e0d\u6210\u5757\u7684\u77e9\u9635\u505a\u7c97\u7c92\u5316<\/span><\/span><\/p>\n

\u4ece\u56fe3\u7684\u6210\u5757\u5212\u5206\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u5bf9\u4e8e\u5206\u7ec4\u77e9\u9635<\/span><\/span>\"image.png\" <\/span><\/sub>\uff0c\u6210\u5757\u7684\u52a8\u529b\u5b66TPM\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u7b80\u5316\u8fc7\u7a0b\uff0c\u800c\u8fd9\u4e2a\u7b80\u5316\u8fc7\u7a0b\u6ee1\u8db3\u9a6c\u5c14\u53ef\u592b\u6027\uff0c\u4e14\u5bf9\u6240\u6709\u521d\u59cb\u72b6\u6001\u90fd\u4fdd\u6301\u4e00\u81f4\u3002\u65e0\u8bba<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u662f\u4ec0\u4e48\uff0c<\/span><\/span>{<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>,<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>}<\/span><\/span><\/span>\u6295\u5f71\u5230<\/span><\/span>\u5b8f\u89c2\u7a7a\u95f4\u4e0a\u7684<\/span><\/span>{<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>,<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>}<\/span><\/span>\u7684<\/span><\/span>P<\/span><\/span>(<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>|<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>)<\/span><\/span>\u90fd\u4fdd\u6301\u4e00\u81f4\u3002<\/span><\/span><\/p>\n

\u5bf9\u4e8e\u4e0d\u6210\u5757\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u6216\u8bb8\u53ef\u4ee5\u7ed9\u5b83\u5f3a\u5236\u5b9a\u4e49\u4e00\u4e2a\u7b80\u5316\u8fc7\u7a0b\u7684TPM\uff0c\u6bd4\u5982<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4f46\u8fd9\u4e2a\u7b80\u5316\u8fc7\u7a0b\u5e76\u4e0d\u80fd\u5bf9\u4efb\u4f55\u5fae\u89c2\u521d\u59cb\u72b6\u6001\u4fdd\u6301\u4e00\u81f4\uff0c\u53ea\u80fd\u5bf9s<\/span><\/span>(t)<\/span><\/sup>=\u03c0=[1 0 0 0]\u9002\u7528<\/span><\/span><\/span>\u3002<\/span><\/p>\n

\u800c<\/span><\/span>s<\/span><\/span>(t)<\/span><\/sup>=\u03c0=[0 1 0 0]\u9002<\/span><\/span><\/span>\u4e0d\u9002\u7528\u8fd9\u4e2a\u7b80\u5316\u8fc7\u7a0b\u3002\u5b83\u9002\u7528\u7684\u662f<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u8fd9\u91cc\u7684\u4e0d\u9002\u7528\u662f\u6307\uff0c\u8fd9\u4e2a\u7b80\u5316\u8fc7\u7a0b\u4e0d\u80fd\u63cf\u8ff0\u4ee5\u8fd9\u4e2a<\/span><\/span>\u03c0<\/span><\/span><\/span>\u4e3a\u521d\u59cb\u72b6\u6001\u51fa\u53d1\u7684\u5fae\u89c2\u72b6\u6001\u5e8f\u5217\u6295\u5f71\u7684\u5b8f\u89c2\u72b6\u6001\u5e8f\u5217\u3002\u6211\u4eec\u770b\u5230\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u6709\u4e24\u4e2a\u7b80\u8fc7\u7a0b <\/span><\/span>P<\/span><\/span>1<\/span><\/span>\u2032<\/span><\/span><\/span>\u548c<\/span><\/span>P<\/span><\/span>2<\/span><\/span>\u2032<\/span><\/span><\/span>\uff0c\u800c\u5b83\u4eec\u5404\u81ea\u53ea\u9002\u7528\u4e8e\u4e00\u4e9b\u5fae\u89c2\u521d\u59cb\u72b6\u6001(starting vector) <\/span><\/span>\u03c0<\/span><\/span><\/span>\uff0c\u5e76\u4e0d\u6ee1\u8db3\u5b9a\u4e492\u4e2d\u7684\u6761\u4ef6\uff0c\u6240\u4ee5<\/span><\/span>\u03a6<\/span><\/span><\/span>\u5bf9\u4e8e\u8fd9\u4e2aTPM\u6765\u8bf4\u4e0d\u662f\u4e00\u4e2a\u6210\u5757\u7684\u5212\u5206\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e2aTPM\u53ea\u5b58\u5728\u4e00\u4e2a\u6210\u5757\u7684\u5212\u5206\uff0c\u5c31\u662f\u4e0d\u505a\u4efb\u4f55\u5206\u7ec4\uff0c\u56e0\u6b64\u5b83\u65e0\u6cd5\u6309\u7167\u6210\u5757\u6027\u7684\u5b9a\u4e49\u8fdb\u884c\u7c97\u7c92\u5316\u3002\u5728\u540e\u9762\u201c\u6210\u5757\u6027\u6982\u5ff5\u7684\u53d8\u79cd\u201d\u7684\u90e8\u5206\uff0c\u6211\u4eec\u4f1a\u63d0\u5230\uff0c\u867d\u7136\u5bf9\u8fd9\u4e2aTPM\u505a\u7684\u5212\u5206\u4e0d\u7b26\u5408\uff08\u5f3a\uff09\u6210\u5757\u6027\u7684\u8981\u6c42\uff0c\u4f46\u662f\u5b83\u5b9e\u9645\u4e0a\u6ee1\u8db3\u5f31\u6210\u5757\u6027\uff08Weak Lumpability\uff09\uff0c\u5373\u7b80\u5316\u8fc7\u7a0b\u5bf9\u90e8\u5206\u5fae\u89c2\u521d\u59cb\u72b6\u6001\u9002\u7528\u3002<\/span><\/span><\/p>\n

<\/span>
<\/span><\/span><\/h2>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

3. \u6210\u5757\u6027\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u901a\u8fc7\u4e0a\u9762\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u5bf9\u6210\u5757\u6027\u6709\u4e86\u521d\u6b65\u7684\u76f4\u89c2\u7406\u89e3\uff1a\u5728\u6210\u5757\u7684\u5212\u5206\u4e2d\uff0c\u6709\u4e24\u4e2a\u5206\u7ec4\uff0c\u6240\u4ee5\u6709\u56db\u4e2a\u6846\u3002\u6bcf\u4e00\u4e2a\u6846\u91cc\uff0c\u6bcf\u4e00\u5217\u76f8\u52a0\u7684\u548c\u90fd\u662f\u4e00\u6837\u7684\u3002\u4f8b\u5982\uff0c\u5728\u5de6\u4e0a\u89d2\u7684\u6846\u4e2d\uff0c<\/span><\/span>0.3<\/span><\/span>+<\/span><\/span>0.3<\/span><\/span>=<\/span><\/span>0.2<\/span><\/span>+<\/span><\/span>0.4<\/span><\/span><\/span>\u3002\u8fd9\u5c31\u662f\u6210\u5757\u6027\u66f4\u901a\u4fd7\u7684\u89e3\u91ca\uff0c\u5c31\u662f\u5b83<\/span><\/span>\u6210\u5757<\/span><\/span><\/b>\u4e86\uff0c\u5728\u67d0\u4e9b\u6587\u732e\u4e2d\uff0c\u4f5c\u8005\u4eec\u4f1a\u76f4\u63a5\u4f7f\u7528\u8fd9\u4e2a\u901a\u4fd7\u7248\u7684\u89e3\u91ca\uff0c\u800c\u4e14\u8fd9\u4e24\u8005\u4e4b\u95f4\u662f\u5b58\u5728\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u5173\u7cfb\u7684<\/span><\/span>[1]<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

<\/span>3.1 \u5b9a\u4e49\u4e09\u79cd\u6982\u7387<\/span><\/span><\/span><\/h3>\n

\u4e3a\u4e86\u540e\u7eed\u8ba8\u8bba\u65b9\u4fbf\uff0c\u6211\u4eec\u9996\u5148\u5f15\u5165\u4e09\u4e2a\u6982\u7387\u7684\u5b9a\u4e49\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u4e3a\u72b6\u6001<\/span><\/span>s<\/span><\/span>m<\/span><\/span><\/sub>\u5230<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub>\u7684\u8f6c\u79fb\u6982\u7387\uff0c\u4ee5\u53ca<\/span><\/span><\/p>\n

<\/section>\n

\u4e3a\u7cfb\u7edf\u4e0a\u4e00\u65f6\u523b\u5904\u4e8e\u5fae\u89c2\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub>\uff0c\u4e0b\u4e00\u65f6\u523b\u5904\u4e8e\u5206\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5fae\u89c2\u6001\u7684\u6982\u7387\uff0c\u4ee5\u53ca\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u4e3a\u7cfb\u7edf\u4e0a\u4e00\u65f6\u523b\u5904\u4e8e\u5206\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5fae\u89c2\u6001\uff0c\u4e0b\u4e00\u65f6\u523b\u5219\u5904\u4e8e\u5206\u7ec4<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5fae\u89c2\u6001\u7684\u6982\u7387\u3002<\/span><\/span><\/p>\n

<\/span>3.2 \u6210\u5757\u6027\u5145\u8981\u6761\u4ef6\u5b9a\u7406<\/span><\/span><\/span><\/h3>\n

\u8fdb\u4e00\u6b65\uff0c\u6587\u732e<\/span><\/span>[1]<\/span><\/span><\/span>\u4e2d\u63d0\u51fa\u4e86\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u5bf9<\/span><\/span>\u7ed9\u5b9a\u5212\u5206 <\/span><\/span>A<\/span><\/span><\/b> \u662f\u5426\u6210\u5757\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u4e3a\uff1a<\/span><\/span><\/p>\n

\u5b9a\u74061\uff1a<\/span><\/span><\/b><\/i><\/p>\n

\u7ed9\u5b9a\u5212\u5206 <\/span><\/span>A<\/span><\/span>\u662f\u6210\u5757\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u4e3a\uff1a<\/span><\/span><\/b><\/p>\n

\u5bf9\u4e8e\u4efb\u610f\u4e00\u5bf9<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub>\uff0c\u6bcf\u4e00\u4e2a\u5c5e\u4e8e<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u7684\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub>\u7684<\/span><\/span>\"image.png\"<\/span><\/sub>\u90fd\u662f\u4e00\u6837\u7684\uff1a<\/span><\/span><\/b><\/p>\n

<\/section>\n

\u5bf9\u4e8e<\/span><\/span>\"image.png\"<\/span><\/sub>\u90fd\u6210\u7acb\u3002<\/span><\/span><\/p>\n

\u6839\u636e\u5f0f\u5b50<\/span><\/span>2<\/span><\/span><\/b>\u7684\u5b9a\u4e49\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u91cc\u7684\u6bcf\u4e00\u4e2a\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u6240\u6709\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u4e4b\u548c\u662f\u76f8\u540c\u7684\uff0c\u5373\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5bf9\u4e8e<\/span><\/span>\u2200<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>,<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub>\u548c<\/span><\/span>\u2200<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>l<\/span><\/span><\/sub>\u2208<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u90fd\u6210\u7acb\u3002<\/span><\/span><\/p>\n

<\/span>3.3 \u6210\u5757\u6027\u7684\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/span><\/span><\/h3>\n

\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u6240\u6709\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>l<\/span><\/span><\/sub><\/span>\u5408\u5e76\u4e3a\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\uff0c\u56e0\u4e3a\u5b83\u4eec\u4ece\u5176\u4ed6\u5b8f\u89c2\u72b6\u6001\u7684\u8f6c\u5165\u6982\u7387\u662f\u4e00\u81f4\u7684\u3002\u540c\u6837\u7684\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5c06<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u6240\u6709\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\u5408\u5e76\u4e3a\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\uff08\u548c<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\uff09\u5230\u5176\u4ed6\u5b8f\u89c2\u72b6\u6001\u7684\u8f6c\u51fa\u6982\u7387\u662f\u4e00\u81f4\u7684\u3002<\/span><\/span><\/p>\n

\u4f8b\u5982\uff0c\u5728\u4e0b\u56fe\u4e2d\uff0c<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u90fd\u5c5e\u4e8e<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub><\/span>\uff0c\u5b83\u4eec\u5230<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u7684\u8f6c\u79fb\u6982\u7387\u662f\u4e00\u6837\u7684\uff1b\u540c\u6837\uff0c<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u90fd\u5c5e\u4e8e<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub><\/span>\uff0c\u5b83\u4eec\u5230\u5b8f\u89c2\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u4e5f\u662f\u4e00\u6837\u7684\u3002\u56e0\u6b64\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u662f<\/span><\/span>P<\/span><\/span><\/span>\u7684\u4e00\u4e2a\u6210\u5757\u5212\u5206\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u56fe4\uff1a\u6210\u5757\u6027\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u5b9e\u4f8b<\/span><\/span>
<\/span><\/p>\n

\u57fa\u4e8e\u8fd9\u4e2a\u6761\u4ef6\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u6210\u5757\u5212\u5206\u7684\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>=<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>P<\/span><\/span>\u2032<\/span><\/span><\/span>\uff1a<\/span><\/span><\/p>\n

\u5b9a\u4e493<\/span><\/span><\/b><\/i>\uff1a<\/span><\/span>\u6210\u5757\u6027\u7684\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/span><\/b><\/p>\n

\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u5fae\u89c2\u72b6\u6001\u96c6\u5408<\/span><\/span>S<\/span><\/span>\uff0c\u4ee5\u53ca\u5fae\u89c2\u52a8\u529b\u5b66\uff0c\u5373\u6240\u6709\u5fae\u89c2\u6001\u8f6c\u79fb\u6982\u7387 <\/span><\/span>\"image.png\"<\/span><\/sub>\u548c\u6210\u5757\u7684\u5212\u5206 <\/span><\/span>A<\/span><\/span>\uff0c\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/span>\"image.png\"<\/span><\/sub>\u7b49\u4e8e<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u4e2d\u4efb\u610f\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub>\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub>\u7684\u6982\u7387\uff1a<\/span><\/span><\/b><\/p>\n

<\/section>\n

\u5bf9\u4e8e<\/span><\/span>\u2200<\/span><\/span>k<\/span><\/span>\u2208<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub>\u90fd\u6210\u7acb\u3002<\/span><\/span><\/p>\n

\u8fd9\u4e2a\u516c\u5f0f\u8868\u660e\uff0c\u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u5230\u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u8f6c\u79fb\u6982\u7387 = \u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u4efb\u610f\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\u5230\u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u8f6c\u79fb\u6982\u7387 = \u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u4efb\u610f\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\u5230\u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u6240\u6709\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u4e4b\u548c\u3002<\/span><\/span><\/p>\n

\u6211\u4eec\u8bb0\u6240\u6709\u7684<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e3a\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u8fd9\u91cc<\/span><\/span>M<\/span><\/span>=<\/span><\/span>|<\/span><\/span>A<\/span><\/span>|<\/span><\/span>\u3002\u7531\u6b64\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u76f4\u63a5\u5b9a\u4e49<\/span><\/span>P<\/span><\/span><\/span>\u548c<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d\uff0c<\/span><\/span>\u03a6<\/span><\/span>T<\/span><\/span><\/sup>\u03a6<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u5bf9\u89d2\u9635\uff0c\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u4e3a\u6bcf\u4e2a<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u5305\u62ec\u4e86\u591a\u5c11\u4e2a\u5fae\u89c2\u72b6\u6001\u7684\u8ba1\u6570\uff0c\u5176\u9006\u77e9\u9635\u5c31\u662f\u628a\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u90e8\u53d6\u5012\u6570\u3002\u7531\u8be5\u516c\u5f0f\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u3002<\/span><\/span><\/p>\n

