An M/G/1 Queue With a Hybrid Discipline

An M/G/1 Queue With a Hybrid Discipline By B. T. DOSHI (Manuscript received October 27,1982) In this paper we analyze the delay in a single-server queue in which the server, when it becomes free, selects for the next service the oldest customer with current delay smaller than T. If no such customer is present, then it selects the youngest customer with the current delay in excess of T. This service discipline is desirable in applications where the success or failure of a service depends on the delay in providing the service. Telephone call processing and steel rolling are two of these applications. We obtain the delay distribution for this service discipline using a combination of level-crossing arguments and renewal theory, and compare this performance with that of the last-in-first-out discipline with respect to the throughput of successfully served customers.