Comparisons of Service Disciplines in a Queueing System with Delay Dependent Customer Behaviour

Abstract

In a variety of data processing and call processing systems the customer, unknown to the system, turns ‘bad’ at a random time after its arrival. That is, serving a customer with waiting time in excess of this random time results in a ‘bad’ (unsuccessful) service. If the performance of such systems is measured by the rate at which it serves good customers (‘goodput’), then this performance is determined by the delay distribution and the distribution of the time at which the customer turns bad. Given the offered load, the service demand of the customers and the customer behavior, the performance is determined by the service discipline. It is then of interest to identify the best discipline and compare its performance with that of other disciplines. These problems are studied here for an M/G/1 queue. Optimal disciplines are derived for two special cases of the customer behavior. For a more complex customer behavior, the ‘goodputs’ under three different disciplines are numerically compared and a desired discipline is identified.