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The optimal batch size of $M/D^N/1$ queue. (English)
Int. J. Oper. Res. 1, No. 4, 396-409 (2006).
Summary: 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 $a+b\times N$, 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.