{"id":1595,"date":"2026-10-30T13:00:00","date_gmt":"2026-10-30T04:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1595"},"modified":"2026-10-27T13:26:37","modified_gmt":"2026-10-27T04:26:37","slug":"qs-mg1-service-variance-20261024","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1595","title":{"rendered":"M\/G\/1\u5f85\u3061\u884c\u5217\u3067\u898b\u308b\u3001\u5e73\u5747\u51e6\u7406\u6642\u9593\u304c\u540c\u3058\u3067\u3082\u5f85\u3061\u6642\u9593\u304c\u5909\u308f\u308b\u7406\u7531"},"content":{"rendered":"<p>\u51e6\u7406\u306e\u5e73\u5747\u304c10\u30df\u30ea\u79d2\u306a\u3089\u3001\u5e73\u5747\u3057\u30661\u79d2\u306b100\u4ef6\u3092\u6271\u3048\u308b\u3002\u3068\u3053\u308d\u304c\u3001\u305d\u3053\u3078\u540c\u3058\u983b\u5ea6\u3067\u4ed5\u4e8b\u3092\u9001\u3063\u3066\u3082\u3001\u6bce\u56de\u307b\u307c\u540c\u3058\u6642\u9593\u3067\u7d42\u308f\u308b\u5834\u5408\u3068\u3001\u3068\u304d\u3069\u304d\u9577\u3044\u51e6\u7406\u304c\u6df7\u3056\u308b\u5834\u5408\u3067\u306f\u3001\u9806\u756a\u3092\u5f85\u3064\u6642\u9593\u304c\u5909\u308f\u308a\u307e\u3059\u3002\u5e73\u5747\u306e\u901f\u3055\u3060\u3051\u3067\u306f\u3001\u5f85\u3061\u884c\u5217\u306e\u69d8\u5b50\u3092\u6c7a\u3081\u304d\u308c\u306a\u3044\u305f\u3081\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u9055\u3044\u3092\u6271\u3048\u308b\u306e\u304c<strong>M\/G\/1\u5f85\u3061\u884c\u5217<\/strong>\u3067\u3059\u3002\u3053\u3053\u3067\u306f\u5230\u7740\u983b\u5ea6\u3068\u5e73\u5747\u51e6\u7406\u6642\u9593\u3092\u56fa\u5b9a\u3057\u3001\u51e6\u7406\u6642\u9593\u306e\u3070\u3089\u3064\u304d\u3060\u3051\u3092\u5909\u3048\u307e\u3059\u3002\u5b9f\u6a5f\u306e\u6027\u80fd\u3092\u4e88\u6e2c\u3059\u308b\u524d\u306b\u3001\u4f55\u3092\u6e2c\u3063\u3066\u6bd4\u8f03\u3059\u3079\u304d\u304b\u3092\u6574\u7406\u3059\u308b\u305f\u3081\u306e\u6570\u7406\u30e2\u30c7\u30eb\u3067\u3059\u3002<\/p>\n<section 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]\u306f\u5e73\u5747\u3092\u53d6\u308b\u8a18\u53f7\u3067\u3059\u3002<\/p>\n<p><strong>W<sub>q<\/sub>\uff1d\u03bb E[S\u00b2] \u00f7 {2(1\u2212\u03c1)}<\/strong><\/p>\n<p>E[S\u00b2]\u306f\u3001\u4e00\u4ef6\u305a\u3064\u306e\u51e6\u7406\u6642\u9593\u3092\u4e8c\u4e57\u3057\u3066\u304b\u3089\u5e73\u5747\u3057\u305f\u5024\u3067\u3059\u3002\u5e73\u5747\u51e6\u7406\u6642\u9593\u3092\u4e8c\u4e57\u3057\u305fm\u00b2\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u95a2\u4fc2\u306f<strong>E[S\u00b2]\uff1dVar(S)\uff0bm\u00b2<\/strong>\u3067\u3001Var(S)\u306f\u5e73\u5747\u304b\u3089\u306e\u6563\u3089\u3070\u308a\u3092\u8868\u3059\u5206\u6563\u3067\u3059\u3002<\/p>\n<p>\u03bb\