\u6839\u636e\u6210\u5757\u5212\u5206 <\/span><\/span>\u03a6<\/span><\/span><\/span>\u5b9a\u4e49\u597d\u5b8f\u89c2\u52a8\u529b\u5b66\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u8d70\u53e6\u4e00\u6761\u8def\u5f84\u4e86\uff1a<\/span><\/span>\u5fae\u89c2\u72b6\u6001->\u7c97\u7c92\u5316->\u5b8f\u89c2\u52a8\u529b\u5b66->\u5b8f\u89c2\u72b6\u6001<\/span><\/span><\/b>\u3002\u6211\u4eec\u53d1\u73b0\uff0c\u8fd9\u6761\u8def\u5f84\u4e0e<\/span><\/span>\u5fae\u89c2\u72b6\u6001->\u5fae\u89c2\u52a8\u529b\u5b66->\u7c97\u7c92\u5316->\u5b8f\u89c2\u72b6\u6001<\/span><\/span><\/b>\u662f\u4e00\u81f4\u7684\u3002<\/span><\/span>\u65e0\u8bba\u4ece\u54ea\u4e2a\u5fae\u89c2\u72b6\u6001\u51fa\u53d1\uff0c\u6700\u7ec8\u90fd\u80fd\u5230\u8fbe\u76f8\u540c\u7684\u5b8f\u89c2\u72b6\u6001\u3002<\/span><\/span><\/b>\u6240\u4ee5\uff0c\u8fd9\u6ee1\u8db3\u4e86<\/span><\/span>\u52a8\u529b\u5b66<\/span><\/span><\/b>\u548c<\/span><\/span>\u7c97\u7c92\u5316<\/span><\/span><\/b>\u8fd9\u4e24\u4e2a<\/span><\/span>\u7b97\u5b50<\/span><\/span><\/b>\u7684<\/span><\/span>\u53ef\u4ea4\u6362\u6027\uff08Exchangeability\uff09<\/span><\/span><\/b>\u3002\u5177\u4f53\u7684\u8bc1\u660e\u5c06\u5728\u540e\u9762\u7684\u2018\u6210\u5757\u6027\u6ee1\u8db3\u7684\u6027\u8d28\u2019\u90e8\u5206\u4ecb\u7ecd\u3002<\/span><\/span><\/p>\n

<\/span>3.4 \u5b9a\u74061\u7684\u8bc1\u660e<\/span><\/span><\/span><\/h3>\n

\u8fd9\u91cc\uff0c\u6211\u4eec\u7ffb\u8bd1\u4e86\u4f5c\u8005\u5728\u4e66<\/span><\/span>[1]<\/span><\/span><\/span>\u4e2d\u63d0\u4f9b\u7684\u5b9a\u74061\u7684\u5fc5\u8981\u6027\u548c\u5145\u5206\u6027\u7684\u8bc1\u660e\u3002<\/span><\/span><\/p>\n

\u5fc5\u8981\u6027\u90e8\u5206\u7684\u8bc1\u660e\uff1a<\/span><\/span><\/b><\/p>\n

\u5fc5\u8981\u6027\u662f\u6307\uff0c\u5982\u679c\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u7684\u5212\u5206 <\/span><\/span>A<\/span><\/span><\/span>\u662f\u6210\u5757\u7684\uff0c\u90a3\u4e48\u5b83\u5fc5\u7136\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\u3002<\/span><\/span><\/p>\n

\u4ece\u6210\u5757\u7684\u5212\u5206\u7684\u5b9a\u4e49\u53ef\u77e5\uff0c<\/span><\/span>A<\/span><\/span><\/span>\u7684\u8f6c\u79fb\u6982\u7387\u6ee1\u8db3\u5b8f\u89c2\u9a6c\u5c14\u53ef\u592b\u6027\uff0c\u4e14\u8fd9\u4e2a\u8f6c\u79fb\u6982\u7387<\/span><\/span>\"image.png\"<\/span><\/sub>\u5bf9\u6bcf\u4e2a<\/span><\/span>\u03c0<\/span><\/span><\/span>\u4fdd\u6301\u4e00\u81f4\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u65e0\u8bba\u4ece\u54ea\u4e2a\u5177\u4f53\u7684\u521d\u59cb\u72b6\u6001<\/span><\/span>\u03c0<\/span><\/span><\/span>\u5f00\u59cb\uff0c\u53ea\u8981\u5b83\u5c5e\u4e8e<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u8fd9\u4e2a\u7fa4\u7ec4\u91cc\uff0c\u5728<\/span><\/span>t<\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span>\u65f6\u523b\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\u90fd\u662f\u76f8\u540c\u7684\u3002<\/span><\/span><\/p>\n

\u6211\u4eec\u8bbe\u8fd9\u4e2a\uff08<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u4efb\u610f\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\u7684\uff09\u5171\u540c\u7684\u8f6c\u79fb\u6982\u7387\u4e3a<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u5f53\u521d\u59cb\u72b6\u6001<\/span><\/span>\u03c0<\/span><\/span><\/span>\u5c5e\u4e8e\u67d0\u4e2a<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u65f6\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/p>\n

\u6240\u4ee5\uff0c\u8fd9\u8868\u660e\uff0c\u5982\u679c\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u7684\u7b80\u5316\u8fc7\u7a0b\u6ee1\u8db3\u6210\u5757\u6027\uff0c\u90a3\u4e48\u4ece\u4efb\u4e00\u96c6\u5408\u5230\u53e6\u4e00\u96c6\u5408\u7684\u8f6c\u79fb\u6982\u7387\u5fc5\u987b\u662f\u4e00\u4e2a\u96c6\u5408\u95f4\u7684\u56fa\u5b9a\u503c\uff0c\u800c\u4e0e\u96c6\u5408\u5185\u7684\u5177\u4f53\u72b6\u6001\uff08\u65e0\u8bba\u662f<\/span><\/span>\u03c0<\/span><\/span><\/span>\u8fd8\u662f<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\uff09\u65e0\u5173\u3002\u8fd9\u4e2a\u56fa\u5b9a\u503c\u6b63\u662f\u5f0f\u5b50<\/span><\/span>5<\/span><\/span><\/b>\u5b9a\u4e49\u7684\u5b8f\u89c2\u72b6\u6001\u8f6c\u79fb\u6982\u7387\uff0c\u6240\u4ee5\u6ee1\u8db3\u4e86\u8be5\u6761\u4ef6\u3002<\/span><\/span><\/p>\n

\u5145\u5206\u6027\u90e8\u5206\u7684\u8bc1\u660e\uff1a<\/span><\/span><\/b><\/p>\n

\u5145\u5206\u6027\u662f\u6307\uff0c\u5982\u679c\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u7684\u67d0\u4e2a\u72b6\u6001\u5212\u5206 <\/span><\/span>A<\/span><\/span><\/span>\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\uff0c\u90a3\u4e48\u5b83\u5c31\u662f\u6210\u5757\u7684\u3002\u6211\u4eec\u9700\u8981\u8bc1\u660e\u7684\u662f\uff0c\u5982\u679c\u4e0a\u8ff0\u6761\u4ef6\u6ee1\u8db3\uff0c\u90a3\u4e48\u9a6c\u5c14\u53ef\u592b\u6027\u6210\u7acb\uff0c\u5373\u5bf9\u4e8e\u4efb\u4f55\u7ed9\u5b9a\u7684<\/span><\/span>t<\/span><\/span><\/span>\uff0c\u8f6c\u79fb\u6982\u7387 <\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\u53ea\u4f9d\u8d56\u4e8e<\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span>\u65f6\u523b\u7684\u5b8f\u89c2\u6001<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u7684\u5b8f\u89c2\u6001<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e<\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span>\u7684<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u5177\u4f53\u72b6\u6001\u662f\u54ea\u4e2a<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u6216\u662f<\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span>\u524d\u7684\u5b8f\u89c2\u72b6\u6001\u3002<\/span><\/span><\/p>\n

\u8fd9\u4e2a\u6761\u4ef6\u8981\u6c42<\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span>\u65f6\u523b\u5c5e\u4e8e<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u7684\u4efb\u4e00\u5fae\u89c2\u6001<\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/sub><\/span>\uff0c\u8f6c\u79fb\u6982\u7387<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u8fd9\u610f\u5473\u7740\u65e0\u8bba\u6211\u4eec\u4ece<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u54ea\u4e2a\u5fae\u89c2\u72b6\u6001\u5f00\u59cb\uff0c\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\u90fd\u662f\u76f8\u540c\u7684\u3002<\/span><\/span><\/p>\n

\u56e0\u6b64\uff0c\u5f53\u6211\u4eec\u5df2\u77e5<\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span>\u7684\u5b8f\u89c2\u72b6\u6001\u662f<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u65f6\uff0c\u8ba1\u7b97<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\u65f6\uff0c\u6211\u4eec\u53ea\u9700\u8981\u4f7f\u7528<\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\uff0c\u800c\u4e0d\u9700\u8981\u5173\u5fc3<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u5177\u4f53\u72b6\u6001\u3002<\/span><\/span><\/p>\n

\u7531\u4e8e\u8f6c\u79fb\u6982\u7387\u53ea\u4f9d\u8d56\u4e8e\u7fa4\u7ec4<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u5177\u4f53\u72b6\u6001\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u6240\u6709\u72b6\u6001\u5408\u5e76\u4e3a\u4e00\u4e2a\u72b6\u6001\uff0c\u5e76\u4e14\u5408\u5e76\u540e\u7684\u94fe\u4ecd\u6ee1\u8db3\u9a6c\u5c14\u53ef\u592b\u6027\u3002\u6240\u4ee5\uff0c\u4e0a\u8ff0\u6761\u4ef6\u4e3a\u6210\u5757\u6027\u7684\u5145\u5206\u6761\u4ef6\u3002<\/span><\/span><\/p>\n

\u4ece\u8fd9\u4e24\u4e2a\u8bc1\u660e\u91cc\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u770b\u5230\u5fae\u89c2\u52a8\u529b\u5b66\u8def\u5f84\u548c\u5b8f\u89c2\u52a8\u529b\u5b66\u8def\u5f84\u7684<\/span><\/span>\u4e00\u81f4\u6027<\/span><\/span><\/b>\u3002\u65e0\u8bba\u6211\u4eec\u4ece<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u54ea\u4e2a\u5177\u4f53\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5f00\u59cb\uff0c\u53ea\u8981\u5f53\u524d\u7684\u5b8f\u89c2\u72b6\u6001\u662f<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/sub><\/span>\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u4e0b\u4e00\u6b65\u8f6c\u79fb\u5230<\/span><\/span>A<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u3002\u8fd9\u8868\u660e\uff0c\u5fae\u89c2<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>->\u5b8f\u89c2<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>\u2212<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>->\u5b8f\u89c2\u52a8\u529b\u5b66-><\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u4e0d\u4f1a\u5f71\u54cd\u672a\u6765\u72b6\u6001\u7684\u9884\u6d4b\uff0c\u56e0\u6b64\u5fae\u89c2\u548c\u5b8f\u89c2\u4e24\u4e2a\u8def\u5f84\u5f97\u51fa\u7684<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u7684\u6982\u7387\u662f\u4e00\u81f4\u7684\u3002\u540c\u6837\u7684\uff0c\u5177\u4f53\u7684\u8bc1\u660e\u5c06\u5728\u540e\u9762\u7684\u2018\u6210\u5757\u6027\u6ee1\u8db3\u7684\u6027\u8d28\u2019\u90e8\u5206\u4ecb\u7ecd\u3002<\/span><\/span><\/p>\n

<\/span>3.5 \u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027<\/span><\/span><\/span><\/h3>\n

\u8bf7\u6ce8\u610f<\/span><\/span><\/b>\uff1a<\/span>\u6210\u5757\u6027\u6709\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u524d\u63d0\uff1a\u6211\u4eec\u9700\u8981\u7ed9\u5b9a\u4e00\u4e2a\u5bf9\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u5212\u5206\uff0c\u7136\u540e\u6839\u636e\u9a6c\u5c14\u79d1\u592b\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u6765\u5224\u65ad\u8fd9\u4e2a\u5212\u5206\u5bf9\u8fd9\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u662f\u5426\u6210\u5757\u3002<\/span><\/span><\/p>\n

\u6240\u4ee5\uff0c\u6b63\u5f0f\u6765\u8bf4\uff0c\u6210\u5757\u6027\u5e76\u4e0d\u662f\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u672c\u8eab\u7684\u5c5e\u6027\uff0c\u800c\u662f\u5bf9\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u67d0\u4e2a\u72b6\u6001\u5212\u5206\u7684\u5c5e\u6027\u3002\u8fd9\u4e00\u524d\u63d0\u4e5f\u63d0\u9192\u6211\u4eec\uff0c\u5728\u8ba8\u8bba\u6210\u5757\u6027\u65f6\uff0c\u5fc5\u987b\u660e\u786e\u72b6\u6001\u5212\u5206\u7684\u65b9\u5f0f\u3002\u4e0d\u540c\u7684\u5212\u5206\u65b9\u5f0f\u53ef\u80fd\u5bfc\u81f4\u4e0d\u540c\u7684\u7ed3\u8bba\u3002\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u53ef\u80fd\u5728\u67d0\u79cd\u5212\u5206\u4e0b\u662f\u6210\u5757\u7684\uff0c\u800c\u5728\u53e6\u4e00\u79cd\u5212\u5206\u4e0b\u5219\u4e0d\u6210\u5757\u3002\u56e0\u6b64\uff0c\u6210\u5757\u6027\u66f4\u591a\u5730\u53cd\u6620\u4e86\u72b6\u6001\u5212\u5206\u4e0e\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u9002\u914d\u6027\uff0c\u800c\u4e0d\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u672c\u8eab\u7684\u7279\u6027\u3002<\/span><\/span><\/p>\n

\u7136\u800c\uff0c\u6709\u65f6\u5019\u4e3a\u4e86\u7b80\u7565\u8868\u8fbe\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027\u4e3a\uff1a<\/span><\/span><\/p>\n

\u5b9a\u4e49\uff1a\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027<\/span><\/span><\/b>\uff1a<\/span><\/span><\/p>\n

\u82e5\u7ed9\u5b9a\u9a6c\u5c14\u79d1\u592b\u94fe<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u4e2a\u6210\u5757\u7684\u72b6\u6001\u5212\u5206<\/span><\/span>A<\/span><\/span><\/span>\uff0c\u4e14\u8be5\u5212\u5206\u4e0d\u80fd\u662f\u5fae\u89c2\u77e9\u9635\u672c\u8eab\uff0c\u5212\u5206\u540e\u7684\u5b8f\u89c2\u6001\u6570\u91cf\u987b\u5c11\u4e8e\u5fae\u89c2\u6001\u6570\u91cf\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u8be5\u94fe<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n


<\/span><\/p>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

4. \u6210\u5757\u6027\u7684\u6b63\u4f8b\u548c\u53cd\u4f8b<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u6709\u4e9b\u5206\u7ec4\u662f\u6210\u5757\u7684\uff0c\u6709\u4e9b\u5206\u7ec4\u662f\u4e0d\u6210\u5757\u7684\u3002\u8fd9\u91cc\uff0c\u6211\u4eec\u7ed9\u51fa\u4e24\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u5206\u522b\u63d0\u4f9b\u4e86\u6b63\u4f8b\u548c\u53cd\u4f8b\u3002<\/span><\/span><\/p>\n

