Title: The optimal batch size of M/D^N/1 queue

Authors: Woojin Chang

Addresses: Department of Industrial Engineering, College of Engineering, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-742, Korea

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.

DOI: 10.1504/IJOR.2006.010212

International Journal of Operational Research, 2006 Vol.1 No.4, pp.396 - 409

Published online: 10 Jul 2006 *

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