u3068m\u3092\u56fa\u5b9a\u3059\u308b\u3068\u3001\u5229\u7528\u7387\u03c1\u3068\u5206\u6bcd\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u6761\u4ef6\u3067\u5206\u6563\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u3001\u5e73\u5747\u5f85\u3061\u306f\u5897\u3048\u307e\u3059\u3002\u51e6\u7406\u305d\u306e\u3082\u306e\u3082\u542b\u3080\u5230\u7740\u304b\u3089\u5b8c\u4e86\u307e\u3067\u306e\u5e73\u5747\u6642\u9593\u306fW<sub>q<\/sub>\uff0bm\u3067\u3042\u308a\u3001\u4e8c\u3064\u3092\u6df7\u305c\u306a\u3044\u3053\u3068\u304c\u5927\u5207\u3067\u3059\u3002<\/p>\n<h2>\u5e73\u574710\u30df\u30ea\u79d2\u3001\u5229\u7528\u738780%\u3067\u4e09\u3064\u3092\u6bd4\u3079\u308b<\/h2>\n<p>\u5230\u7740\u7387\u309280\u4ef6\/\u79d2\u3001\u5e73\u5747\u51e6\u7406\u6642\u9593\u309210\u30df\u30ea\u79d2\u306b\u305d\u308d\u3048\u307e\u3059\u3002\u5229\u7528\u7387\u306f\u3059\u3079\u306680%\u3067\u3059\u3002\u4e00\u3064\u76ee\u306f\u6bce\u56de10\u30df\u30ea\u79d2\u3067\u7d42\u308f\u308b\u4e00\u5b9a\u6642\u9593\u306e\u51e6\u7406\u3002\u4e8c\u3064\u76ee\u306f\u5e73\u574710\u30df\u30ea\u79d2\u306e\u6307\u6570\u5206\u5e03\u3002\u4e09\u3064\u76ee\u306f\u5404\u4ed5\u4e8b\u304c\u72ec\u7acb\u306b90%\u306e\u78ba\u7387\u30675\u30df\u30ea\u79d2\u300110%\u306e\u78ba\u7387\u306755\u30df\u30ea\u79d2\u306b\u306a\u308b\u51e6\u7406\u3067\u3059\u3002<\/p>\n<p>\u4e09\u3064\u76ee\u306e\u5e73\u5747\u306f0.9\u00d75\uff0b0.1\u00d755\uff1d10\u30df\u30ea\u79d2\u3067\u3059\u304c\u3001\u4e8c\u4e57\u306e\u5e73\u5747\u306f0.9\u00d75\u00b2\uff0b0.1\u00d755\u00b2\uff1d325\u30df\u30ea\u79d2\u00b2\u3067\u3059\u3002\u300c10\u4ef6\u306b\u5fc5\u305a1\u4ef6\u9577\u3044\u300d\u3068\u3044\u3046\u898f\u5247\u7684\u306a\u4e26\u3073\u3067\u306f\u306a\u304f\u3001\u305d\u308c\u305e\u308c\u306e\u51e6\u7406\u6642\u9593\u304c\u72ec\u7acb\u306b\u6c7a\u307e\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<div style=\"overflow-x:auto\">\n<table style=\"min-width:600px\">\n<thead>\n<tr>\n<th>\u51e6\u7406\u6642\u9593\u306e\u5206\u5e03<\/th>\n<th>E[S\u00b2]<\/th>\n<th>\u5e73\u5747\u5f85\u3061 W<sub>q<\/sub><\/th>\n<th>\u51e6\u7406\u3092\u542b\u3080\u5e73\u5747<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6bce\u56de10 ms<\/td>\n<td>100 ms\u00b2<\/td>\n<td>20 ms<\/td>\n<td>30 ms<\/td>\n<\/tr>\n<tr>\n<td>\u5e73\u574710 ms\u306e\u6307\u6570\u5206\u5e03<\/td>\n<td>200 ms\u00b2<\/td>\n<td>40 ms<\/td>\n<td>50 ms<\/td>\n<\/tr>\n<tr>\n<td>90%\u304c5 ms\u300110%\u304c55 ms<\/td>\n<td>325 ms\u00b2<\/td>\n<td>65 ms<\/td>\n<td>75 ms<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<figure><img decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-mg1-service-variance-20261024-figure-791599d309ba.png\" alt=\"\u5230\u7740\u738780\u4ef6\u6bce\u79d2\u3001\u5e73\u5747\u51e6\u7406\u6642\u959310\u30df\u30ea\u79d2\u3001\u5229\u7528\u738780\u30d1\u30fc\u30bb\u30f3\u30c8\u3092\u56fa\u5b9a\u3057\u305fM\/G\/1\u30e2\u30c7\u30eb\u3002\u51e6\u7406\u6642\u9593\u304c\u4e00\u5b9a\u306a\u3089\u5e73\u5747\u5f85\u306120\u30df\u30ea\u79d2\u3001\u6307\u6570\u5206\u5e03\u306a\u308940\u30df\u30ea\u79d2\u300190\u30d1\u30fc\u30bb\u30f3\u30c8\u304c5\u30df\u30ea\u79d2\u306710\u30d1\u30fc\u30bb\u30f3\u30c8\u304c55\u30df\u30ea\u79d2\u306a\u308965\u30df\u30ea\u79d2\u3002\" style=\"max-width:100%;height:auto\"><figcaption>QS\u72ec\u81ea\u8a08\u7b97\u3002\u5230\u7740\u7387\u3068\u5e73\u5747\u51e6\u7406\u6642\u9593\u3092\u56fa\u5b9a\u3057\u3001\u51e6\u7406\u6642\u9593\u306e\u5206\u5e03\u3060\u3051\u3092\u5909\u66f4\u3002\u68d2\u306f\u51e6\u7406\u3092\u59cb\u3081\u308b\u307e\u3067\u306e\u5e73\u5747\u5f85\u3061\u3067\u3001\u51e6\u7406\u305d\u306e\u3082\u306e\u306e10\u30df\u30ea\u79d2\u306f\u542b\u307f\u307e\u305b\u3093\u3002<\/figcaption><\/figure>\n<p>\u6df7\u5408\u3057\u305f\u4f8b\u306e\u5f85\u3061\u306f\u4e00\u5b9a\u6642\u9593\u306e\u4f8b\u306e3.25\u500d\u3067\u3059\u3002\u51e6\u7406\u62c5\u5f53\u3092\u9045\u304f\u3057\u305f\u308f\u3051\u3067\u3082\u3001\u4ed5\u4e8b\u306e\u5230\u7740\u3092\u5897\u3084\u3057\u305f\u308f\u3051\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u6bce\u56de10\u30df\u30ea\u79d2\u306b\u305d\u308d\u3048\u3066\u3082\u5e73\u5747\u5f85\u3061\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u305b\u3093\u3002\u5230\u7740\u304c\u30e9\u30f3\u30c0\u30e0\u306a\u306e\u3067\u3001\u77ed\u3044\u9593\u9694\u3067\u4ed5\u4e8b\u304c\u7d9a\u3051\u3066\u5c4a\u304f\u3053\u3068\u304c\u3042\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<h2>\u5c11\u306a\u3044\u9577\u6642\u9593\u51e6\u7406\u304c\u3001\u306a\u305c\u5f8c\u308d\u306e\u4ed5\u4e8b\u306b\u52b9\u304f\u306e\u304b<\/h2>\n<p>\u51e6\u7406\u4e2d\u306e\u30b5\u30fc\u30d0\u30fc\u3092\u30e9\u30f3\u30c0\u30e0\u306a\u6642\u523b\u306b\u89b3\u5bdf\u3059\u308b\u3068\u3001\u9577\u3044\u51e6\u7406\u306e\u9014\u4e2d\u306b\u5f53\u305f\u308a\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u4eca\u56de\u306e\u6df7\u5408\u4f8b\u3067\u306f55\u30df\u30ea\u79d2\u306e\u4ed5\u4e8b\u306f\u4ef6\u6570\u306e10%\u3067\u3059\u304c\u3001\u51e6\u7406\u306b\u4f7f\u3046\u6642\u9593\u306e\u5272\u5408\u306f0.1\u00d755\u00f710\uff1d55%\u3067\u3059\u3002\u4ef6\u6570\u3067\u5c11\u6570\u3067\u3082\u3001\u30b5\u30fc\u30d0\u30fc\u306e\u5fd9\u3057\u3044\u6642\u9593\u306e\u534a\u5206\u4ee5\u4e0a\u3092