Optimal scheduling of parallel queues using stochastic flow models

We consider a classic scheduling problem for optimally allocating a resource to multiple competing users and place it in the framework of Stochastic Flow Models (SFMs). We derive Infinitesimal Perturbation Analysis (IPA) gradient estimators for the average holding cost with respect to resource allocation parameters. These estimators are easily obtained from a sample path of the system without any knowledge of the underlying stochastic process characteristics. Exploiting monotonicity properties of these IPA estimators, we prove the optimality of the well-known cμ-rule for an arbitrary finite number of queues and stochastic processes under non-idling policies and linear holding costs. Further, using the IPA derivative estimates obtained along with a gradient-based optimization algorithm, we find optimal solutions to similar problems with nonlinear holding costs extending current results in the literature.