Date: July 22, 2022

Time: 11:00 a.m.

Location: Faculty of Science – 3230 Herzberg building (Dean’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/M^{a,b}/C Queueing System

**Abstract: ** Bulk-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.

In this talk, the exact analyses to determine queue-length distributions for a complex bulk-service, multi-server queueing system GI/M^{a,b}/C where interarrival times follow an arbitrary distribution are derived. The introduction of quorum “a” 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’s Formula for the system GI/M^{a,b}/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.