\u6211\u4eec\u7528\u5230\u7684\u662f\u8fd9\u6837\u4e00\u4e2a\u8f6c\u79fb\u77e9\u9635\uff1a<\/span><\/span><\/p>\n

<\/section>\n

4.1 \u6b63\u4f8b<\/span><\/span><\/span><\/h4>\n

\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c123\u884c\u90fd\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u628a<\/span><\/span>{<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub>}<\/span><\/span><\/span>\u5206\u5728\u4e00\u7ec4<\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/sub><\/span>\uff0c\u5e76\u628a\u72b6\u6001<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u5206\u5728\u53e6\u5916\u4e00\u7ec4<\/span><\/span>A<\/span><\/span>2<\/span><\/span><\/sub><\/span>\uff0c\u662f\u4e00\u4e2a\u6210\u5757\u7684\u5212\u5206\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8ba1\u7b97\u4e00\u4e0b\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u8ba1\u7b97\u7ed3\u679c\u7b26\u5408\u5b9a\u74061\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5212\u5206\u662f\u6210\u5757\u7684\u3002\u800c\u5bf9\u5e94\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u4e3a\uff1a<\/span><\/span>\"image.png\"<\/span><\/sub><\/p>\n

4.2 \u53cd\u4f8b<\/span><\/span><\/span><\/h4>\n

\u73b0\u5728\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u53cd\u4f8b\uff1a\u628a\u72b6\u60011\u30012\u5206\u4e3a\u4e00\u7ec4\uff0c\u72b6\u60013\u30014\u5206\u4e3a\u53e6\u4e00\u7ec4\u3002\u540c\u6837\u7684\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u4e00\u4e0b\u3002\u8fd9\u6b21\u6211\u4eec\u9700\u8981\u5bf93\u548c4\u5206\u5f00\u8ba1\u7b97\u4e86\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u8fd9\u91cc\u6211\u4eec\u5c31\u80fd\u770b\u5230\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5f53\u540c\u4e00\u7ec4\u7684\u4e24\u4e2a\u72b6\u6001<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u5bf9\u5176\u4ed6\u7ec4\u7684\u8f6c\u79fb\u6982\u7387\u4e0d\u4e00\u6837\u7684\u8bdd\uff0c\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a<\/span><\/span>\"image.png\"<\/span><\/sub>\u7684\u53d6\u503c\u662f<\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\u6216<\/span>\"image.png\"<\/span>\u3002<\/span><\/span><\/p>\n

\u5982\u679c\u6211\u4eec\u5f3a\u884c\u6309\u7167\u8fd9\u6837\u6765\u5206\u7ec4\uff0c\u5047\u8bbe<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u8fd9\u6837\u7684\u7c97\u7c92\u5316\u7ed3\u679c\u8fdd\u80cc\u4e86\u6210\u5757\u6027\u4e00\u5f00\u59cb\u7684\u5b9a\u4e492\uff0c\u5373<\/span>\u7c97\u7c92\u5316\u540e\u7684<\/span><\/span>\u8f6c\u79fb\u6982\u7387\u5bf9\u6240\u6709\u7684\u521d\u59cb\u5fae\u89c2\u72b6\u6001<\/span><\/span>\u03c0<\/span><\/span>\u90fd\u9002\u7528<\/span><\/span><\/b>\u3002\u56e0\u4e3a\u5f53<\/span><\/span>\u03c0<\/span><\/span>=<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u7684\u65f6\u5019\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u8fd9\u4e2a\u8f6c\u79fb\u6982\u7387\u5c31\u662f\u9519\u7684\uff0c\u5373\u4f7f<\/span><\/span>\u03c0<\/span><\/span>\u2260<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\uff0c\u4efb\u4f55\u521d\u59cb\u5fae\u89c2\u72b6\u6001<\/span><\/span>\u03c0<\/span><\/span><\/span>\u90fd\u4f1a\u5728\u67d0\u65f6\u523b<\/span><\/span>n<\/span><\/span><\/span>\u8fbe\u5230<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u5e76\u5bfc\u81f4\u8f6c\u79fb\u6982\u7387\u51fa\u9519\u3002<\/span><\/span><\/p>\n

<\/span>4.3 \u4e00\u4e2a\u66f4\u590d\u6742\u7684\u6b63\u4f8b<\/span><\/span><\/span><\/h4>\n

\u4e09\u4e2a\u76f8\u540c\u72b6\u6001\u7684\u4f8b\u5b50\u53ef\u80fd\u7a0d\u5fae\u6709\u70b9\u7b80\u5355\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u7a0d\u5fae\u590d\u6742\u4e00\u70b9\u7684\u4f8b\u5b50\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5bf9\u4e8e\u8fd9\u4e2a\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\uff0c<\/span><\/span>{<\/span><\/span>{<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>}<\/span><\/span>,<\/span><\/span>{<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>}<\/span><\/span>}<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6210\u5757\u7684\u5206\u7ec4\u3002\u5206\u7ec4\u540e\u7684\u8f6c\u79fb\u77e9\u9635\u4e3a\uff1a <\/span><\/span>\"image.png\"<\/span><\/sub><\/p>\n


<\/span><\/span><\/h2>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

5. \u6210\u5757\u6027\u6ee1\u8db3\u7684\u6027\u8d28<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7c97\u7c92\u5316\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u6709\u591a\u4e2a\u76ee\u6807\uff1a<\/span><\/span><\/p>\n

    \n
  1. \n
    \u964d\u4f4e\u538b\u7f29\u540e\u7684\u52a8\u529b\u5b66\u7ef4\u5ea6\uff0c\u4ee5\u7b80\u5316\u6a21\u578b\u590d\u6742\u6027\uff1b<\/span><\/span><\/section>\n<\/li>\n
  2. \n
    \u4fdd\u7559\u52a8\u529b\u5b66\u4e2d\u6709\u7528\u7684\u4fe1\u606f\uff0c\u4ee5\u786e\u4fdd\u6a21\u578b\u7684\u6709\u6548\u6027\uff1b<\/span><\/span><\/section>\n<\/li>\n
  3. \n
    \u4fdd\u6301\u538b\u7f29\u524d\u540e\u8fc7\u7a0b\u7684\u4e00\u81f4\u6027\uff0c\u4ee5\u786e\u4fdd\u6a21\u578b\u7684\u53ef\u9760\u6027\u3002<\/span><\/span><\/section>\n<\/li>\n<\/ol>\n

    \u7136\u800c\uff0c\u8fd9\u4e9b\u76ee\u6807\u4e4b\u95f4\u5f80\u5f80\u5b58\u5728\u77db\u76fe\uff1a\u538b\u7f29\u7684\u7ef4\u5ea6\u8d8a\u591a\uff0c\u4fdd\u7559\u7684\u4fe1\u606f\u5c31\u8d8a\u5c11\uff0c\u538b\u7f29\u524d\u540e\u7684\u4e00\u81f4\u6027\u5c31\u8d8a\u96be\u4fdd\u6301\u3002\u6210\u5757\u6027\u4f5c\u4e3a\u4e00\u79cd\u8f83\u4e3a\u4e25\u683c\u7684\u5212\u5206\u65b9\u5f0f\uff0c\u867d\u7136\u5728\u538b\u7f29\u7ef4\u5ea6\u4e0a\u53ef\u80fd\u4e0d\u5982\u5176\u4ed6\u65b9\u6cd5\u663e\u8457\uff0c\u4f46\u5b83\u80fd\u591f\u4fdd\u7559\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u6240\u6709\u6709\u7528\u7684\u4fe1\u606f\uff0c\u5e76\u4e14\u786e\u4fdd\u7c97\u7c92\u5316\u524d\u540e\u8fc7\u7a0b\u7684\u4e00\u81f4\u6027\u3002<\/span><\/span><\/p>\n

    \u9664\u6b64\u4e4b\u5916\uff0c\u6210\u5757\u6027\u7684\u5212\u5206\u53ca\u5bf9\u5e94\u7684\u52a8\u529b\u5b66\u7684\u7c97\u7c92\u5316\u8fd8\u5177\u5907\u5f88\u591a\u826f\u597d\u7684\u6027\u8d28\u3002<\/span><\/span><\/p>\n

    <\/span>5.1 \u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027<\/span><\/span><\/span><\/h3>\n

    \u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027\u662f\u6307\uff0c\u5728\u5c06\u5fae\u89c2\u72b6\u6001\u7c97\u7c92\u5316\u4e3a\u5b8f\u89c2\u72b6\u6001\u540e\uff0c\u6211\u4eec\u5c31\u4e0d\u518d\u9700\u8981\u5fae\u89c2\u72b6\u6001\u4e86\uff0c\u53ea\u7528\u5b8f\u89c2\u72b6\u6001\u5c31\u80fd\u9884\u6d4b\u540e\u7eed\u7684\u5b8f\u89c2\u72b6\u6001\u3002<\/span><\/span><\/p>\n

    \u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u5c31\u53ef\u4ee5\u6700\u5927\u5316\u5730\u9884\u6d4b<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u800c\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u867d\u7136\u80fd\u63d0\u4f9b\u4e00\u4e9b\u989d\u5916\u4fe1\u606f\uff0c\u4f46\u662f\u5bf9\u4e8e\u9884\u6d4b<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5e76\u65e0\u5e2e\u52a9\u3002\u8fd9\u610f\u5473\u7740\u6761\u4ef6\u4e92\u4fe1\u606f<\/span><\/span>I<\/span><\/span>(<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>;<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup>|<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>)<\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span>\u3002\u5b8f\u89c2\u52a8\u529b\u5b66\u4e0d\u9700\u8981\u4efb\u4f55\u6765\u81ea\u5fae\u89c2\u72b6\u6001\u7684\u4fee\u6b63\uff0c\u5c31\u80fd\u72ec\u7acb\u4e14\u6b63\u786e\u5730\u53cd\u6620\u7cfb\u7edf\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u7684\u6f14\u5316\u3002<\/span><\/span><\/p>\n

    \u5c3d\u7ba1\u6210\u5757\u6027\u5212\u5206\u80fd\u591f\u51c6\u786e\u9884\u6d4b\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u4f46\u5b83\u65e0\u6cd5\u786e\u4fdd\u50cf\u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u56e0\u679c\u6001\u90a3\u6837\u7684\u5fae\u89c2\u6700\u5927\u9884\u6d4b\u6027\u3002\u56e0\u4e3a\u5728\u805a\u7c7b\u8fc7\u7a0b\u4e2d\u4f1a\u635f\u5931\u5fae\u89c2\u72b6\u6001\u7684\u4fe1\u606f\uff0c\u4f7f\u5f97\u6211\u4eec\u65e0\u6cd5\u8fa8\u522b\u67d0\u4e2a<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u5177\u4f53\u662f\u54ea\u4e2a\u5fae\u89c2\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u3002\u8fd9\u4e2a\u4fe1\u606f\u7684\u635f\u5931\u662f\u4e0d\u53ef\u9006\u7684\uff0c\u6240\u4ee5\u4ece\u5fae\u89c2\u7c97\u7c92\u5316\u5230\u5b8f\u89c2\u4e4b\u540e\uff0c\u5c31\u65e0\u6cd5\u518d\u8fd8\u539f\u5230\u5fae\u89c2\u4e86\u3002<\/span><\/span><\/p>\n

    <\/span>5.2 \u6210\u5757\u5212\u5206\u548c\u7c97\u7c92\u5316\u7684\u53ef\u4ea4\u6362\u6027<\/span><\/span><\/span><\/h3>\n

    \u4e3a\u4e86\u8bf4\u660e\u6240\u8c13\u7684\u53ef\u4ea4\u6362\u6027\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u7ed8\u5236\u4e86\u7c97\u7c92\u5316\u64cd\u4f5c\u548c\u52a8\u529b\u5b66\u6f14\u5316\u7b97\u5b50\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u793a\u610f\u56fe\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

    <\/section>\n

    \u56fe5\uff1a\u7c97\u7c92\u5316\u56fe\u4f8b<\/span><\/span><\/p>\n

    \u56fe5\u5c55\u793a\u4e86\u4ece\u67d0\u4e2a\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u51fa\u53d1\uff0c\u5230\u8fbe\u4e0b\u4e00\u523b\u7684\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u7684\u4e24\u6761\u8def\u5f84<\/span><\/span>[2]<\/span><\/span><\/span>\uff1a<\/span><\/span><\/p>\n

      \n
    1. \n
      \u5148\u7ecf\u8fc7\u5fae\u89c2\u52a8\u529b\u5b66\u8fbe\u5230<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u518d\u8fdb\u884c\u7c97\u7c92\u5316\u5f97\u5230<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span><\/section>\n<\/li>\n
    2. \n
      \u5148\u8fdb\u884c\u7c97\u7c92\u5316\u5f97\u5230<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\uff0c\u518d\u7ecf\u8fc7\u5b8f\u89c2\u52a8\u529b\u5b66\u5230\u8fbe<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span><\/section>\n<\/li>\n<\/ol>\n

      \u5982\u679c\u6211\u4eec\u628a\u7c97\u7c92\u5316\u548c\uff08\u5b8f\u89c2\/\u5fae\u89c2\uff09\u52a8\u529b\u5b66\u770b\u4f5c\u662f\u4e24\u4e2a\u7b97\u5b50\uff0c\u90a3\u8fd9\u4e24\u4e2a\u7b97\u5b50\u7684\u53ef\u4ea4\u6362\u6027\u6307\u7684\u662f\uff1a\u65e0\u8bba\u4ece\u54ea\u4e2a\u5fae\u89c2\u72b6\u6001\u5206\u5e03\u51fa\u53d1\uff0c\u8d70\u8fd9\u4e24\u6761\u8def\u5f84\u5f97\u5230\u7684<\/span><\/span>A<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>+<\/span><\/span><\/sup>1<\/span><\/span><\/sup>)<\/span><\/span><\/sup><\/span>\u7684\u5206\u5e03\u662f\u4e00\u6837\u7684\uff0c\u5373\uff0c<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>\u03a6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>=<\/span><\/span>s<\/span><\/span>(<\/span><\/span><\/sup>t<\/span><\/span><\/sup>)<\/span><\/span><\/sup>P<\/span><\/span>\u03a6<\/span><\/span><\/b>\u3002<\/span><\/span><\/p>\n

      \u5bf9\u4e8e\u4e00\u4e2a\u6210\u5757\u7684<\/span><\/span>P<\/span><\/span><\/span>\uff0c\u548c\u5b83\u7684\u6210\u5757\u5212\u5206<\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u6211\u4eec\u9996\u5148\u5c55\u793a<\/span><\/span>\"image.png\"<\/span><\/sub>\u7684\u4f8b\u5b50\uff0c\u5176\u4ed6\u60c5\u51b5\u7c7b\u4f3c\u3002<\/span><\/span><\/p>\n

      \u5bf9\u4e8e\u8fd9\u4e2a<\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u6211\u4eec\u77e5\u9053<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/span><\/p>\n

      \u7531\u4e8e<\/span><\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\u548c<\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\u5404\u81ea\u7b49\u4e8e\u591a\u4e2a\u5143\u7d20\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u8fd9\u76f8\u5f53\u4e8e\u5c06<\/span><\/span>P<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c\u6309\u7167\u5212\u5206\u8fdb\u884c\u52a0\u603b\uff0c\u800c<\/span><\/span>P<\/span><\/span>\u03a6<\/span><\/span><\/span>\u4e2d\u540c\u4e00\u7ec4\u7684\u884c\u662f\u76f8\u540c\u7684\u3002<\/span><\/span><\/p>\n

