{"id":6694,"date":"2018-09-21T10:40:38","date_gmt":"2018-09-21T09:40:38","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6694"},"modified":"2022-12-03T23:02:02","modified_gmt":"2022-12-03T22:02:02","slug":"la-file-m-m-1","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/el-archivo-mm-1\/","title":{"rendered":"La cola M \/ M \/ 1"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6694\" class=\"elementor elementor-6694\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d96fc12 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d96fc12\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-74aee66\" data-id=\"74aee66\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8d24995 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8d24995\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Proceso de Markov<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b630415\" data-id=\"b630415\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f1efdfa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f1efdfa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-2161422\" data-id=\"2161422\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bda1c9c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"bda1c9c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/File_M\/M\/1\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8ca27fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8ca27fc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-afd0ef5\" data-id=\"afd0ef5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-586139f elementor-widget elementor-widget-progress\" data-id=\"586139f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"progress.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<span class=\"elementor-title\" id=\"elementor-progress-bar-586139f\">\n\t\t\t\tDificultad\t\t\t<\/span>\n\t\t\n\t\t<div aria-labelledby=\"elementor-progress-bar-586139f\" class=\"elementor-progress-wrapper\" role=\"progressbar\" aria-valuemin=\"0\" aria-valuemax=\"100\" aria-valuenow=\"25\" aria-valuetext=\"25% (Facile)\">\n\t\t\t<div class=\"elementor-progress-bar\" data-max=\"25\">\n\t\t\t\t<span class=\"elementor-progress-text\">F\u00e1cil<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-progress-percentage\">25%<\/span>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4334defa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4334defa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1d935574\" data-id=\"1d935574\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3ecf86b4 elementor-widget elementor-widget-text-editor\" data-id=\"3ecf86b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/el-archivo-mm-1\/#File-MM1\" >Cola M \/ M \/ 1<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"File-MM1\"><\/span>Cola M \/ M \/ 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Una cola M \/ M \/ 1 sigue una ley exponencial para la llegada y el servicio de los clientes. Una cola M \/ M \/ 1 se representa de la siguiente manera:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6697\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba56.png\" alt=\"Cola M \/ M \/ 1\" width=\"363\" height=\"194\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba56.png 363w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba56-300x160.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/figure>\n<\/div>\n\n<p>En la mayor\u00eda de los casos, el cliente de un servicio est\u00e1 incluido en el n\u00famero de clientes del <a href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/colas\/\">cola<\/a>.<\/p>\n\n<p>El n\u00famero de clientes en la cola es modelado por el <a href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/cadenas-de-markov-en-tiempo-discreto\/\">cadena de markov<\/a> siguiente tiempo continuo:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6698\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba57.png\" alt=\"Cola M \/ M \/ 1\" width=\"459\" height=\"115\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba57.png 459w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba57-300x75.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/figure>\n<\/div>\n\n<p>Las probabilidades estacionarias existen porque la cadena es irreducible. Denote por p (n) la probabilidad de que el n\u00famero de clientes en la cola N (t) = n cuando t tiende a infinito. Las ecuaciones de equilibrio dan el siguiente sistema:<\/p>\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" class=\"alignnone wp-image-6699\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba58.png\" alt=\"Cola M \/ M \/ 1\" width=\"268\" height=\"141\" title=\"\"><\/figure>\n\n<p>Si establecemos \u03c1 = \u03bb \/ \u03bc entonces encontramos p (n) = \u03c1<sup>no<\/sup>p (0), lo que implica:<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6700\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba59.png\" alt=\"Cola M \/ M \/ 1\" width=\"252\" height=\"94\" title=\"\"><\/figure>\n\n<p>Deducimos que la cola es estable si \u03c1 &lt;1. Es decir, el tiempo medio de procesamiento del cliente es estrictamente menor que el tiempo medio de llegada de un cliente (es decir, el tiempo medio entre la llegada de 2 clientes). La cola es inestable si \u03c1\u22651, en este caso los clientes se acumulan ad infinitum en la cola.<\/p>\n\n<p>Todos los par\u00e1metros de rendimiento se calculan en estado estable si la cola es estable. Si aplicamos la ley de Little y las medidas de rendimiento a las colas M \/ M \/ 1 (y m\u00e1s generalmente a las colas M \/ M \/ S), con \u03c1 = A:<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6702\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba60.png\" alt=\"Archivo M \/ M \/ S\" width=\"870\" height=\"430\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba60.png 870w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba60-300x148.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba60-768x380.png 768w\" sizes=\"(max-width: 870px) 100vw, 870px\" \/><\/figure>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Wiki Proceso de Markov Inicio Dificultad F\u00e1cil 25% Cola M\/M\/1 Una cola M\/M\/1 sigue una ley exponencial para la llegada y el servicio del cliente. \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":5007,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6694","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=6694"}],"version-history":[{"count":6,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6694\/revisions"}],"predecessor-version":[{"id":18686,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6694\/revisions\/18686"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/5007"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=6694"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}