\u5360\u3081\u307e\u3059\u3002<\/p>\n<p>\u51e6\u7406\u4e2d\u3067\u3042\u308b\u3053\u3068\u3092\u6761\u4ef6\u306b\u3001\u305d\u306e\u4ed5\u4e8b\u304c\u7d42\u308f\u308b\u307e\u3067\u306e\u6b8b\u308a\u6642\u9593\u3092\u5e73\u5747\u3059\u308b\u3068\u3001E[S\u00b2]\u00f7(2m)\u306b\u306a\u308a\u307e\u3059\u3002\u6df7\u5408\u4f8b\u3067\u306f16.25\u30df\u30ea\u79d2\u3001\u4e00\u5b9a10\u30df\u30ea\u79d2\u306a\u30895\u30df\u30ea\u79d2\u3067\u3059\u3002\u5358\u7d14\u306b\u300c\u5e73\u5747\u51e6\u7406\u6642\u9593\u306e\u534a\u5206\u300d\u3068\u3059\u308b\u3068\u3001\u9577\u3044\u4ed5\u4e8b\u306b\u51fa\u4f1a\u3044\u3084\u3059\u3044\u52b9\u679c\u3092\u843d\u3068\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n<p>\u65b0\u3057\u3044\u4ed5\u4e8b\u306e\u5f85\u3061\u306b\u306f\u3001\u3053\u306e\u6b8b\u308a\u6642\u9593\u306b\u52a0\u3048\u3001\u3059\u3067\u306b\u524d\u3067\u9806\u756a\u3092\u5f85\u3064\u4ed5\u4e8b\u306e\u51e6\u7406\u3082\u52a0\u308f\u308a\u307e\u3059\u3002\u5230\u7740\u304c\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u3067\u3001\u73fe\u5728\u306e\u72b6\u614b\u3092\u5148\u8aad\u307f\u3057\u306a\u3044\u3068\u3044\u3046\u6761\u4ef6\u306e\u4e0b\u3067\u306f\u3001\u5230\u7740\u6642\u306e\u89b3\u5bdf\u3068\u6642\u9593\u5e73\u5747\u3092\u7d50\u3073\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u4ed5\u7d44\u307f\u304c\u3001\u516c\u5f0f\u306b\u4e8c\u4e57\u306e\u5e73\u5747\u3068\u6df7\u96d1\u306e\u4fc2\u65701\/(1\u2212\u03c1)\u304c\u73fe\u308c\u308b\u80cc\u666f\u3067\u3059\u3002<\/p>\n<h2>\u6027\u80fd\u3092\u6bd4\u8f03\u3059\u308b\u3068\u304d\u306f\u3001\u3069\u306e\u6642\u9593\u3092\u6e2c\u308b\u304b\u3092\u305d\u308d\u3048\u308b<\/h2>\n<p>\u4f8b\u3048\u3070\u540c\u3058\u5e73\u574710\u30df\u30ea\u79d2\u306e\u51e6\u7406\u7cfb\u3092\u4e8c\u3064\u6bd4\u3079\u308b\u306a\u3089\u3001\u53d7\u4ed8\u304b\u3089\u5b8c\u4e86\u307e\u3067\u306e\u6642\u9593\u3060\u3051\u3067\u306a\u304f\u3001\u5b9f\u969b\u306b\u51e6\u7406\u62c5\u5f53\u3092\u5360\u6709\u3057\u305f\u6642\u9593\u3092\u5206\u3051\u3066\u96c6\u8a08\u3057\u307e\u3059\u3002\u305d\u306e\u5e73\u5747\u3001\u4e8c\u4e57\u306e\u5e73\u5747\u3001\u9577\u3044\u51e6\u7406\u306e\u983b\u5ea6\u3092\u898b\u308c\u3070\u3001\u300c\u5e73\u5747\u306f\u540c\u3058\u3060\u304c\u9577\u6642\u9593\u306e\u51e6\u7406\u304c\u6df7\u3056\u308b\u300d\u3068\u3044\u3046\u9055\u3044\u3092\u6349\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u3057\u3001\u53d7\u4ed8\u304b\u3089\u5b8c\u4e86\u307e\u3067\u306e\u5fdc\u7b54\u6642\u9593\u3092\u305d\u306e\u307e\u307eS\u3068\u3057\u3066\u5f0f\u3078\u5165\u308c\u308b\u3068\u3001\u3059\u3067\u306b\u767a