      \u53e6\u4e00\u65b9\u9762\uff0c<\/span><\/span>\u03a6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u542b\u4e49\u662f\u5c06<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c\u6309\u7167<\/span><\/span>\u03a6<\/span><\/span><\/span>\u590d\u5236\u5230\u5bf9\u5e94\u7684\u5fae\u89c2\u72b6\u6001\u7684\u884c\u4e2d\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0<\/span><\/span>\u03a6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u548c<\/span><\/span>P<\/span><\/span>\u03a6<\/span><\/span><\/span>\u7684\u7ed3\u679c\u662f\u4e00\u6837\u7684\u3002<\/span><\/span><\/p>\n

      \u63a8\u5e7f\u5230\u6240\u6709<\/span><\/span>\u03a6<\/span><\/span><\/span>\u7684\u60c5\u51b5\u7684\u8bc1\u660e\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

      \u9996\u5148\uff0c<\/span>\"image.png\"<\/span>\uff0c\u5373\u5c06<\/span><\/span>P<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c\u6309\u7167\u5212\u5206\u8fdb\u884c\u52a0\u603b\u3002<\/span><\/span><\/p>\n

      \u800c<\/span><\/span>\u03a6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u662f\u628a<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c\u6309\u7167<\/span><\/span>\u03a6<\/span><\/span><\/span>\u590d\u5236\u5230\u5bf9\u5e94\u7684\u5fae\u89c2\u72b6\u6001\u7684\u884c\u4e2d\uff0c\u6240\u4ee5\u5f53<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>k<\/span><\/span><\/sub>=<\/span><\/span>1<\/span><\/span><\/span>\u65f6\uff0c<\/span><\/span><\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/p>\n

      \u6839\u636e\u6210\u5757\u6027\u7684\u5b9a\u4e49\uff0c\u5f53<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>k<\/span><\/span><\/sub>=<\/span><\/span>1<\/span><\/span><\/span>\uff0c\u5373\u72b6\u6001<\/span><\/span>i<\/span><\/span><\/span>\u5c5e\u4e8e\u7b2c<\/span><\/span>k<\/span><\/span><\/span>\u7ec4\u65f6\uff0c\u72b6\u6001<\/span><\/span>i<\/span><\/span><\/span>\u8f6c\u79fb\u5230\u7b2c<\/span><\/span>j<\/span><\/span><\/span>\u7ec4\u7684\u6982\u7387<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u6240\u4ee5<\/span><\/span>\u03a6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>=<\/span><\/span>P<\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u4ea4\u6362\u5f8b\u6210\u7acb\u3002<\/span><\/span><\/p>\n

      <\/span>5.3 \u4e00\u81f4\u6027<\/span><\/span><\/span><\/h3>\n

      \u5f53\u6211\u4eec\u5bf9\u4e00\u4e2a\u6210\u5757\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u4f7f\u7528\u57fa\u4e8e\u6210\u5757\u6027\u5212\u5206\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u6784\u5efa\u4e86\u5b8f\u89c2\u52a8\u529b\u5b66\u540e\uff0c\u8be5\u5b8f\u89c2\u52a8\u529b\u5b66\u4e0e\u672c\u6765\u7684\u5fae\u89c2\u52a8\u529b\u5b66\u4f1a\u4fdd\u6301\u4e00\u81f4 (Consistent)\u3002<\/span><\/span><\/p>\n

      \u5728\u672c\u8bcd\u6761\u7b2c8\u7ae0\uff0c\u6211\u4eec\u4f1a\u6307\u51fa\u57fa\u4e8e\u6210\u5757\u6027\u5212\u5206\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u548cHOM\u7c97\u7c92\u5316\u65b9\u6cd5\u7684\u7ed3\u679c\u4e00\u81f4\uff0c\u800c\u56e0\u4e3a\u5b9e\u9a8c\u8bc1\u660e\u4e86HOM\u7c97\u7c92\u5316\u65b9\u6cd5\u80fd\u591f\u4fdd\u8bc1\u4e00\u81f4\u6027\uff0c\u56e0\u6b64\u57fa\u4e8e\u6210\u5757\u6027\u5212\u5206\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u4e5f\u80fd\u4fdd\u8bc1\u4e00\u81f4\u6027\u3002<\/span><\/span><\/p>\n

      \u5177\u4f53\u7684\u52a8\u529b\u5b66\u7684\u4e00\u81f4\u6027\u68c0\u9a8c\u65b9\u6cd5\u8bf7\u53c2\u8003\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/span><\/p>\n

      <\/span>
      <\/span><\/span><\/h2>\n

      \n
      \n
      \n
      \n
      \n

      <\/span><\/section>\n

      <\/span><\/section>\n
      \n
      <\/section>\n<\/section>\n<\/section>\n
      \n

      6. \u6210\u5757\u6027\u6982\u5ff5\u7684\u53d8\u79cd<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/span><\/section>\n

      <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


      <\/span><\/p>\n

      \u5c3d\u7ba1\u6210\u5757\u6027\u5177\u6709\u8bb8\u591a\u4f18\u826f\u7684\u7279\u6027\uff0c\u4f46\u5b83\u672c\u8eab\u662f\u4e00\u4e2a\u975e\u5e38\u4e25\u683c\u7684\u6761\u4ef6\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u4e0d\u5141\u8bb8\u4e00\u5b9a\u7684\u8bef\u5dee\uff0c\u51e0\u4e4e\u5f88\u96be\u627e\u5230\u6ee1\u8db3\u6210\u5757\u6027\u7684\u5212\u5206\uff0c\u4ece\u800c\u96be\u4ee5\u5bf9\u9a6c\u5c14\u79d1\u592b\u94fe\u8fdb\u884c\u6709\u6548\u7684\u7c97\u7c92\u5316\u3002\u56e0\u6b64\uff0c\u6210\u5757\u6027\u884d\u751f\u51fa\u4e86\u591a\u79cd\u53d8\u79cd\u6982\u5ff5\uff0c\u8fd9\u4e9b\u53d8\u79cd\u901a\u8fc7\u653e\u5bbd\u67d0\u4e9b\u9650\u5236\u6761\u4ef6\uff0c\u4f7f\u5f97\u5728\u5b9e\u9645\u95ee\u9898\u4e2d\u66f4\u5bb9\u6613\u627e\u5230\u6709\u6548\u7684\u5212\u5206\uff0c\u5e76\u7814\u7a76\u8fd9\u4e9b\u5212\u5206\u5728\u591a\u5927\u7a0b\u5ea6\u4e0a\u4fdd\u7559\u4e86\u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027\u3001\u53ef\u4ea4\u6362\u6027\u3001\u4e00\u81f4\u6027\u7b49\u91cd\u8981\u6027\u8d28\u3002<\/span><\/span><\/p>\n

      <\/span>6.1 \u5f3a\u6210\u5757\u6027 Strong\/Ordinary Lumpability<\/span><\/span><\/span><\/h3>\n

      \u4e3a\u4e86\u4e0e\u66f4\u591a\u7684\u6210\u5757\u6027\u62d3\u5c55\u6982\u5ff5\u76f8\u533a\u5206\uff0c\u4e0a\u8ff0\u6210\u5757\u6027\u6982\u5ff5\u4e5f\u88ab\u4eba\u4eec\u79f0\u4e3a\u5f3a\u6210\u5757\u6027\uff08Strong lumpability\uff09 \uff0c\u6216\u79f0\u4f5c\u539f\u59cb\u6210\u5757\u6027\uff08ordinary lumpability\uff09\u3002\u8fd9\u79cd\u6210\u5757\u6027\u662f\u9650\u5236\u8f83\u4e25\u683c\u7684\u4e00\u79cd\u6210\u5757\u6027\u6982\u5ff5\u3002\u5b83\u8981\u6c42\u77e9\u9635\u5177\u6709\u4e25\u683c\u7684\u5206\u5757\u6027\uff0c\u5373\u540c\u4e00\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u72b6\u6001\u5230\u5176\u4ed6\u5206\u7ec4\u7684\u8f6c\u51fa\u6982\u7387\u5fc5\u987b\u5b8c\u5168\u76f8\u540c\u3002<\/span><\/span><\/p>\n

      \u8fd9\u91cc\u7684’Strong’\u662f\u4e0e\u4e0b\u9762\u7684’weak’\u76f8\u5bf9\u7684\u6982\u5ff5\uff0c\u6307\u7684\u662f\u7b80\u5316\u8fc7\u7a0b\u5fc5\u987b\u5bf9\u4efb\u610f\u521d\u59cb\u72b6\u6001\u5206\u5e03\u90fd\u4fdd\u6301\u4e00\u81f4\u3002<\/span><\/span><\/p>\n

      \u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6b64\u4f8b\u5b50\u4e2d\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u5f3a\u6210\u5757\u7684\u5206\u7ec4\u3002<\/span><\/span><\/p>\n

      <\/span>6.2 \u5f31\u6210\u5757\u6027 Weak Lumpability<\/span><\/span><\/span><\/h3>\n

      \u5f31\u6210\u5757\u6027\uff08weak lumpability\uff09<\/span><\/span>[1]<\/span><\/span><\/span>\u662f\u6307\u7b80\u5316\u8fc7\u7a0b\u4ec5\u5bf9\u67d0\u4e9b\u521d\u59cb\u72b6\u6001\u6ee1\u8db3\u6210\u5757\u6027\uff0c\u800c\u4e0d\u662f\u5bf9\u6240\u6709\u521d\u59cb\u72b6\u6001\u90fd\u6ee1\u8db3\u3002<\/span><\/span><\/p>\n

      \u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u7b80\u5316\u8fc7\u7a0b\uff0c\u4ece<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u51fa\u53d1\u65f6\u80fd\u6ee1\u8db3\u6210\u5757\u6027\uff08\u5f0f\u5b50<\/span><\/span>2<\/span><\/span><\/b>\uff09\uff0c\u4f46\u4ece<\/span><\/span>s<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u51fa\u53d1\u65f6\u4e0d\u6ee1\u8db3\u3002\u5f53<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u5230<\/span><\/span>s<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e4b\u95f4\u4e0d\u8fde\u901a\uff0c\u4e14\u521d\u59cb\u72b6\u6001\u4e3a<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u65f6\uff0c\u7531\u4e8e\u6c38\u8fdc\u4e0d\u4f1a\u5230\u8fbe<\/span><\/span>s<\/span><\/span>j<\/span><\/span><\/sub><\/span>\uff0c\u8be5\u7b80\u5316\u8fc7\u7a0b\u4f1a\u4e00\u76f4\u6ee1\u8db3\u6210\u5757\u6027\u3002<\/span><\/span><\/p>\n

      \u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6b64\u4f8b\u5b50\u4e2d\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u5f3a\u6210\u5757\u7684\u5206\u7ec4\u3002<\/span><\/span><\/p>\n

      \u6211\u4eec\u7559\u610f\u5230\uff0c\u8be5\u9a6c\u5c14\u79d1\u592b\u94fe\u4ece<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u6216\u8005<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u72b6\u6001\u51fa\u53d1\u65f6\uff0c\u6c38\u8fdc\u4e0d\u4f1a\u5230\u8fbe<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u3002\u6240\u4ee5\u5f53\u6211\u4eec\u628a<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u5212\u6210\u4e00\u7ec4\uff0c\u5373\u5206\u7ec4\u4e3a<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u65f6\uff0c\u5206\u7ec4\u540e\u7684\u7b80\u5316\u8fc7\u7a0b\uff0c\u5982<\/span><\/span>\"image.png\"<\/span><\/sub>\u4ecd\u6ee1\u8db3\u5f0f\u5b50<\/span><\/span>2<\/span><\/span><\/b>\u7684\u9a6c\u5c14\u79d1\u592b\u6027\u7ea6\u675f\u3002\u6240\u4ee5\uff0c\u5bf9\u4e8e<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u6216\u8005<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u9879\u975e\u96f6\uff0c\u800c<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u9879\u4e3a\u96f6\u7684\u521d\u59cb\u72b6\u6001\u5206\u5e03<\/span><\/span>\u03c0<\/span><\/span><\/span>\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u662f\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

      \u5bf9\u4e8e<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u9879\u975e\u96f6\u7684\u521d\u59cb\u72b6\u6001\u5206\u5e03<\/span><\/span>\u03c0<\/span><\/span><\/span>\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u5206\u7ec4\u4e0d\u6ee1\u8db3\u5f0f\u5b50<\/span><\/span>2<\/span><\/span><\/b>\u3002\u6240\u4ee5\uff0c\u8be5\u5206\u7ec4\u4ec5\u5bf9\u67d0\u4e9b\u521d\u59cb\u72b6\u6001\u5206\u5e03\u6210\u5757\uff0c\u6545\u4e3a\u5f31\u6210\u5757\u5206\u7ec4\u3002<\/span><\/span><\/p>\n

      <\/span>6.3 \u7cbe\u786e\u6210\u5757\u6027 Exact Lumpability<\/span><\/span><\/span><\/h3>\n

      \u5728\u5f3a\u6210\u5757\u6027\u4e2d\uff0c\u8981\u6c42\u5206\u7ec4\u5185\u6bcf\u4e00<\/span><\/span>\u884c<\/span><\/span><\/b>\u7684\u52a0\u603b\u76f8\u540c\uff0c\u5373\u540c\u4e00\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u72b6\u6001\u5230\u5176\u4ed6\u5206\u7ec4\u7684<\/span><\/span>\u8f6c\u51fa<\/span><\/span><\/b>\u6982\u7387\u76f8\u540c\u3002<\/span><\/span><\/p>\n

      \u800c\u5728<\/span><\/span>\u7cbe\u786e\u6210\u5757\u6027\uff08exact lumpability\uff09\u4e2d<\/span><\/span><\/b>\uff0c\u5219\u8981\u6c42\u5206\u7ec4\u5185\u7684\u6bcf\u4e00<\/span><\/span>\u5217<\/span><\/span><\/b>\u7684\u52a0\u603b\u76f8\u540c\uff0c\u5373\u540c\u4e00\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u72b6\u6001\u4ece\u5176\u4ed6\u5206\u7ec4\u7684<\/span><\/span>\u8f6c\u5165<\/span><\/span><\/b>\u6982\u7387\u76f8\u540c\u3002<\/span><\/span><\/p>\n

      \u5728\u6587\u732e<\/span><\/span>[3]<\/span><\/span><\/span>\u4e2d\u7ed9\u51fa\u7684\u6b63\u5f0f\u5b9a\u4e49\u662f\uff1a<\/span><\/span>P<\/span><\/span><\/span>\u7684<\/span><\/span>\u8f6c\u7f6e<\/span><\/span><\/b>\u7ecf\u8fc7<\/span><\/span>\u884c\u5f52\u4e00\u5316<\/span><\/span><\/b>\u662f\u5f3a\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

      \u53e6\u5916\uff0c\u6587\u732e<\/span><\/span>[3]<\/span><\/span><\/span>\u8fd8\u6307\u51fa\uff0c\u7cbe\u786e\u6210\u5757\u7684<\/span><\/span>P<\/span><\/span><\/span>\u4e5f\u662f\u5f31\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

      \u5728\u5f3a\u6210\u5757\u6027\u7684\u4f8b\u5b50\u4e2d\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u5f3a\u6210\u5757\u7684\u5206\u7ec4\uff0c\u4f46\u4e0d\u662f\u4e00\u4e2a\u7cbe\u786e\u6210\u5757\u7684\u5206\u7ec4\u3002<\/span><\/span><\/p>\n

