Time-Inhomogenous Bulk Server Queue in Discrete Time: A Transportation Type Problem

This paper studies the queue length distributions of a discrete time bulk server queue with time-inhomogenous compound Poisson input in which service is provided in time-inhomogenous batches and the interarrival times of the server have a general distribution. We assume that the service epochs form a renewal process. This sort of queue occurs during peak periods at intermediate bus stops, where passengers are waiting to catch a bus. In the queueing literature, this problem is known as a transportation type problem. The joint distribution of the number of customers waiting at any epoch and the remaining time before the next arrival of the server is obtained. The results are then extended to cover the case in which the waiting space is limited.