NEW BOUNDS FOR EXPECTED DELAY IN FIFO GI GI/C QUEUES/

Most bounds for expected delay, E[D], in GI/Gl/c queues are modificati ons of bounds for the GI/GI/1 case. In this paper we exploit a new del ay recursion for the GI/GI/c queue to produce bounds of a different so rt when the traffic intensity rho = lambda/mu = E[S]/E[T] is less than the integer portion of the number of servers divided by two. (S and T denote generic service and interarrival times, respectively.) We deri ve two different families of new bounds for expected delay, both in te rms of moments of S and T. Our first bound is applicable when E[S-2] < infinity. Our second bound for the first time does not require finite variance of S; it only involves terms of the form E[S-beta], where 1 < beta < 2. We conclude by comparing our bounds to the best known boun d of this type, as well as values obtained from simulation.