Sample path properties of the G/D/m queue

Infinitesimal perturbation analysis is a technique for estimating gradients of performance measures in stochastic discrete-event systems-which are often used to model computer/communications networks and manufacturing systems-from a single simulation of the system. In Fu and Hu, the application of infinitesimal perturbation analysis to multi-server queues was developed, and the consistency of the estimates was investigated, with an analytical proof provided for the exponential case (the M/M/m queue) and a heuristic limit argument presented for the general case. Here, the authors use sample path analysis to give a consistency proof for the case of deterministic service times (the G/D/m queue). The key result needed for the proof is convexity of the sample performance.