Use of a Gate to Reduce the Variance of Delays in Queues With Random Service

Switching systems, particularly electromechanical switching systems, are often constructed so t h a t if several customers are awaiting service simultaneously, they will receive service in what is essentially random order, i.e., a server which becomes idle will choose its next customer at random from t h e queue of customers awaiting service. Such an arrangement may be satisfactory when the traffic intensity is low> b u t as the intensity increases, a progressively greater number of 1403 1404 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1 9 7 3 customers will have to wait an undesirably long time, and the quality of service may become unacceptable. There are available, however, methods of providing service other than "random service"; the most obvious one is service in order of arrival. The quality of service, which depends in part on the variance of the waiting time, will still diminish as the traffic intensity increases, but not as quickly as when random service is used. In fact, order-ofarrival service is the "best" discipline (at least when the order of service does not depend on individual service times) in the sense that, for a given traffic intensity, and hence mean waiting time, the variance of the waiting time is smallest. 1 Unfortunately, it may not be worthwhile (or even possible) to build a system which offers service in order of arrival. One is therefore led to consider an intermediary queue discipline, one for which the variance of the equilibrium waiting time lies between that of random service and that of order-of-arrival service.