{"id":8033,"date":"2011-01-04T06:12:42","date_gmt":"2011-01-04T13:12:42","guid":{"rendered":"https:\/\/staging.opexlearning.com\/resources\/?p=8033"},"modified":"2014-10-04T06:05:16","modified_gmt":"2014-10-04T11:05:16","slug":"queueing-theory-definition","status":"publish","type":"post","link":"https:\/\/staging.opexlearning.com\/resources\/queueing-theory-definition\/8033\/","title":{"rendered":"Queueing Theory Definition, Equations, and Applications"},"content":{"rendered":"<div class=\"a296a24fa2fc69ef5487857f02f111e8\" data-index=\"9\" style=\"float: none; margin:10px 0 10px 0; text-align:center;\">\n<script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\r\n<!-- Single Post readerboard -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:inline-block;width:728px;height:90px\"\r\n     data-ad-client=\"ca-pub-8207522353004717\"\r\n     data-ad-slot=\"1144967431\"><\/ins>\r\n<script>\r\n(adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\n<\/div>\n<p>Below is a Definition of Queueing Theory, a glossary, and vocabulary. Knowing the concepts below will help you better understand these articles on <a title=\"queue\" href=\"https:\/\/staging.opexlearning.com\/resources\/queueing-theory\/\">Queues<\/a>.<\/p>\n<ul>\n<li>Queue: A line (or buffer or inventory) feeding a number of servers<\/li>\n<li>Server: An operation fed by a queue.<\/li>\n<li>Arrival rate (\u00ce\u00bb): Mean number of arrivals per unit time (usually per hour or day).<\/li>\n<li>Service rate (\u00ce\u00bc): Mean number of customers that can be served at 100% utilization by each individual server per unit time (usually per hour or day). At the individual\u00a0workstation level, the service rate will equal capacity.<\/li>\n<li>Channels (M): The number of parallel operations connected to an individual queue. For example, if\u00a0each queue has 2 operations then it will have two channels.<\/li>\n<li>Utilization (u): A measure of how \u201cbusy\u201d the system is. It is generally defined as the ratio of\u00a0throughput to capacity. Note that u = \u00ce\u00bb\/(\u00ce\u0153\u00ce\u00bc) if \u00ce\u00bb &lt; \u00ce\u0153\u00ce\u00bc, i.e. the utilization is less\u00a0than 100%. (Also, note that while the Greek letter \u00ce\u00bc\u2014 or mu\u2014 looks a bit like\u00a0u, they are in fact two different variables.)<\/li>\n<li>Phase: A queue and its connected servers, or routes to a server.<\/li>\n<li>Balking: When a person, who would otherwise have entered a line, decides not to enter\u00a0it.<\/li>\n<li>Reneging: When a person, who has entered a line, later decides to leave it without being\u00a0served.<\/li>\n<li>Interarrival Time: The time between when one customer arrives at a queue and when the next\u00a0customer arrives.<\/li>\n<li>Service Time: The time it takes for one particular server to complete a customer\u2019s service.\u00a0The average service time will be the same as the cycle time.<\/li>\n<\/ul>\n<p>And now for some equations you&#8217;ll need to know.<\/p>\n<ul>\n<li>CV: The coefficient of variation. This is a measure of a random variable\u2019s\u00a0variability. For a random variable x, CVx is defined as Standard Deviation (x)\u00a0x mean (x) CV = .<\/li>\n<li>CVIAT: The coefficient of variation of the interarrival time. The greater the CVIAT, the\u00a0\u201clumpier\u201d the arrival rate.<\/li>\n<li>CVST: The coefficient of variation of the service time. The smaller the CVST, the\u00a0more \u201cconsistent\u201d a server is.<\/li>\n<li>Lq: The average number of people in a line awaiting service.<\/li>\n<li>Wq: The average length of time a customer waits before being served.<\/li>\n<\/ul>\n<p>After you have become familiar with the terms above, go ahead and read the articles on <a title=\"queueing theory\" href=\"https:\/\/staging.opexlearning.com\/resources\/queueing-theory\/\">Queueing Theory<\/a>.<\/p>\n<!--CusAds0-->\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Below is a Definition of Queueing Theory, a glossary, and vocabulary. Knowing the concepts below will help you better understand these articles on Queues. Queue: A line (or buffer or inventory) feeding a number of servers Server: An operation fed by a queue. Arrival rate (\u00ce\u00bb): Mean number of arrivals per unit time (usually per [&hellip;]<\/p>\n","protected":false},"author":12327,"featured_media":9716,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[29],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Definition of Queueing Theory and Examples<\/title>\n<meta name=\"description\" content=\"Definition of Queueing Theory terms and applications, including simple equations you can apply 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