Iterative Algorithms for Bulk Arrival, Bulk Service Queues with Poisson and Non-Poisson Arrivals

Iterative numerical procedures are investigated for the study of queue lengths and waiting times in bulk arrival, bulk service queues. For queues with compound Poisson arrivals, the procedure uses the imbedded Markov chain to study a variety of vehicle dispatching strategies. The technique is easy to implement, numerically stable and, for most problems that arise in transportation, computationally faster than other approaches that have been proposed. For queues with non-Poisson arrivals, an iterative scheme is devised for calculating a discretized form of the waiting time distribution using the concept of unfinished work. Numerical experiments with different discretization strategies indicate that a high level of accuracy can be attained at a very moderate cost.