Queueing with limited waiting time and multiple heterogeneous servers

Abstract

A Poisson stream of customers arrive at a muitiple parallel serving facility consisting of n heterogeneous servers. The service time density functions are all negative exponential and may all have different means. Any customer reaching the serving is either immediately served, if at least one server is free, or waits his turn. The waiting, however, is limited by some t. If the customer``s service has not commenced within time t after his arrival, he is lost. The arrival enters the queue and is served on a first-come, first-served basis unless it reneges (leaves the queue). If on arrival more than one server is free, the server to be used is chosen at random. The results obtained are for stationary-state and include (1) state probabilities; (2) probability of acquiring service and probability of loss; (3) distribution functions and mean values of waiting times in queue. Certain important special cases are derived from the preceding, namely, (1) homogeneous servers (2) no regeneing.