Delay Moment Bounds for Multiserver Queues with Infinite Variance Service Times

Abstract

In this paper we consider 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, , 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, , where is the generic service time and is the generic interarrival time, satisfy . 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 . 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.

Keywords:

• Multiserver Queues
• Delay Bounds
• Moment Conditions
• Infinite Variance
• Semi-cyclic Service Discipline