Most bounds for expected delay, E[D], in GI/G/c queues are modifications of bounds for the GI/G/1 case. In this paper we exploit a new delay recursion for the GI/G/c queue to produce bounds of a different sort when the traffic intensity ρ = λ/μ = 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 derive two different families of new bounds for expected delay, both in terms of moments of S and T. Our first bound is applicable when E[S2] < ∞. Our second bound for the first time does not require finite variance of S; it only involves terms of the form E[Sβ], where 1 < β < 2. We conclude by comparing our bounds to the best known bound of this type, as well as values obtained from simulation.
