The Output of Multiserver Queuing Systems

Abstract

We derive a recurrence relation for ξ n , the time until the n th departure measured from T 0 , any well-defined instant in time. While the recurrence, valid for the G / G / s queue, is generally not easy to work with, in certain cases we can use it to obtain the distribution and moments of ξ n . We obtain limited results for the M / M / s queue but investigate the M / D / s queue in detail. For the M / D / s queue, the results are used to determine the range of system parameters, p / s (the average utilization per server) and s , for which the distribution of ξ s can be approximated by one of the gamma type. The quality of the approximation for a given p and s provides insight as to when the output of the M / D / s queue is “nearly Poisson.”