      \u6211\u4eec\u518d\u4e3e\u4e00\u4e2a\u4f8b\u5b50\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6b64\u4f8b\u5b50\u4e2d\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u4e0d\u662f\u4e00\u4e2a\u5f3a\u6210\u5757\u7684\u5206\u7ec4\uff0c\u4f46\u662f\u4e00\u4e2a\u7cbe\u786e\u6210\u5757\u7684\u5206\u7ec4\uff0c\u8fd9\u662f\u56e0\u4e3a\u6bcf\u4e00\u4e2a\u5206\u5757\u7684\u5217\u6c42\u548c\u540e\u7684\u6982\u7387\u90fd\u76f8\u7b49\u3002<\/span><\/span><\/p>\n

      <\/span>6.4 \u4e25\u683c\u6210\u5757\u6027 Strict Lumpability<\/span><\/span><\/span><\/h3>\n

      \u4e25\u683c\u6210\u5757\u6027\uff08strict lumpability\uff09<\/span><\/span>[3]<\/span><\/span><\/span>\u662f\u6307\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u540c\u65f6\u6ee1\u8db3\u5f3a\u6210\u5757\u6027\u548c\u7cbe\u786e\u6210\u5757\u6027\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u540c\u4e00\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u72b6\u6001\u4e0d\u4ec5\u4ece\u53e6\u4e00\u4e2a\u5206\u7ec4\u7684\u8f6c\u5165\u6982\u7387\u76f8\u7b49\uff0c\u800c\u4e14\u5230\u53e6\u4e00\u4e2a\u5206\u7ec4\u7684\u8f6c\u51fa\u6982\u7387\u4e5f\u76f8\u7b49\u3002\u8fd9\u662f\u76ee\u524d\u6211\u4eec\u5df2\u77e5\u7684\u6700\u5f3a\u7684\u4e00\u79cd\u6210\u5757\u6027\u3002<\/span><\/span><\/p>\n

      \u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6b64\u4f8b\u5b50\u4e2d\uff0c<\/span><\/span>[<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>,<\/span><\/span>[<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>]<\/span><\/span>]<\/span><\/span><\/span>\u65e2\u662f\u4e00\u4e2a\u5f3a\u6210\u5757\u7684\u5206\u7ec4\uff0c\u53c8\u662f\u4e00\u4e2a\u7cbe\u786e\u6210\u5757\u7684\u5206\u7ec4\u3002<\/span><\/span><\/p>\n

      <\/span>6.5 \u51c6\u6210\u5757\u6027 Quasi Lumpability<\/span><\/span><\/span><\/h3>\n

      \u5f3a\u6210\u5757\u6027\u5bf9\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u7684\u5206\u5757\u6027\u8981\u6c42\u975e\u5e38\u4e25\u683c\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5f88\u96be\u627e\u5230\u5b8c\u5168\u6ee1\u8db3\u5f3a\u6210\u5757\u6027\u7684\u77e9\u9635\uff0c\u5373\u4f7f\u77e9\u9635\u53d7\u5230\u5fae\u5c0f\u6270\u52a8\uff0c\u4e5f\u53ef\u80fd\u4e0d\u518d\u6ee1\u8db3\u6210\u5757\u6027\u3002\u4e3a\u4e86\u8003\u8651\u8fd9\u79cd\u6270\u52a8\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e0d\u6210\u5757\u4f46\u975e\u5e38\u63a5\u8fd1\u6210\u5757\u7684\u60c5\u51b5<\/span><\/span>[4]<\/span><\/span><\/span>\uff1a<\/span><\/span><\/p>\n

      \u5982\u679c\u4e00\u4e2a\u77e9\u9635 <\/span><\/span>P<\/span><\/span><\/span>\u53ef\u4ee5\u88ab\u5206\u89e3\u4e3a<\/span><\/span>P<\/span><\/span>=<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/span><\/sup>+<\/span><\/span>P<\/span><\/span>\u03f5<\/span><\/span><\/sup><\/span>\uff0c\u5176\u4e2d<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6210\u5757\u7684\u77e9\u9635\uff0c\u800c<\/span><\/span>P<\/span><\/span>\u03f5<\/span><\/span><\/sup><\/span>\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u90fd\u5c0f\u4e8e<\/span><\/span>\u03f5<\/span><\/span><\/span>\uff0c<\/span><\/span>P<\/span><\/span><\/span>\u5c31\u662f\u4e00\u4e2a<\/span><\/span>\u03f5<\/span><\/span><\/span>-\u51c6\u6210\u5757\u7684\u77e9\u9635\u3002<\/span><\/span><\/p>\n

      \u6bd4\u5982\u8bf4\uff0c\u6211\u4eec\u5bf9\u4e0a\u9762\u7684\u6210\u5757\u7684\u4f8b\u5b50\u52a0\u4e0a\u4e00\u70b9\u6270\u52a8\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u5c31\u80fd\u83b7\u5f97\u4e00\u4e2a<\/span><\/span>\u03f5<\/span><\/span><\/span>-\u51c6\u6210\u5757\u7684\u77e9\u9635\uff0c\u5176\u4e2d<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0.02<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

      <\/span>6.6 \u6bd4\u4f8b\u6210\u5757\u6027 Proportional Lumpability<\/span><\/span><\/span><\/h3>\n

      \u6bd4\u4f8b\u6210\u5757\u6027\uff08Proportional Lumpability\uff09<\/span><\/span>[5]<\/span><\/span><\/span>\u662f\u57fa\u4e8e\u8fde\u7eed\u65f6\u95f4\u9a6c\u5c14\u79d1\u592b\u94fe\uff08<\/span><\/span>CTMC<\/span><\/span><\/b>\uff09\u63d0\u51fa\u7684\uff0c\u7528\u4e8e\u653e\u677e\u6210\u5757\u6027\u9650\u5236\u7684\u6982\u5ff5\u3002\u76ee\u524d\u5c1a\u672a\u53d1\u73b0\u6709\u7814\u7a76\u76f4\u63a5\u5c06\u8be5\u6982\u5ff5\u5e94\u7528\u4e8e\u79bb\u6563\u65f6\u95f4\u9a6c\u5c14\u79d1\u592b\u94fe\uff08<\/span><\/span>DTMC<\/span><\/span><\/b>\uff09\u3002<\/span><\/span><\/p>\n

      \u5982\u679c\u5c06 DTMC \u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635<\/span><\/span>P<\/span><\/span><\/span>\u89c6\u4e3a\u4e00\u4e2a\u5dee\u5206\u7b97\u5b50\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5927\u6982\u628aCTMC\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635 <\/span><\/span>Q<\/span><\/span><\/span>\u770b\u4f5c\u662f\u4e00\u4e2a\u5fae\u5206\u7b97\u5b50\uff0c\u8be6\u60c5\u8bf7\u53c2\u9605\u9a6c\u5c14\u79d1\u592b\u94fe\u3002<\/span><\/span>Q<\/span><\/span><\/span>\u77e9\u9635\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

      \u4ee4<\/span><\/span>I<\/span><\/span><\/span>\u4e3a\u4e00\u4e2a\u53ef\u6570\u96c6\uff0c<\/span><\/span>I<\/span><\/span><\/span>\u4e0a\u7684\u77e9\u9635<\/span><\/span>Q<\/span><\/span>=<\/span><\/span>(<\/span><\/span>q<\/span><\/span>i<\/span><\/span><\/sub>j<\/span><\/span><\/sub>:<\/span><\/span>i<\/span><\/span>,<\/span><\/span>j<\/span><\/span>\u2208<\/span><\/span>I<\/span><\/span>)<\/span><\/span><\/span>\u82e5\u6ee1\u8db3\u4e0b\u9762\u4e09\u4e2a\u6761\u4ef6\uff0c\u5219\u79f0\u5176\u4e3a<\/span><\/span>Q<\/span><\/span><\/span>\u77e9\u9635\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6709\u4e0a\u9762\u4e09\u4e2a\u6761\u4ef6\u53ef\u77e5<\/span><\/span>Q<\/span><\/span><\/span>\u77e9\u9635\u7684\u6bcf\u4e00\u884c\u4e2d\u7684\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u53ef\u4ee5\u4e3a\u4efb\u610f\u975e\u8d1f\u5b9e\u6570\uff0c\u53ea\u9700\u8981\u6ee1\u8db3\u6bcf\u884c\u975e\u5bf9\u89d2\u5143\u7d20\u4e4b\u548c\u6709\u9650\u8fd9\u4e00\u4e2a\u9650\u5236\uff1a<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u7531\u4e8e\u6761\u4ef63\u4f7f\u6bcf\u4e00\u884c\u7684\u884c\u548c\u4e3a\u96f6\uff0c\u6240\u4ee5\u5bf9\u89d2\u7ebf\u5143\u7d20<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span>Q<\/span><\/span><\/span>\u77e9\u9635\u7684\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20<\/span><\/span>q<\/span><\/span>i<\/span><\/span><\/sub>j<\/span><\/span><\/sub><\/span>\u63cf\u8ff0\u7684\u662f\u72b6\u6001<\/span><\/span>i<\/span><\/span><\/span>\u8f6c\u79fb\u5230\u72b6\u6001<\/span><\/span>j<\/span><\/span><\/span>\u7684\u2018\u901f\u7387\u2019\uff08rate\uff09\u3002<\/span><\/span><\/p>\n

      \u5f3a\u6210\u5757\u6027\u5728CTMC\u8bbe\u5b9a\u4e0b\u8ddfDTMC\u662f\u7c7b\u4f3c\u7684\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u662f\uff1a<\/span><\/span><\/p>\n

      \u5bf9\u4e8e<\/span><\/span>Q<\/span><\/span><\/span>\u77e9\u9635\uff0c\u5fae\u89c2\u7684\u79bb\u6563\u72b6\u6001\u7a7a\u95f4<\/span><\/span>S<\/span><\/span><\/span>\uff0c\u5206\u7ec4\u540e\u7684\u5b8f\u89c2\u72b6\u6001\u7a7a\u95f4<\/span><\/span>A<\/span><\/span><\/span>\uff0c\u5982\u679c<\/span><\/span>Q<\/span><\/span><\/span>\u6ee1\u8db3\u5f3a\u6210\u5757\u6027\u7684\u8bdd\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u5176\u4e2d\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e3a\u5fae\u89c2\u72b6\u6001<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub><\/span>\u5230\u5b8f\u89c2\u72b6\u6001<\/span><\/span>A<\/span><\/span>m<\/span><\/span><\/sub><\/span>\u7684\u8f6c\u79fb\u901f\u7387\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5c5e\u4e8e\u540c\u4e00\u7ec4\u7684\u4efb\u610f\u5fae\u89c2\u72b6\u6001\u8f6c\u79fb\u5230\u5b8f\u89c2\u72b6\u6001\u7684\u2018\u901f\u7387\u2019\u662f\u4e00\u6837\u7684\u3002<\/span><\/span><\/p>\n

      \u5728CTMC\u8bbe\u5b9a\u4e0b\uff0c\u6bd4\u4f8b\u6210\u5757\u7684\u6b63\u5f0f\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

      \u5bf9<\/span><\/span>S<\/span><\/span><\/span>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u72b6\u6001\uff0c\u5b58\u5728\u4e00\u4e2a\u51fd\u6570<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4f7f\u5f97\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u6211\u4eec\u79f0\u8fd9\u6837\u7684CTMC\u5bf9\u5206\u7ec4<\/span><\/span>A<\/span><\/span><\/span> \u662f <\/span><\/span>\u03ba<\/span><\/span><\/span>-\u6bd4\u4f8b\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

      \u4e0d\u50cfDTMC\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635<\/span><\/span>P<\/span><\/span><\/span>\u6709\u4e00\u4e2a\u6bcf\u884c\u52a0\u548c\u4e3a1\u7684\u6761\u4ef6\uff0cCTMC\u8bbe\u5b9a\u4e0b\u6bcf\u884c\u7684\u8f6c\u51fa\u901f\u7387\uff0c\u4e5f\u5c31\u662f\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u4e4b\u548c<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5e76\u6ca1\u6709\u6570\u503c\u4e0a\u7684\u7ea6\u675f\u3002<\/span><\/span><\/p>\n

      \u6240\u4ee5\uff0c\u6bd4\u4f8b\u6210\u5757\u6027\u63cf\u8ff0\u7684\u662f\uff0c\u5bf9\u4e00\u4e2a\u672c\u6765\u5f3a\u6210\u5757\u7684<\/span><\/span>Q<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c<\/span><\/span>i<\/span><\/span><\/span>\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570<\/span><\/span>\u03ba<\/span><\/span>(<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/sub>)<\/span><\/span><\/span>\uff0c\u4f7f\u5f97\u6bcf\u884c\u7684\u8f6c\u51fa\u901f\u7387\u90fd\u4e0d\u4e00\u81f4\u7684\u60c5\u51b5\u3002\u53cd\u8fc7\u6765\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u5bf9\u4e8e\u4e00\u4e2a<\/span><\/span>Q<\/span><\/span><\/span>\u7684\u6bcf\u4e00\u884c\u7684\u8f6c\u51fa\u901f\u7387\u8fdb\u884c\u4e00\u4e2a\u2018\u5bf9\u9f50\u2019\u540e\u80fd\u83b7\u5f97\u4e00\u4e2a\u5f3a\u6210\u5757\u7684<\/span><\/span>Q<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u8bdd\uff0c\u90a3\u4e48<\/span><\/span>Q<\/span><\/span><\/span>\u5c31\u662f\u6bd4\u4f8b\u6210\u5757\u7684\u3002\u56e0\u4e3a\uff0c<\/span><\/span><\/p>\n

      <\/section>\n

      \u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e3a\u5f3a\u6210\u5757\u77e9\u9635<\/span><\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\u3002<\/span><\/span><\/p>\n

      \u76ee\u524d\uff0c\u6682\u65f6\u6ca1\u6709\u5728DTMC\u4e0a\u7684\u6bd4\u4f8b\u6210\u5757\u6027\u5b9a\u4e49\u3002\u867d\u7136CTMC\u4e0a\u7684\u5b9a\u4e49\u6bd4\u8f83\u7b80\u5355\uff0c\u4f46\u65e0\u6cd5\u76f4\u63a5\u8fc1\u79fb\u5230DTMC\u4e0a\u3002\u8fd9\u662f\u56e0\u4e3a\u4eceCTMC\u7684\u901f\u7387\u77e9\u9635<\/span><\/span>Q<\/span><\/span><\/span>\u5230DTMC\u7684\u8f6c\u79fb\u77e9\u9635<\/span><\/span>P<\/span><\/span><\/span>\u4e4b\u95f4\u9700\u8981\u7ecf\u8fc7\u4e00\u4e2a<\/span><\/span>\"image.png\"<\/span><\/sub>\u7684\u6cf0\u52d2\u5c55\u5f00\u8f6c\u6362\uff0c<\/span><\/span>t<\/span><\/span><\/span>\u4e3a\u6b65\u957f\u65f6\u95f4\u3002<\/span><\/span><\/p>\n

      \u6240\u4ee5\uff0c<\/span><\/span>Q<\/span><\/span><\/span>\u548c<\/span><\/span>Q<\/span><\/span>\u2032<\/span><\/span>=<\/span><\/span>K<\/span><\/span>Q<\/span><\/span><\/span>\u5bf9\u5e94\u7684\u8f6c\u79fb\u77e9\u9635\u5206\u522b\u4e3a<\/span><\/span>\"image.png\"<\/span><\/sub>\u548c<\/span><\/span>\"image.png\"<\/span><\/sub><\/sub>\uff0c\u5e76\u65e0\u7b80\u5355\u7684\u5bf9\u5e94\u5173\u7cfb\u3002<\/span><\/span><\/p>\n