\u751f\u3057\u3066\u3044\u308b\u5f85\u3061\u3092\u51e6\u7406\u6642\u9593\u3068\u3057\u3066\u6570\u3048\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u5272\u308a\u8fbc\u307f\u3001\u4e26\u5217\u51e6\u7406\u3001\u512a\u5148\u9806\u4f4d\u3001\u8907\u6570\u6bb5\u306e\u5f85\u3061\u304c\u3042\u308b\u74b0\u5883\u3067\u306f\u3001\u3069\u3053\u30921\u53f0\u306e\u51e6\u7406\u62c5\u5f53\u3068\u307f\u306a\u3059\u306e\u304b\u3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href=\"https:\/\/ocw.mit.edu\/courses\/6-263j-data-communication-networks-fall-2002\/65d9ab519ec4851af812f4b89ffaeedc_Lectures8_9.pdf\">Eytan Modiano\uff0fMIT 6.263J\uff082002\u5e74\u79cb\uff09Lectures 8 &amp; 9: M\/G\/1 Queues<\/a>\uff1a\u524d\u63d0\u3001P-K\u516c\u5f0f\u3001M\/M\/1\u30fbM\/D\/1\u306e\u6bd4\u8f03\u3001\u6b8b\u4f59\u51e6\u7406\u6642\u9593\u304b\u3089\u306e\u5c0e\u51fa\u3002<\/li>\n<li><a href=\"https:\/\/web.stanford.edu\/class\/ee384x\/EE384X\/handouts\/H10.pdf\">Stanford EE384X Handout 10: Packet Switch Architectures I<\/a>\uff1a19\u301c21\u30da\u30fc\u30b8\u306eM\/GI\/1\u3001\u4ed5\u4e8b\u91cf\u306e\u56f3\u3001\u51e6\u7406\u6642\u9593\u4e00\u5b9a\u306e\u5834\u5408\u306e\u5e30\u7d50\u3002\u7248\u306e\u65e5\u4ed8\u306f\u672a\u78ba\u8a8d\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u51e6\u7406\u306e\u5e73\u5747\u304c10\u30df\u30ea\u79d2\u306a\u3089\u3001\u5e73\u5747\u3057\u30661\u79d2\u306b100\u4ef6\u3092\u6271\u3048\u308b\u3002\u3068\u3053\u308d\u304c\u3001\u305d\u3053\u3078\u540c\u3058\u983b\u5ea6\u3067\u4ed5\u4e8b\u3092\u9001\u3063\u3066\u3082\u3001\u6bce\u56de\u307b\u307c\u540c\u3058\u6642\u9593\u3067\u7d42\u308f\u308b\u5834\u5408\u3068\u3001\u3068\u304d\u3069\u304d\u9577\u3044\u51e6\u7406\u304c\u6df7\u3056\u308b\u5834\u5408\u3067\u306f\u3001\u9806\u756a\u3092\u5f85\u3064\u6642\u9593\u304c\u5909\u308f\u308a\u307e\u3059\u3002\u5e73\u5747\u306e\u901f\u3055\u3060\u3051\u3067\u306f\u3001\u5f85\u3061 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1584,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[30],"tags":[321],"class_list":["post-1595","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computing","tag-mg1-queue"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-mg1-service-variance-20261024-featured-f1c4448fc24e.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1595"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1595\/revisions"}],"predecessor-version":[{"id":1596,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1595\/revisions\/1596"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1584"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}