Consistency of infinitesimal perturbation analysis for the GI/G/m queue

We extend the infinitesimal perturbation analysis algorithm developed for the GI/G/1 queue to the GI/G/m queue. The primary difference is the need for additional accumulators for each server. For the M/M/2 queue, a consistency proof is given which is extendable to the M/M/m queue. For the more general GI/G/m queue, a heuristic argument is given as to why the algorithm works. In this argument, it is seen that the need for the servers to be identical is crucial for the corrections of the algorithm. Numerical results are provided.