      \u4e0b\u9762\u662fCTMC\u7684\u5f3a\u6210\u5757\u6027\u548c\u6bd4\u4f8b\u6210\u5757\u6027\u4f8b\u5b50\u793a\u610f\u56fe\uff1a<\/span><\/span><\/p>\n

      <\/section>\n

      \u56fe8\uff1aCTMC\u7684\u5f3a\u6210\u5757\u6027\u548c\u6bd4\u4f8b\u6210\u5757\u6027\u4f8b\u5b50\u793a\u610f\u56fe\u3002Q<\/span><\/span>1<\/span><\/sub>, Q<\/span><\/span>2<\/span><\/sub>\u4e3a\u5f3a\u6210\u5757Q\u77e9\u9635\uff0cQ<\/span><\/span><\/span><\/span>3<\/span><\/sub>\u4e3a\u6bd4\u4f8b\u6210\u5757Q\u77e9\u9635\uff0cP<\/span><\/span><\/span>1<\/span><\/sub>, P<\/span><\/span>2<\/span><\/sub>, P<\/span><\/span>3<\/span><\/sub>\u4e3a\u5bf9\u5e94\u7684DTMC TPM\u3002<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5176\u4e2d\uff0c<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/span>\u4e3a\u5f3a\u6210\u5757\u7684Q\u77e9\u9635\uff0c\u8bbe<\/span><\/span>t<\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span>\u4ee3\u5165<\/span><\/span>P<\/span><\/span>(<\/span><\/span>t<\/span><\/span>)<\/span><\/span>=<\/span><\/span>e<\/span><\/span>x<\/span><\/span>p<\/span><\/span>(<\/span><\/span>t<\/span><\/span>Q<\/span><\/span>)<\/span><\/span><\/span>\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u5f3a\u6210\u5757\u7684<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u3002<\/span><\/span><\/p>\n

      \u4e3a\u4ec0\u4e48\u5f3a\u6210\u5757\u7684Q\u77e9\u9635\u80fd\u5f97\u5230\u5f3a\u6210\u5757\u7684P\u77e9\u9635\u5462\uff1f\u5f53\u6211\u4eec\u8ba1\u7b97P\u77e9\u9635\u65f6\uff0c\u6211\u4eec\u9700\u8981\u8fdb\u884c\u6cf0\u52d2\u5c55\u5f00\u3002\u8fd9\u91cc\u6211\u4eec\u68c0\u67e5\u4e00\u4e0b\u5c55\u5f00\u4e2d\u7684<\/span><\/span>(<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/sub>)<\/span><\/span>2<\/span><\/span><\/sup><\/span>\u9879\u3002\u4ee5\u8fd9\u4e2a\u4f8b\u5b50\u4e3a\u4f8b\uff0c<\/span><\/span>q<\/span><\/span>13<\/span><\/span><\/sub>+<\/span><\/span>q<\/span><\/span>14<\/span><\/span><\/sub>=<\/span><\/span>q<\/span><\/span>23<\/span><\/span><\/sub>+<\/span><\/span>q<\/span><\/span>24<\/span><\/span><\/sub><\/span>\u3002\u901a\u8fc7\u8ba1\u7b97\u5f97\u77e5\uff0c<\/span><\/span><\/p>\n

      <\/section>\n

      \u8fd9\u91cc\u6211\u4eec\u53ea\u8ba1\u7b97\u4e86<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4f46\u7c7b\u4f3c\u7684\u8ba1\u7b97\u53ef\u4ee5\u653e\u5728<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u7684\u4efb\u610f\u7684\u5206\u7ec4\u91cc\u3002<\/span><\/span><\/p>\n

      \u540c\u6837\u7684\uff0c\u6211\u4eec\u80fd\u7528\u7c7b\u4f3c\u7684\u65b9\u5f0f\u6765\u8ba1\u7b97<\/span><\/span>Q<\/span><\/span><\/span>\u7684\u4efb\u610f\u5e42\u77e9\u9635<\/span><\/span>Q<\/span><\/span>n<\/span><\/span><\/sup><\/span>\uff0c\u53d1\u73b0<\/span><\/span>Q<\/span><\/span>n<\/span><\/span><\/sup><\/span>\u4e5f\u662f\u5f3a\u6210\u5757\u7684\u3002\u6240\u4ee5\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e5f\u662f\u5f3a\u6210\u5757\u7684\u3002<\/span><\/span><\/p>\n

      \u63a5\u7740\uff0c\u6211\u4eec\u628a<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u4e2d<\/span><\/span>\u6240\u6709\u5143\u7d20<\/span><\/span><\/b>\u4e58\u4ee52\uff0c\u5f97\u5230<\/span><\/span>Q<\/span><\/span>2<\/span><\/span><\/sub><\/span>\uff0c\u4f1a\u5f97\u5230\u53e6\u4e00\u4e2a\u8ddf<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u4e0d\u4e00\u6837\u7684\u5f3a\u6210\u5757\u7684<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u3002\u8fd9\u8bf4\u660e\uff0c\u5728Q\u77e9\u9635\u4e0a\u7684\u6539\u52a8\uff0c\u53cd\u6620\u5230P\u77e9\u9635\u4e0a\u5e76\u4e0d\u662f\u7b80\u5355\u7684\u7ebf\u6027\u5173\u7cfb\u3002<\/span><\/span><\/p>\n

      \u6211\u4eec\u53d1\u73b0<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u8f83<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u5c0f\uff0c\u800c\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u5219\u8f83\u5927\u3002\u8fd9\u662f\u56e0\u4e3a\u5728<\/span><\/span>Q<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u4e2d\uff0c\u968f\u673a\u6e38\u8d70\u7c92\u5b50\u4ece\u6bcf\u4e2a\u72b6\u6001\u79bb\u5f00\u7684\u901f\u7387\u90fd\u589e\u5927\u4e86\uff0c\u6240\u4ee5\u4f1a\u503e\u5411\u6d41\u5411\u5176\u4ed6\u72b6\u6001\uff0c\u800c\u4e0d\u662f\u56de\u5230\u672c\u72b6\u6001\u3002<\/span><\/span><\/p>\n

      \u6700\u540e\uff0c\u6211\u4eec\u628a<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u4e2d<\/span><\/span>\u7b2c\u4e8c\u884c\u5143\u7d20<\/span><\/span><\/b>\u4e58\u4ee52\uff0c\u5f97\u5230\u4e00\u4e2a\u6bd4\u4f8b\u6210\u5757\u7684<\/span><\/span>Q<\/span><\/span>3<\/span><\/span><\/sub><\/span>\uff0c\u5e76\u5f97\u5230\u5bf9\u5e94\u7684<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u3002\u56e0\u4e3a\u5bf9\u7b2c\u4e8c\u884c\u8fdb\u884c\u4e86\u6539\u52a8\uff0c\u6240\u4ee5<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u4e2d<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u5c31\u4e0d\u518d\u6ee1\u8db3\u80fd\u653e\u5728\u540c\u4e00\u7ec4\u91cc\u7684\u6761\u4ef6\uff0c\u4f46<\/span><\/span>s<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub><\/span>\u4ecd\u80fd\u5212\u5206\u5728\u540c\u4e00\u7ec4\u91cc\u3002\u6240\u4ee5\uff0c<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u7684\u5f3a\u6210\u5757\u5206\u7ec4\u4e3a<\/span><\/span>{<\/span><\/span>1<\/span><\/span>}<\/span><\/span>,<\/span><\/span>{<\/span><\/span>2<\/span><\/span>}<\/span><\/span>,<\/span><\/span>{<\/span><\/span>3<\/span><\/span>,<\/span><\/span>4<\/span><\/span>}<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

      \u5728\u8be5\u4f8b\u5b50\u4e2d\uff0c\u867d\u7136\u4ece<\/span><\/span>Q<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u5230<\/span><\/span>Q<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u4e4b\u95f4\u7684\u64cd\u4f5c\u6bd4\u8f83\u7b80\u5355\uff0c \u4f46<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub><\/span>\u548c<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u4e4b\u95f4\u5e76\u6ca1\u6709\u4e00\u4e2a\u660e\u663e\u7684\u5bf9\u5e94\u5173\u7cfb\u3002\u6bd4\u8f83\u6e05\u695a\u7684\u662f\uff0c\u5f53\u6211\u4eec\u628a<\/span><\/span>Q<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u7684<\/span><\/span>\u7b2c2\u884c<\/span><\/span><\/b>\u901f\u7387\u8c03\u5feb\u4e86\u4e4b\u540e\uff0c\u505c\u7559\u5728<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u7684\u6982\u7387\u53d8\u5c0f\u4e86\uff0c\u6240\u4ee5<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/sub><\/span>\u7684<\/span><\/span>\u7b2c2\u5217<\/span><\/span><\/b>\u5c31\u53d8\u5c0f\u4e86\u3002<\/span><\/span><\/p>\n

      \u8fd9\u516d\u79cd\u6210\u5757\u6027\u7684\u5b9a\u4e49\u6309\u7167\u9650\u5236\u4e25\u683c\u5ea6\u5927\u6982\u7684\u6392\u5e8f\u662f\uff1a<\/span><\/span><\/p>\n

      \u51c6\u6210\u5757 Quasi < \u6bd4\u4f8b\u6210\u5757 Proportional < \u5f31\u6210\u5757 Weak < \u7cbe\u51c6\u6210\u5757 Exact < \u5f3a\u6210\u5757 Strong\/Ordinary < \u4e25\u683c\u6210\u5757 Strict<\/span><\/span><\/p>\n

      <\/span>
      <\/span><\/span><\/h2>\n

      \n
      \n
      \n
      \n
      \n

      <\/span><\/section>\n

      <\/span><\/section>\n
      \n
      <\/section>\n<\/section>\n<\/section>\n
      \n

      7. \u6210\u5757\u6027\u548c\u7c97\u7c92\u5316<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/span><\/section>\n

      <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


      <\/span><\/p>\n

      \u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7c97\u7c92\u5316\u53ef\u4ee5\u7406\u89e3\u4e3a\u5bf9\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u6982\u7387\u77e9\u9635\uff08TPM\uff09\u8fdb\u884c\u5206\u7ec4\uff0c\u5f97\u5230\u4e00\u4e2a\u5206\u7ec4\u77e9\u9635<\/span><\/span>\u03a6<\/span><\/span><\/span>\u548c\u5b83\u5bf9\u5e94\u7684\u5b8f\u89c2TPM<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u3002\u8fd9\u4e00\u8fc7\u7a0b\u901a\u5e38\u53ef\u4ee5\u5206\u4e3a\u4e24\u90e8\uff1a\u5148\u8fdb\u884c\u72b6\u6001\u5212\u5206<\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u518d\u57fa\u4e8e<\/span><\/span>\u03a6<\/span><\/span><\/span>\u83b7\u53d6<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

      \u5bf9\u72b6\u6001\u7a7a\u95f4\u505a\u7c97\u7c92\u5316\u6709\u786c\u5212\u5206\u548c\u8f6f\u5212\u5206\u4e24\u79cd\u3002\u8f6f\u5212\u5206\u53ef\u4ee5\u770b\u4f5c\u628a\u5fae\u89c2\u72b6\u6001\u6253\u6563\u91cd\u6784\u6210\u4e86\u4e00\u4e9b\u5b8f\u89c2\u72b6\u6001\uff0c\u800c\u786c\u5212\u5206\u5219\u66f4\u4e3a\u4e25\u683c\uff0c\u76f4\u63a5\u5c06\u82e5\u5e72\u4e2a\u5fae\u89c2\u72b6\u6001\u5212\u5206\u4e3a\u4e00\u4e2a\u7ec4\u3002\u672c\u6587\u4ec5\u8ba8\u8bba\u786c\u5212\u5206\uff0c\u4e0d\u6d89\u53ca\u8f6f\u5212\u5206\u3002<\/span><\/span><\/p>\n

      \u6210\u5757\u6027\u662f\u5bf9\u7b2c\u4e00\u6b65\uff0c\u5373\u5bf9<\/span><\/span>\u03a6<\/span><\/span><\/span>\u7684\u7ea6\u675f\u8981\u6c42\uff1b\u800c\u4e0a\u9762\u63d0\u5230\u7684\u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027\u3001\u53ef\u4ea4\u6362\u6027\u548c\u4e00\u81f4\u6027\u662f\u5bf9<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u7684\u7ea6\u675f\u3002<\/span><\/span><\/p>\n

      \u4ece\u524d\u9762\u7684\u6210\u5757\u6027\u516c\u5f0f<\/span><\/span>2<\/span><\/span><\/b>\u548c\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u89c2\u5730\u7406\u89e3\uff1a\u5f53\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u5b58\u5728\u5757\u72b6\u7ed3\u6784\uff0c\u6216\u8005\u72b6\u6001\u660e\u663e\u53ef\u4ee5\u88ab\u5212\u5206\u4e3a\u51e0\u7c7b\u65f6\uff0c\u6839\u636e\u8fd9\u6837\u7684\u5212\u5206\uff0c\u8be5\u77e9\u9635\u5c31\u662f\u6210\u5757\u7684\u3002\u5bf9\u4e8e\u7b80\u5355\u7684<\/span><\/span>P<\/span><\/span><\/span>\uff0c\u5982\u56fe8\u4e2d\u7684<\/span>\"image.png\"<\/span>\u6240\u793a\uff0c\u6211\u4eec\u80fd\u591f\u6839\u636e\u4e0a\u9762\u7684\u5b9a\u74061\u5f88\u5feb\u7684\u627e\u51fa\u5b83\u7684\u6210\u5757\u5212\u5206<\/span><\/span>\u03a6<\/span><\/span><\/span>\uff0c\u5e76\u901a\u8fc7\u5b9a\u4e493\u8fc5\u901f\u8ba1\u7b97\u51fa\u5bf9\u5e94\u7684<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

      <\/span>7.1 \u57fa\u4e8e\u6210\u5757\u6027\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\uff08\u672a\u7ed9\u5b9a\u6210\u5757\u7684\u5212\u5206\u7684\u60c5\u51b5\uff09<\/span><\/span><\/span><\/h3>\n
      <\/section>\n

      \u56fe8\uff1aZhang<\/span><\/span>[6]<\/span><\/span><\/span> \u6587\u7ae0\u4e2d\u7684\u793a\u610f\u56fe\u3002\u56fe\u4e2d\u5de6\u9762\u56db\u4e2a\u77e9\u9635\u90fd\u662f\u6210\u5757\u7684\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\uff0c\u800c\u53f3\u9762\u7684P<\/span><\/span>2<\/span><\/sub>\u662f\u4e00\u4e2a\u566a\u58f0\u77e9\u9635\uff0c(P<\/span><\/span><\/span>1<\/span><\/sub>)<\/span><\/span>T<\/span><\/sup> P<\/span><\/span><\/span>2<\/span><\/sub> = 0<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u7136\u800c\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u7ecf\u5e38\u9047\u5230\u7684\u77e9\u9635\u53ef\u80fd\u5e76\u4e0d\u5b8c\u7f8e\u3002\u4f8b\u5982\uff0c\u6210\u5757\u7684\u77e9\u9635\u7684\u72b6\u6001\u6392\u5e8f\u53ef\u80fd\u88ab\u6253\u4e71\uff08\u5982\u56fe8\u4e2d\u7684<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub><\/span>\uff09\uff0c\u6216\u8005\u77e9\u9635\u5305\u542b\u4e86\u5982<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/sub><\/span>\u7684\u566a\u58f0\uff08\u5982\u56fe8\u4e2d\u7684<\/span><\/span>P<\/span><\/span><\/span>\uff0c<\/span><\/span>P<\/span><\/span>=<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/sub>+<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/sub><\/span>\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\uff09\u3002<\/span><\/span><\/p>\n

