The conditional distribution of the residual service time in the Mn/G/1 queue

The conditional distribution of the residual service time in the Mn/G/1 queue

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Article ID: iaor2010916
Volume: 24
Issue: 3
Start Page Number: 364
End Page Number: 375
Publication Date: Jul 2008
Journal: Stochastic Models
Authors:
Keywords: M/G/1 queues
Abstract:

We study a single server queueing system with general service time distribution and memoryless inter-arrival times. The arrival rate is not constant but varies with the number of customers in the system. A recursive formula for the conditional distribution of the remaining service time given the queue length is derived for an arbitrary epoch. It is also shown that this conditional distribution holds for arrival epochs. The recursion for the corresponding Laplace-Stieltjes transforms and expected values is given in a simple formula.

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