An M/M/1 queue with a general bulk service rule

In: Naval research logistics: an international journal, Band 32, Heft 4, S. 595-603

Abstract

AbstractA model of an M/M/1, bulk queue with service rates dependent on the batch size is developed. The operational policy is to commence service when at least L customers are available with a maximum batch size of K. Arriving customers are not allowed to join in‐process service. The solution procedure utilizes the matrix geometric methodology and reduces to obtaining the inverse of a square matrix of dimension K + 1 ‐ L. For the case where the service rates are not batch size dependent, the limiting probabilities can be written in closed form. A numerical example illustrates the variability of the system cost as a function of the minimum batch service size L.