      \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u901a\u5e38\u9762\u4e34\u7684\u662f\u50cf<\/span><\/span>P<\/span><\/span><\/span>\u8fd9\u6837\u7684\u77e9\u9635\u3002\u6211\u4eec\u65e2\u65e0\u6cd5\u786e\u5b9a\u5b83\u662f\u5426\u6210\u5757\uff0c\u4e5f\u65e0\u6cd5\u51b3\u5b9a\u5b83\u7684\u5212\u5206\uff0c\u751a\u81f3\u4e0d\u77e5\u9053\u5b83\u7684\u9a6c\u5c14\u79d1\u592b\u79e9\u3002<\/span><\/span><\/p>\n

      \u9488\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0cAnru Zhang<\/span><\/span>[6]<\/span><\/span><\/span>\u63d0\u51fa\u4e86\u4e00\u79cd\u5bfb\u627e\u6700\u4f18\u5212\u5206\u7684\u65b9\u6cd5\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u6700\u4f18\u7684\u5212\u5206\uff0c\u5e76\u57fa\u4e8e\u8fd9\u4e2a\u5212\u5206\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u662f\u5426\u6210\u5757\u3002\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

        \n
      1. \n
        \u83b7\u53d6\u4e00\u4e2an*n\u7ef4\u7684\u9a6c\u5c14\u79d1\u592b\u77e9\u9635P\uff0c\u6216\u8005\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u9891\u7387\u91c7\u6837\uff1b<\/span><\/span><\/section>\n<\/li>\n
      2. \n
        \u83b7\u53d6<\/span><\/span>r<\/span><\/span><<\/span><\/span>n<\/span><\/span><\/span> \u7684\u9a6c\u5c14\u79d1\u592b\u79e9\uff0c\u6216\u6307\u5b9a\u4e00\u4e2a<\/span><\/span>r<\/span><\/span><\/span>\uff1b<\/span><\/span><\/section>\n<\/li>\n
      3. \n
        \u5bf9P\u8fdb\u884cSVD\u5206\u89e3\uff0c<\/span><\/span>P<\/span><\/span>=<\/span><\/span>U<\/span><\/span>\u03a3<\/span><\/span>V<\/span><\/span>T<\/span><\/span><\/sup><\/span>\uff0c\u5176\u4e2dU\u4e3a\u5de6\u5947\u5f02\u5411\u91cf\uff0cV\u4e3a\u53f3\u5947\u5f02\u5411\u91cf\u3002<\/span><\/span><\/section>\n<\/li>\n
      4. \n
        \u901a\u8fc7\u4e0b\u5217\u516c\u5f0f\u5f97\u5230\u6700\u4f18\u5212\u5206 <\/span><\/span>\u03a9<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u03a9<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>\u03a9<\/span><\/span>r<\/span><\/span><\/sub><\/span><\/section>\n<\/li>\n<\/ol>\n
        <\/span><\/sub><\/span><\/section>\n

        \u5176\u4e2d\uff0c<\/span><\/span>v<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u662f\u7b2c<\/span><\/span>s<\/span><\/span><\/span>\u7c7b<\/span><\/span>\u03a9<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u7684\u7279\u5f81\u5411\u91cf\u3002<\/span><\/span><\/p>\n

        \u8fd9\u4e2a\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u5728\u6700\u4f18\u7684\u5212\u5206\u4e2d\uff0c<\/span><\/span>\u03a9<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u4e2d\u7684\u72b6\u6001<\/span><\/span>i<\/span><\/span><\/span>\u7684\u53f3\u5947\u5f02\u5411\u91cf\u4f1a\u548c<\/span><\/span>v<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u8ddd\u79bb\u6700\u5c0f\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u8ba9\u6bcf\u4e2a\u5fae\u89c2\u6001\u7684\u53f3\u7279\u5f81\u5411\u91cf\u548c\u5b83\u5bf9\u5e94\u7684\u5b8f\u89c2\u6001\u7684\u53f3\u7279\u5f81\u5411\u91cf\u5c3d\u53ef\u80fd\u63a5\u8fd1\u3002<\/span><\/span>
        <\/span><\/p>\n

        \u8fd9\u4e2a\u7b97\u6cd5\u770b\u8d77\u6765\u975e\u5e38\u719f\u6089\uff0c\u5b9e\u9645\u4e0a\u5b83\u4e0e k-Means \u805a\u7c7b\u7b97\u6cd5\u975e\u5e38\u76f8\u4f3c\u3002\u8ba9<\/span><\/span>v<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u548c\u7ec4\u91cc\u7684<\/span><\/span>V<\/span><\/span>[<\/span><\/span>i<\/span><\/span>,<\/span><\/span>:<\/span><\/span>r<\/span><\/span>]<\/span><\/span><\/span>\u8ddd\u79bb\u6700\u5c0f\u7684\u65b9\u6cd5\uff0c\u5c31\u662f\u8ba9<\/span><\/span>v<\/span><\/span>s<\/span><\/span><\/sub><\/span>\u6210\u4e3a<\/span><\/span>V<\/span><\/span>[<\/span><\/span>i<\/span><\/span>,<\/span><\/span>:<\/span><\/span>r<\/span><\/span>]<\/span><\/span><\/span>\u8fd9\u82e5\u5e72\u4e2a\u70b9\u7684\u4e2d\u5fc3\u3002<\/span><\/span><\/p>\n

        \u56de\u987e\u4e00\u4e0bk-Means\u7b97\u6cd5\u628an\u4e2a\u70b9\u805a\u6210r\u7c7b\u7684\u76ee\u6807\u51fd\u6570\uff0c\u5176\u4e2d\u7b2c<\/span><\/span>i<\/span><\/span><\/span>\u4e2a\u70b9\u88ab\u5f52\u5230\u7b2c<\/span><\/span>c<\/span><\/span>i<\/span><\/span><\/sup><\/span>\u7c7b\uff0c\u800c<\/span><\/span>\u03bc<\/span><\/span>j<\/span><\/span><\/sub><\/span>\u4e3a\u7b2c<\/span><\/span>j<\/span><\/span><\/span>\u7c7b\u70b9\u7684\u4e2d\u5fc3\u70b9\uff1a<\/span><\/span><\/p>\n

        <\/section>\n

        \u6211\u4eec\u770b\u5230\u8fd9\u4e24\u4e2a\u76ee\u6807\u51fd\u6570\u975e\u5e38\u76f8\u4f3c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e0a\u8ff0\u7b97\u6cd5\u6216 k-Means \u805a\u7c7b\u6765\u83b7\u53d6\u6700\u4f18\u7684\u72b6\u6001\u5212\u5206\uff0c\u8fdb\u800c\u5224\u65ad\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u7684\u6210\u5757\u6027\u3002<\/span><\/span><\/p>\n

        <\/span>
        <\/span><\/span><\/h2>\n

        \n
        \n
        \n
        \n
        \n

        <\/span><\/section>\n

        <\/span><\/section>\n
        \n
        <\/section>\n<\/section>\n<\/section>\n
        \n

        8. \u6210\u5757\u6027\u7684\u76f8\u5173\u6982\u5ff5<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/span><\/section>\n

        <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/span><\/p>\n

        <\/span>8.1 \u56e0\u679c\u6001<\/span><\/span><\/span><\/h3>\n

        \u56e0\u679c\u6001\u662f\u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u4e00\u4e2a\u6982\u5ff5\uff0c\u4e3b\u8981\u7528\u4e8e\u5bf9\u5386\u53f2\u72b6\u6001\u5e8f\u5217\u7684\u7c97\u7c92\u5316\u5212\u5206\uff0c\u8be6\u60c5\u8bf7\u53c2\u8003<\/span>\u8ba1\u7b97\u529b\u5b66<\/span><\/a>\u3002<\/span><\/span><\/p>\n

        \u5b9a\u4e49<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u53ca\u4ee5\u524d\u7684\u5386\u53f2\u72b6\u6001\u5e8f\u5217\u4e3a<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u672a\u6765\u72b6\u6001<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e3a<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u4ee5\u540e\u7684\u72b6\u6001\u5e8f\u5217\u3002<\/span><\/span><\/p>\n

        \u5bf9\u5386\u53f2\u72b6\u6001\u5e8f\u5217<\/span><\/span><\/span>\"image.png\"<\/span><\/sub>\u8fdb\u884c\u5212\u5206\u540e\u5f97\u5230\u7684\u5b8f\u89c2\u6001\u96c6\u5408<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5176\u4e3a\u56e0\u679c\u6001\u7684\u5145\u8981\u6761\u4ef6\u662f\uff1a<\/span><\/span><\/p>\n

        \u5bf9\u4e8e\u4efb\u610f\u7684\u5b8f\u89c2\u6001<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub><\/span>\uff0c\u6709\uff1a<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/p>\n

        \u628a\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u5206\u7ec4\u548c\u56e0\u679c\u6001\u7406\u8bba\u4e2d\u7684\u7c97\u7c92\u5316\u5212\u5206\u8fdb\u884c\u5bf9\u6bd4\uff0c\u6211\u4eec\u53d1\u73b0\u6210\u5757\u6027\u7684\u8981\u6c42\u548c\u56e0\u679c\u6001\u7684\u8981\u6c42\u975e\u5e38\u76f8\u4f3c\uff1a\u5b83\u4eec\u90fd\u7ed9\u51fa\u4e86\u4e00\u79cd\u5bf9\u672a\u6765\u72b6\u6001\u505a\u9884\u6d4b\u7684\u7b49\u4ef7\u6027\u3002\u4f46\u662f\uff0c\u4e8c\u8005\u53c8\u6709\u533a\u522b\uff0c\u533a\u522b\u6709\u4ee5\u4e0b\u4e09\u70b9\uff1a<\/span><\/span><\/p>\n

        1. \u9a6c\u5c14\u53ef\u592b\u6027\u5047\u8bbe<\/span><\/span><\/b><\/p>\n

        \u56e0\u679c\u6001\u5e76\u6ca1\u6709\u9a6c\u5c14\u79d1\u592b\u6027\u7684\u5047\u8bbe\uff0c\u4f46\u6211\u4eec\u603b\u53ef\u4ee5\u628a\u4e00\u4e2a\u5e8f\u5217\u770b\u6210\u662f\u4e00\u4e2a\u72b6\u6001\uff0c\u4e8e\u662f\u5c31\u80fd\u5f97\u5230\u5e8f\u5217\u6620\u5c04\u5230\u5e8f\u5217\u7684\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u3002\u5728\u8be5\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u6bd4\u8f83\u56e0\u679c\u6001\u5bf9\u5e94\u7684\u5212\u5206\u6620\u5c04\u548c\u6ee1\u8db3\u6210\u5757\u6027\u7684\u5212\u5206\u3002<\/span><\/span><\/p>\n

        2. \u5fae\u89c2\u548c\u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027<\/span><\/span><\/b><\/p>\n

        \u4e0a\u6587\u63d0\u5230\uff0c\u56e0\u679c\u6001\u7684\u72b6\u6001\u5212\u5206\u65b9\u5f0f\u80fd\u4fdd\u6301\u5fae\u89c2\u5c42\u9762\u4e0a\u7684\u6700\u5927\u9884\u6d4b\u6027\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u6839\u636e\u5fae\u89c2\u72b6\u6001\u627e\u5230\u5bf9\u5e94\u7684\u56e0\u679c\u6001\u4e4b\u540e\uff0c\u5373\u4f7f\u6211\u4eec\u4e0d\u77e5\u9053\u539f\u672c\u7684\u5fae\u89c2\u72b6\u6001\u4e86\uff0c\u6211\u4eec\u8fd8\u662f\u80fd\u51c6\u786e\u7684\u5f97\u5230\u672a\u6765\u7684<\/span><\/span>\u5fae\u89c2<\/span><\/span><\/b>\u72b6\u6001\u7684\u5206\u5e03\u3002<\/span><\/span><\/p>\n

        \u800c\u6210\u5757\u6027\u4e0e\u5176\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u6839\u636e\u5fae\u89c2\u72b6\u6001\u627e\u5230\u5bf9\u5e94\u7684\u5b8f\u89c2\u72b6\u6001\u4e4b\u540e\uff0c\u80fd\u591f\u51c6\u786e\u7684\u5f97\u5230\u672a\u6765\u7684<\/span><\/span>\u5b8f\u89c2<\/span><\/span><\/b>\u72b6\u6001\u7684\u5206\u5e03\u3002\u4f46\u662f\u5728\u7c97\u7c92\u5316\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u4e22\u5931\u5fae\u89c2\u72b6\u6001\u7684\u8fa8\u522b\u4fe1\u606f\uff0c\u800c\u8fd9\u4e2a\u4fe1\u606f\u7684\u635f\u5931\u662f\u4e0d\u53ef\u9006\u7684\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u5c31\u65e0\u6cd5\u4ece\u5b8f\u89c2\u72b6\u6001\u518d\u8fd8\u539f\u5230\u5fae\u89c2\u72b6\u6001\u4e86\u3002<\/span><\/span><\/p>\n

        \u6240\u4ee5\uff0c\u56e0\u679c\u6001\u540c\u65f6\u4fdd\u6301\u4e86\u5fae\u89c2\u548c\u5b8f\u89c2\u7684\u6700\u5927\u9884\u6d4b\u6027\uff0c\u800c\u6210\u5757\u6027\u53ea\u80fd\u4fdd\u6301\u5b8f\u89c2\u7684\u6700\u5927\u9884\u6d4b\u6027\u3002<\/span><\/span><\/p>\n

        3. \u56e0\u679c\u6001\u6bd4\u6210\u5757\u6027\u66f4\u4e25\u683c\uff0c\u5212\u5206\u7684\u6210\u5757\u6027\u662f\u6ee1\u8db3\u56e0\u679c\u6001\u8981\u6c42\u7684\u5fc5\u8981\u6761\u4ef6<\/span><\/span><\/b><\/p>\n

        \u6309\u7167\u4e0a\u9762\u7684\u53d9\u8ff0\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u56e0\u679c\u6001\u662f\u6bd4\u6210\u5757\u6027\u66f4\u4e25\u683c\u7684\u9650\u5236\uff0c\u56e0\u4e3a\u5b83\u8981\u6c42\u5728\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u4e2d\uff0c\u5c5e\u4e8e\u540c\u4e00\u4e2a\u56e0\u679c\u6001\u4e2d\u7684\u72b6\u6001\u7684\u884c\u5fc5\u987b\u5b8c\u5168\u4e00\u81f4\u3002<\/span><\/span><\/p>\n

        \u56e0\u679c\u6001\u7684\u5212\u5206\u4e00\u5b9a\u662f\u4e00\u79cd\u6210\u5757\u7684\u72b6\u6001\u5212\u5206\uff0c\u4f46\u53cd\u4e4b\u5219\u4e0d\u4e00\u5b9a\u3002\u6240\u4ee5\u8bf4\uff0c\u5212\u5206\u7684\u6210\u5757\u6027\u662f\u6ee1\u8db3\u56e0\u679c\u6001\u8981\u6c42\u7684\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\u3002<\/span><\/span>
        <\/span><\/p>\n

        \u4e8c\u8005\u4e4b\u95f4\u7684\u533a\u522b\u4e5f\u53ef\u4ee5\u7528\u4e0b\u56fe\u8fdb\u884c\u76f4\u89c2\u8868\u793a\uff1a<\/span><\/span><\/p>\n

