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A Multi-Server Queue with Thresholds for the Acceptance of Customers into Service.
Interim technical rept.,
DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
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A queue with Poisson arrivals is served by N identical exponential servers. When a server becomes free, he can serve a group of customers of size at most b. He is not allowed to process a group of size less than a, 1 or a or b. The actual size of each group served depends on the number of waiting customers. The queue is studied as a Markov process. In the stable case, the stationary probability vector of this process has a simple, readily computable form. Using this form, the stationary waiting time distribution, which is analytically intractable, may be expressed in an algorithmically useful form. Several questions, related to the optimal design of such a service system, may be algorithmically investigated. This model serves to illustrate the advantages of the algorithmic approach. The design criteria are not analytically tractable in general. Author
APPROVED FOR PUBLIC RELEASE