{"id":21917,"date":"2022-07-20T07:39:29","date_gmt":"2022-07-20T11:39:29","guid":{"rendered":"https:\/\/carleton.ca\/math\/?p=21917"},"modified":"2022-07-20T07:39:57","modified_gmt":"2022-07-20T11:39:57","slug":"applied-probability-seminar","status":"publish","type":"post","link":"https:\/\/carleton.ca\/math\/2022\/applied-probability-seminar\/","title":{"rendered":"Applied Probability Seminar"},"content":{"rendered":"<p>Date: July 22, 2022<br \/>\nTime:\u00a0 11:00 a.m.<br \/>\nLocation: Faculty of Science &#8211; 3230 Herzberg building (Dean&#8217;s boardroom), Carleton University<br \/>\nOn-line through zoom: <a href=\"https:\/\/carleton-ca.zoom.us\/j\/97483042994\">https:\/\/carleton-ca.zoom.us\/j\/97483042994<\/a><br \/>\nCost: Free<br \/>\nSpeaker: Dr. Jing Gai ( Royal Military College of Canada)<br \/>\nTitle: The exact analyses of GI\/M<sup>a,b<\/sup>\/C Queueing System<\/p>\n<p><strong>Abstract:\u00a0<\/strong>\u00a0\u00a0Bulk-service queueing systems have been widely applied in many areas in daily life, for example, a group (or batch) of customers in transportation systems need to be served simultaneously. While the single-server queueing systems work in some of the cases, the multi-servers are unavoidable to efficiently handle most of the complex applications. Compared to the well-developed single-service or single-server queueing systems, the multi-server queueing systems are more complex and harder to deal with, especially when the interarrival-time distribution is arbitrary.<\/p>\n<p>In this talk, the exact analyses to determine queue-length distributions for a complex bulk-service, multi-server queueing system GI\/M<sup>a,b<\/sup>\/C where interarrival times follow an arbitrary distribution are derived. The introduction of quorum \u201ca\u201d further increases the complexity of the model, a two-dimensional Markov chain has to be involved. An elegant analytic solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.) and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively. The closed-form relations for these probabilities at three epochs are derived by using a standard level crossing analysis. The waiting-time distribution is discussed. The Little\u2019s Formula for the system GI\/M<sup>a,b<\/sup>\/C is verified theoretically and numerically. The closed form formulas for calculating the moments of queue-length at three epochs and the mean waiting-time will be provided.<\/p>\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Date: July 22, 2022 Time:\u00a0 11:00 a.m. Location: Faculty of Science &#8211; 3230 Herzberg building (Dean&#8217;s boardroom), Carleton University On-line through zoom: https:\/\/carleton-ca.zoom.us\/j\/97483042994 Cost: Free Speaker: Dr. Jing Gai ( Royal Military College of Canada) Title: The exact analyses of GI\/Ma,b\/C Queueing System Abstract:\u00a0\u00a0\u00a0Bulk-service queueing systems have been widely applied in many areas in daily [&hellip;]<\/p>\n","protected":false},"author":44,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1,15],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - 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