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176 – Modeling
The Posterior Service Time in an M/G/1 Queue with a Workload Barrier and Extreme Prior Service Times
Sponsor: Section on Statistical Computing
Keywords: M/G/1 queue, bounded workload, truncated service times, regenerative process, renewal theory, integral equations, level crossing
Percy H. Brill
University of Windsor
Mei Ling Huang
Brock University
This article considers an M/G/1 queue with workload barrier at level K > 0. Prior service times are continuous random variables. The policy for arrivals re the barrier is: service times that would cause the workload to exceed K are truncated at K. We give the posterior pdf and expected value of the posterior service time due to the barrier, the expected number served in a busy period, and related quantities. We use a metric for the distance between the prior and posterior pdfs of service time. We specialize results to the case where prior service times have a no-mean Pareto(II) distribution.