Delay Moment Bounds for Multiserver Queues with Infinite Variance Service Times

In this paper we consider GI/GI/s First-In-First-Out (FIFO) queues. For such queues, upper bounds for stationary mean delay expressed in terms of the moments of the interarrival and service time distributions are particularly useful. For many years, most upper bounds for mean delay, E(D), required service times to have finite second moment; it was not until Scheller-Wolf and Sigman (1997b) developed bounds using a new delay recursion that delay bounds were obtained when service times had infinite second moment. However, these bounds required that the system load, rho = E(S)/E(T), where S is the generic service time and T is the generic interarrival time, satisfy rho <left perpendicular s/2 right perpendicular. Since that paper first appeared, new recursions for delay have appeared in the literature which imply that improved bounds can be obtained. This paper updates and extends the moment bounds of Scheller-Wolf and Sigman (1997b) in response to these developments, to include all cases when rho <s. We show that, in general, bounds can be improved when there is a gap between the order of service time moments necessary to ensure finite mean delay (see Scheller-Wolf (2003)) and the actual service time moment that is finite in the system.