Alternative representation and perturbation analysis in a routing problem

An infinitesimal perturbation analysis (IPA) algorithm for estimating the sensitivities with respect to the routing parameters of the average delay in a system of parallel queues is proposed. When a conventional representation of the system is used, IPA estimates of the sensitivities with respect to the routing parameters are zero with probability one and hence do not provide any useful information. An alternative representation of the system is proposed, and it is shown that the IPA estimators in this case are typically zero. It is then shown that the statistical properties of the estimators in this case are equivalent to those of IPA estimators in an equivalent system in which the parameters are parameters of the service time distribution. The latter system is extensively studied, and the results can be used directly in the above routing problem