Approximations in Multi-Server Poisson Queues
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Our major objective is to obtain an approximation for the average time spent waiting in queue by a customer in an MGk queueing system--call it W sub Q. This is done by means of an approximation assumption presented, which is shown to be asymptotically valid both in heavy and in light traffic. The approximation assumption is used to derive an approximation for W sub Q. Numerical comparison with tables given by Hillier-Lo in the special case of Erlang service times indicate that the approximation, which depends on the service distribution only through its first two moments, works remarkably well. In addition, as a by-product of our analysis, we also obtain approximations for the distribution of the number of busy servers and the mean length and number of customers in a busy period. These latter approximations depend on the service distribution only through its mean. The approximation assumption is valid and leads to the exact result in the case of a limited capacity system where no queue is allowed to form.
- Operations Research