{"id":374,"date":"2007-03-29T03:28:30","date_gmt":"2007-03-29T10:28:30","guid":{"rendered":"https:\/\/staging.opexlearning.com\/resources\/374\/queueing-disneyland-and-fastpass"},"modified":"2014-10-03T11:04:44","modified_gmt":"2014-10-03T16:04:44","slug":"queueing-disneyland-and-fastpass","status":"publish","type":"post","link":"https:\/\/staging.opexlearning.com\/resources\/queueing-disneyland-and-fastpass\/374\/","title":{"rendered":"Disneyland Wait Times and Queueing Theory and Impact of Fast Pass"},"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>In a previous article, I discussed the <a href=\"https:\/\/staging.opexlearning.com\/resources\/psychology-of-queueing-disneyland\/372\/\">Psychology of Queueing<\/a> and my experience at Disneyland while on <a title=\"waiting at disneyland theme parks\" href=\"https:\/\/staging.opexlearning.com\/resources\/psychology-of-queueing-disneyland\/372\/\">vacation with my family<\/a>.\u00a0\u00a0 In this post, I want to briefly talk about FastPass at Disneyland, in the context of <a title=\"queueing theory\" href=\"https:\/\/staging.opexlearning.com\/resources\/queueing-theory\/\">Queueing<\/a>.<\/p>\n<p>FastPass is a feature that Disneyland offers its customers, wherein a customer is invited to obtain a pass, redeemable only at a certain time and ends at a certain time.\u00a0 The idea is that during those times, theoretically, the lines will be shorter and the wait time will be shorter also.\u00a0 Below is a picture of what that looks like at Disneyland.<\/p>\n<p>As you can see from the picture above, the customers are invited to return between 4:25PM to 5:25PM, with the idea that the wait time will be shorter.\u00a0 Disneyland calls this offering FastPass.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9902 size-full\" title=\"impact of fast pass on wait times at disneyland\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2007\/03\/disneyland-fastpass-queueing-theory.jpg\" alt=\"disneyland wait times and queueing\" width=\"500\" height=\"375\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2007\/03\/disneyland-fastpass-queueing-theory.jpg 500w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2007\/03\/disneyland-fastpass-queueing-theory-300x225.jpg 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nAs I thought more about FastPass, I think it is a simple Queueing calculation; If I&#8217;m thinking about this correctly, then, we need to know the following items:<\/p>\n<ol>\n<li>\u00ce\u00bb = Arrival Rate, or more specific, the time between arrivals.\u00a0 For most queues, we can assume that the arrival distribution can be approximated by a Poisson distribution; which means that the time between arrivals are not deterministic, but random.<\/li>\n<li>\u00ce\u00bc = Service Rate, or more specific the time for a arrival to be serviced.<\/li>\n<\/ol>\n<p>Then, Disneyland probably has historical data on when this particular ride is least congested, and I&#8217;m assuming it&#8217;s between the hours of 4:25PM and 5:25PM.\u00a0 Disneyland, then, can calculate, given historical congestion data and the Arrival Rate and the Service Rate, the probability of N arrivals during this 60 minute period:<\/p>\n<blockquote><p>(P<sub>n<\/sub> = (\u00ce\u00bbT)<sup>n<\/sup>\/n!)e<sup>-\u00ce\u00bbT<\/sup><\/p><\/blockquote>\n<p>Where T is period T, in our Disneyland example, it is 60 minutes.<\/p>\n<p>Let&#8217;s assume that Arrival Rate = 15, and we want to know the probability of 4 arrivals during this 60 minute period.\u00a0 Then, we get the following:<\/p>\n<blockquote><p>(P<sub>4<\/sub> = (15*1.0)<sup>4<\/sup>\/4!)e<sup>-15*1.0<\/sup><\/p><\/blockquote>\n<p>The result of the equation above would give a % of probability of 4 arrivals during a 60 minute period.<\/p>\n<p><strong>Does FastPass Work?<\/strong><\/p>\n<p>I&#8217;m not sure.\u00a0 Our family went on plenty of rides and, on some, I saw noticed that FastPass seemed to work, whereas on others, FastPass was no faster than the regular line.<\/p>\n<p>Like most things, the equations we come up with are clean and neat.\u00a0 But, when they meet everyday life and empirical data, things get a little muddy and much more complex.<\/p>\n<p><strong>Enough Pontificating<\/strong><\/p>\n<p>We had a great vacation at Disneyland.\u00a0 We&#8217;re already planning our next vacation &#8212; we&#8217;re thinking Hawaii.\u00a0 I can&#8217;t wait.<\/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>In a previous article, I discussed the Psychology of Queueing and my experience at Disneyland while on vacation with my family.\u00a0\u00a0 In this post, I want to briefly talk about FastPass at Disneyland, in the context of Queueing. FastPass is a feature that Disneyland offers its customers, wherein a customer is invited to obtain a [&hellip;]<\/p>\n","protected":false},"author":12327,"featured_media":9902,"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":[641,643,642,640],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Disneyland Wait Times and Queueing Theory<\/title>\n<meta name=\"description\" content=\"Disneyland Wait Times and Queueing Theory and the impact of 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