Multi‐server Batch‐service Systems

I. J. B. F. Adan and J. A C. Resing

Statistica Neerlandica, 2000, vol. 54, issue 2, 202-220

Abstract: In this paper we analyse a multi‐server batch‐service queueing model. Customers arrive one by one according to a Poisson process. They are served in batches under the following threshold policy: when a server becomes available a new batch of waiting customers is taken into service as soon as their number reaches a threshold a. The maximum allowable batch size is equal to b. Two classes of batch service time distributions are considered: Coxian‐2 and Erlang‐r distributions. In both cases the queueing model can be described by a Markov process. For this process it is shown that the equilibrium probabilities for states with all servers busy can be expressed as a finite sum of geometric terms. This form is used to derive a closed form expression for the waiting time distribution.

Date: 2000
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