Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues

A general class of vehicle dispatching strategies for bulk arrival, bulk service queues is examined which consist of some combination of vehicle holding and cancellation strategies. The moments of the length of the queue at vehicle departure instants and in continuous time are solved for exactly using transform methods. Relationships between the moments of the waiting time and queue length distributions are developed without further use of transforms, resulting in an exact expression for the expected waiting time and an approximation for the variance. A simple approach for calculating the roots of a particular function, needed to find the moments of the queue length distribution, is presented and used to demonstrate that this task can be accomplished very easily. Finally, the model is used to compare alternative vehicle dispatching strategies in terms of costs and levels of service.