A queueing-location model with expected service time dependent queueing disciplines

This paper considers the problem of locating a single server on a network operating as an M/G/1 queue, in which queued calls are serviced by a class of queueing disciplines which depend solely on expected service time information. The model is analyzed as an M/G/1 non-preemptive priority queueing model, with location-dependetn priorities. Extreme case analysis with respect to the average arrival rate of calls is discussed. The connection between queueing discipline chosen and the optimal location of the facility is shown for a two-node network. Numerical examples illustrate our results. A major observation is that the Shortest Expected Job First (SEJF) queueing discipline yields a location which is closer to the Hakimi median of [20] than that produced by any Work Conserving Single Priority (WCSP) queueing discipline. Correspondingly, the Longest Expected Job First (LEJF) queueing discipline yields a location which is further from the Hakimi median than that produced by any WCSP queueing discipline.