The M/G/1 queue with finite workload capacity

The M/G/1 queue with finite workload capacity

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Article ID: iaor2004850
Country: Netherlands
Volume: 39
Issue: 1
Start Page Number: 7
End Page Number: 22
Publication Date: Sep 2001
Journal: Queueing Systems
Authors: ,
Keywords: M/G/1 queues
Abstract:

We consider the M/G/1 queueing system in which customers whose admission to the system would increase the workload beyond a prespecified finite capacity limit are not accepted. Various results on the distribution of the workload are derived; in particular, we give explicit formulas for its stationary distribution for M/M/1 and in the general case, under the preemptive last-in-first-out discipline, for the joint stationary distribution of the number of customers in the system and their residual service times. Furthermore, the Laplace transform of the length of a busy period is determined. Finally, for M/D/1 the busy period distribution is derived in closed form.

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