{"id":4803,"date":"2025-05-07T15:30:10","date_gmt":"2025-05-07T10:00:10","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4803"},"modified":"2025-07-18T15:30:10","modified_gmt":"2025-07-18T10:00:10","slug":"graph-of-optimization-of-cost","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/industrial-engineering\/graph-of-optimization-of-cost","title":{"rendered":"Graph of Optimization of Cost"},"content":{"rendered":"<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4804\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/Graph-of-Optimization-of-Cost.jpg\" alt=\" Graph of Optimization of Cost \" width=\"230\" height=\"142\" \/><\/p>\n<h2 style=\"text-align: justify;\">Representation of Queueing Model<\/h2>\n<p style=\"text-align: justify;\"><strong>Kendalls Lee Notation:<\/strong><br \/>\nThe general form of notation is<\/p>\n<p style=\"text-align: center;\">(a\/b\/c ) : (d\/e\/f )<\/p>\n<p style=\"text-align: justify;\">Here,<\/p>\n<ul>\n<li style=\"text-align: justify;\">a = Probability distribution for arrival pattern.<\/li>\n<li style=\"text-align: justify;\">b = Probability distribution for service pattern.<\/li>\n<li style=\"text-align: justify;\">c = Number of servers.<\/li>\n<li style=\"text-align: justify;\">d = Service rule or service order.e =<\/li>\n<li style=\"text-align: justify;\">number of customers allowed in the system<\/li>\n<li style=\"text-align: justify;\">f = Size of calling population.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">Queueing Model 1 (M\/M\/1) : (FIFO\/\u221e\/\u221e)<\/p>\n<ul>\n<li style=\"text-align: justify;\">M=Arrival pattern with Poisson distribution.<\/li>\n<li style=\"text-align: justify;\">M=Service rate is exponentially distributed.<\/li>\n<li style=\"text-align: justify;\">1 = Number of server.<\/li>\n<li style=\"text-align: justify;\">FIFO = Service rule,<\/li>\n<li style=\"text-align: justify;\">\u221e = customer number allowed<\/li>\n<li style=\"text-align: justify;\">\u221e = Size of calling population<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Assumption (\u03bb &lt; \u00b5): : When mean arrival rate (\u03bb) is greater than mean service rate, there will be never ending queue and it leads to queue explosion.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4805 size-full aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/probability.jpg\" alt=\"Probability\" width=\"466\" height=\"693\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/probability.jpg 466w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/probability-202x300.jpg 202w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/p>\n<h4 style=\"text-align: justify;\"><strong> Remember:<\/strong><\/h4>\n<p style=\"text-align: justify;\">In queuing model the assumption is that, if random variable is independently and identically distributed random variable then only we can assume it as Poisson distribution.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4806 size-full aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/queueing-model.jpg\" alt=\"Queueing model\" width=\"614\" height=\"336\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/queueing-model.jpg 614w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/queueing-model-300x164.jpg 300w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/industrial-engineering\/queueing-theory\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/industrial-engineering\/inventory-control\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-industrial-engineering\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Industrial Engineering?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Representation of Queueing Model Kendalls Lee Notation: The general form of notation is (a\/b\/c ) : (d\/e\/f ) Here, a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1505,10],"tags":[1513,1514,1512],"class_list":["post-4803","post","type-post","status-publish","format-standard","hentry","category-industrial-engineering","category-me","tag-kendalls-lee-notation","tag-poisson-distribution","tag-queueing-model"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4803"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4803\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}