A Multiserver Queue with Thresholds for the Acceptance of Customers into Service
Operations Research · 1982 · Volume 30 · Issue 5
Abstract
A queue with Poisson arrivals is served by N identical exponential servers. When a server becomes free, a group of customers of size at most b can be served. The server is not allowed to process a group of size less than a , 1 ≤ a ≤ 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.
Keywords
682 batch clearing of items, 686 batch service queue with thresholds, 705 Markovian queue
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