        \"\u56e0\u679c\u6001\u4e0e\u6210\u5757\u6027\u7684\u5bf9\u6bd4\"<\/section>\n

        \u8be5\u56fe\u5c55\u793a\u4e86\u6211\u4eec\u662f\u600e\u4e48\u5904\u7406\u548c\u7406\u89e3\u56e0\u679c\u6001\u548c\u6210\u5757\u6027\u7684\u3002\u9996\u5148\uff0c\u6211\u4eec\u628a\u6bcf\u6761\u5e8f\u5217\u770b\u4f5c\u662f\u4e00\u4e2a\u72b6\u6001\uff0c\u628a\u5e8f\u5217\u538b\u7f29\u5230\u4e86\u4e00\u4e2a<\/span><\/span>t<\/span><\/span><\/span>\u65f6\u523b\u7684\u72b6\u6001\u7a7a\u95f4\uff0c\u5e76\u7528\u4e00\u4e2a\u8f6c\u79fb\u77e9\u9635\u6765\u63cf\u8ff0\u72b6\u6001\uff08\u5e8f\u5217\uff09\u4e4b\u95f4\u7684\u8f6c\u79fb\u6982\u7387\u3002<\/span><\/span><\/p>\n

        \u5728\u56e0\u679c\u6001\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5bf9\u6bd4\u8f6c\u79fb\u77e9\u9635\u7684\u884c\uff0c\u628a\u76f8\u540c\u7684\u884c\u5212\u5206\u6210\u4e00\u7ec4\uff1b\u800c\u5728\u6210\u5757\u6027\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u540c\u65f6\u8003\u8651\u77e9\u9635\u7684\u884c\u4e0e\u5217\uff0c\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e00\u884c\u5230\u67d0\u51e0\u5217\u7684\u8f6c\u79fb\u6982\u7387\u6765\u505a\u5206\u7ec4\u3002<\/span><\/span><\/p>\n


        <\/span><\/p>\n

        \u53c2\u8003\u6587\u732e<\/span><\/span><\/section>\n
        1. Kemeny, John G., and J. Laurie Snell. <\/span><\/span>Finite markov chains<\/span><\/span><\/i>. Vol. 26. Princeton, NJ: van Nostrand, 1969. https:\/\/www.math.pku.edu.cn\/teachers\/yaoy\/Fall2011\/Kemeny-Snell_Chapter6.3-4.pdf<\/span><\/span><\/span><\/span><\/section>\n
        2. <\/span><\/span><\/span><\/span>Coarse graining. <\/span><\/span>Encyclopedia of Mathematics.<\/span><\/span><\/i> URL: http:\/\/encyclopediaofmath.org\/index.php?title=Coarse_graining&oldid=16170<\/span><\/span><\/span><\/section>\n
        3. <\/span><\/span><\/span>Buchholz, Peter. “Exact and ordinary lumpability in finite Markov chains.” <\/span><\/span>Journal of applied probability<\/span><\/span><\/i> 31.1 (1994): 59-75.<\/span><\/span><\/span><\/section>\n
        4. Franceschinis, Giuliana, and Richard R. Muntz. “Bounds for quasi-lumpable Markov chains.” Performance Evaluation 20.1-3 (1994): 223-243.<\/span><\/span><\/span><\/section>\n
        5. Piazza, Carla, and Sabina Rossi. “Reasoning about proportional lumpability.” International Conference on Quantitative Evaluation of Systems. Cham: Springer International Publishing, 2021.<\/span><\/span><\/span>
        <\/span><\/section>\n
        6. Zhang, Anru, and Mengdi Wang. “Spectral state compression of markov processes.” <\/span><\/span>IEEE transactions on information theory<\/span><\/span><\/i> 66.5 (2019): 3202-3231.<\/span><\/span><\/span><\/section>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/span><\/section>\n<\/section>\n<\/blockquote>\n

        <\/span><\/section>\n
        <\/section>\n

        <\/span><\/section>\n
        \n
        \n
        \n
        \n

        \u52a0\u5165\u6211\u4eec<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


        <\/span><\/section>\n
        \u4eb2\u7231\u7684\u793e\u533a\u6210\u5458\u548c\u77e5\u8bc6\u7231\u597d\u8005\uff1a<\/span><\/span><\/section>\n

        <\/span><\/section>\n
        \u6211\u4eec\u6b63\u5728\u5bfb\u627e\u5bf9\u77e5\u8bc6\u5206\u4eab\u5145\u6ee1\u70ed\u60c5\u7684\u5fd7\u613f\u8005\uff0c\u52a0\u5165\u6211\u4eec\u7684\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u7f16\u5199\u56e2\u961f\uff01\u65e0\u8bba\u4f60\u662f\u67d0\u4e2a\u9886\u57df\u7684\u4e13\u5bb6\uff0c\u8fd8\u662f\u5bf9\u67d0\u4e00\u4e3b\u9898\u6709\u6d53\u539a\u5174\u8da3\uff0c\u6211\u4eec\u90fd\u6b22\u8fce\u4f60\u7684\u52a0\u5165\u3002\u901a\u8fc7\u7f16\u5199\u548c\u7f16\u8f91\u767e\u79d1\u8bcd\u6761\uff0c\u4f60\u5c06\u6709\u673a\u4f1a\u4e3a\u5168\u7403\u8bfb\u8005\u63d0\u4f9b\u51c6\u786e\u3001\u6743\u5a01\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u63d0\u5347\u81ea\u5df1\u7684\u5199\u4f5c\u548c\u7814\u7a76\u80fd\u529b\u3002<\/span><\/span><\/section>\n

        <\/span><\/section>\n

        \u6211\u4eec\u9700\u8981\u7684\u5e2e\u52a9<\/span><\/span><\/strong><\/span><\/p>\n

        \u7f16\u5199\u65b0\u7684\u96c6\u667a\u767e\u79d1\u8bcd\u6761\uff0c\u6db5\u76d6\u590d\u6742\u7cfb\u7edf\u3001\u4eba\u5de5\u667a\u80fd\u7b49\u591a\u4e2a\u9886\u57df<\/span><\/span><\/p>\n

        \u66f4\u65b0\u548c\u5b8c\u5584\u73b0\u6709\u8bcd\u6761\uff0c\u786e\u4fdd\u4fe1\u606f\u7684\u51c6\u786e\u6027\u548c\u65f6\u6548\u6027<\/span><\/span><\/p>\n

        \u6821\u5bf9\u548c\u5ba1\u6838\u5176\u4ed6\u5fd7\u613f\u8005\u63d0\u4ea4\u7684\u5185\u5bb9\uff0c\u786e\u4fdd\u8bcd\u6761\u8d28\u91cf<\/span><\/span><\/section>\n

        <\/span><\/span><\/strong><\/span><\/section>\n

        \u6211\u4eec\u5e0c\u671b\u4f60\u5177\u5907<\/span><\/span><\/strong><\/span><\/p>\n

        \u826f\u597d\u7684\u5199\u4f5c\u80fd\u529b\uff0c\u80fd\u591f\u6e05\u6670\u3001\u7b80\u6d01\u5730\u8868\u8fbe\u590d\u6742\u7684\u6982\u5ff5<\/span><\/span><\/p>\n

        \u5bf9\u67d0\u4e00\u9886\u57df\u6709\u6df1\u5165\u4e86\u89e3\u6216\u6d53\u539a\u5174\u8da3<\/span><\/span><\/p>\n

        \u5177\u5907\u57fa\u672c\u7684\u7f51\u7edc\u641c\u7d22\u548c\u4fe1\u606f\u6574\u7406\u80fd\u529b<\/span><\/span><\/p>\n

        \u6709\u8d23\u4efb\u5fc3\u548c\u56e2\u961f\u5408\u4f5c\u7cbe\u795e\uff0c\u613f\u610f\u4e3a\u77e5\u8bc6\u5171\u4eab\u8d21\u732e\u529b\u91cf<\/span><\/span><\/p>\n

        \u5982\u679c\u4f60\u5bf9\u77e5\u8bc6\u5206\u4eab\u5145\u6ee1\u70ed\u60c5\uff0c\u613f\u610f\u4e3a\u5168\u7403\u8bfb\u8005\u63d0\u4f9b\u6709\u4ef7\u503c\u7684\u4fe1\u606f\uff0c\u8bf7\u7acb\u5373\u52a0\u5165\u6211\u4eec\uff01<\/span><\/span><\/section>\n

        <\/span><\/section>\n
        <\/section>\n
        \u626b\u7801\u586b\u8868\uff0c\u6dfb\u52a0\u8d1f\u8d23\u4eba\u5fae\u4fe1<\/span><\/span><\/section>\n

        <\/span><\/span><\/section>\n
        \u8ba9\u6211\u4eec\u4e00\u8d77\uff0c\u7528\u77e5\u8bc6\u8fde\u63a5\u4e16\u754c\uff01<\/span><\/span><\/section>\n

        <\/span><\/section>\n

        <\/span><\/section>\n
        \n
        \n
        \n
        \n

        \u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u516d\u5b63<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


        <\/span><\/section>\n

        \u5728\u9713\u8679\u706f\u7684\u95ea\u70c1\u3001\u8681\u7fa4\u7684\u7cbe\u5bc6\u534f\u4f5c\u3001\u4eba\u7c7b\u610f\u8bc6\u7684\u8bde\u751f\u4e2d\uff0c\u9690\u85cf\u7740\u5fae\u89c2\u4e0e\u5b8f\u89c2\u4e4b\u95f4\u6df1\u523b\u7684\u56e0\u679c\u5173\u8054\u2014\u2014\u8fd9\u4e9b\u770b\u4f3c\u7b80\u5355\u7684\u4e2a\u4f53\u884c\u4e3a\uff0c\u5982\u4f55\u8de8\u8d8a\u5c3a\u5ea6\uff0c\u6d8c\u73b0\u51fa\u4ee4\u4eba\u60ca\u53f9\u7684\u590d\u6742\u73b0\u8c61\uff1f\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u4e3a\u6211\u4eec\u63ed\u793a\u4e86\u7b54\u6848\uff1a\u590d\u6742\u7cfb\u7edf\u7684\u5b8f\u89c2\u7279\u5f81\u65e0\u6cd5\u901a\u8fc7\u5fae\u89c2\u5143\u7d20\u7684\u7b80\u5355\u53e0\u52a0\u89e3\u91ca\uff0c\u800c\u662f\u6e90\u4e8e\u591a\u5c3a\u5ea6\u52a8\u6001\u4ea4\u4e92\u4e2d\u6d8c\u73b0\u7684\u56e0\u679c\u7ed3\u6784\u3002\u4ece\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u9a71\u52a8\u7684\u52a8\u6001\u53ef\u9006\u6027\u5206\u6790\uff0c\u5230\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3\u7684\u91cf\u5316\u5de5\u5177\uff0c\u7814\u7a76\u8005\u4eec\u6b63\u9010\u6b65\u6784\u5efa\u8d77\u4e00\u5957\u8de8\u8d8a\u6570\u5b66\u3001\u7269\u7406\u4e0e\u4fe1\u606f\u79d1\u5b66\u7684\u7406\u8bba\u6846\u67b6\uff0c\u8bd5\u56fe\u89e3\u7801\u590d\u6742\u7cfb\u7edf\u7684\u201c\u6d8c\u73b0\u5bc6\u7801\u201d\u3002<\/span><\/span><\/p>\n


        <\/span><\/p>\n

        \u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u7ec4\u7ec7\u5bf9\u672c\u8bdd\u9898\u611f\u5174\u8da3\u7684\u670b\u53cb\uff0c\u6df1\u5165\u7814\u8bfb\u76f8\u5173\u6587\u732e\uff0c\u6fc0\u53d1\u79d1\u7814\u7075\u611f\u3002<\/span><\/span><\/p>\n


        <\/span><\/p>\n

        \u8bfb\u4e66\u4f1a\u5c06\u4ece2025\u5e743\u670816\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u65e99:00-11:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba110\u5468\u5de6\u53f3\u3002\u6bcf\u5468\u8fdb\u884c\u7ebf\u4e0a\u4f1a\u8bae\uff0c\u4e0e\u4e3b\u8bb2\u4eba\u7b49\u793e\u533a\u6210\u5458\u5f53\u9762\u4ea4\u6d41\uff0c\u4e4b\u540e\u53ef\u4ee5\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6301\u7eed\u5b66\u4e60\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/span><\/p>\n


        <\/span><\/span><\/p>\n

        \"\u56fe\u7247\"<\/span><\/a><\/section>\n
        \n


        <\/span><\/span><\/p>\n

        \u8be6\u60c5\u8bf7\u89c1\uff1a\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u2014\u2014\u52a8\u529b\u5b66\u3001\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3<\/a><\/span><\/span><\/p>\n


        <\/span><\/p>\n<\/section>\n


        <\/span><\/p>\n

        \u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/p>\n

        1.<\/span><\/strong>\u8ba1\u7b97\u529b\u5b66\uff08\u56e0\u679c\u6001\u7406\u8bba\uff09| \u96c6\u667a\u767e\u79d1<\/a><\/span><\/strong><\/span><\/section>\n
        2.<\/span><\/strong>\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff5c\u96c6\u667a\u767e\u79d1<\/a><\/span><\/strong><\/span><\/section>\n
        3.<\/span><\/strong>\u673a\u5668\u5b66\u4e60\u6846\u67b6NIS+\uff1a\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u8bc6\u522b\u201c\u56e0\u679c\u6d8c\u73b0\u201d | NSR<\/a><\/span><\/strong><\/span><\/section>\n
        4. <\/span><\/strong><\/span>\u6e38\u620f\u5316\u79d1\u7814\u2014\u2014\u8ba9\u6211\u4eec\u7a81\u7834\u5185\u5377\u3001\u5171\u7814\u6d8c\u73b0<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
        <\/strong>5. <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/section>\n

        6. \u52a0\u5165\u96c6\u667a\uff0c\u73a9\u8f6c\u590d\u6742\uff0c\u5171\u521b\u6591\u56fe\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u7ebf\u4e0b\u5fd7\u613f\u8005\u62db\u52df<\/span><\/a><\/span><\/strong><\/p>\n

        7. <\/span>\u7cfb\u7edf\u79d1\u5b66\u524d\u6cbf\u5341\u8bb2\uff1a\u7406\u89e3\u81ea\u7136\u3001\u751f\u547d\u4e0e\u793e\u4f1a\u7684\u590d\u6742\u6027<\/span><\/a><\/span><\/strong><\/p>\n


        <\/span><\/strong><\/span><\/section>\n


        <\/span><\/p>\n

        \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c<\/span>\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

        \u5bfc\u8bed \u6210\u5757\u6027\uff08Lumpability\uff09\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7c97\u7c92\u5316\u7406\u8bba\u4e2d\u4e00\u79cd\u63cf\u8ff0\u662f\u5426\u53ef\u805a\u7c7b\u6216\u53ef\u7c97\u7c92\u5316\u7684\u6982\u5ff5\uff0c\u6700\u65e9\u7531Kemeny\u548cSnell\u5728\u51761969\u5e74\u7684\u8457\u4f5cFinite Markov Chains[1]\u4e2d\u63d0\u51fa\u3002Lump\u4e00\u8bcd\u6709\u2018\u5757\u2019\u7684\u610f\u601d\u3002\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u662f\u5426\u53ef\u6210\u5757\uff08lumpable\uff09\uff0c\u5c31\u662f\u8981\u5224\u5b9a\u662f\u5426\u5b58\u5728…<\/p>\n","protected":false},"author":0,"featured_media":61195,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/61296"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=61296"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/61296\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/61195"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=61296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=61296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=61296"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=61296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}