The optimal batch size of M/D N /1 queue

Woojin Chang

International Journal of Operational Research, 2006, vol. 1, issue 4, 396-409

Abstract: A single-server, infinite-capacity queue with Poisson input and deterministic bulk service rule is considered. The service time of a batch of a given size is a + b × N, where a is the common service time for all customers in a batch such as a set-up time, b is the individual service time for each customer, and N is the batch size. The queue is analysed using embedded Markov chain techniques. An explicit expression for the mean steady-state waiting time and an estimate of the optimal batch size minimising the mean steady-state waiting time are obtained. Our results are consistent with numerical computations.

Keywords: queueing systems; Poisson arrivals; bulk service; batch size optimisation; average waiting time. (search for similar items in EconPapers)
Date: 2006
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