The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure

This paper develops a general framework for analyzing a wide class of vehicle dispatching strategies for bulk arrival, bulk service queues. We provide a simple derivation of the queue length transform for the embedded Markov chain, and present a new computational procedure for finding the moments of the queue length distribution. Extensive computational tests demonstrate that the new procedure is significantly faster and more stable than the standard method, from the literature, that requires solving a set of simultaneous linear equations. We give formulas for the mean and variance of the length of the queue for the general case of compound Poisson arrivals, random batch capacities, general service times and a general control strategy.