Revisiting the optimality of the cμ-rule with Stochastic Flow Models

We revisit, in the context of Stochastic Flow Models (SFMs), a classic scheduling problem for optimally allocating a resource to multiple competing users. For the two-user case, we establish the optimality of the well-known cμ-rule for arbitrary stochastic processes using calculus of variations arguments as well as an Infinitesimal Perturbation Analysis (IPA) approach. The latter allows us to derive an explicit sensitivity estimate of the cost function with respect to a controllable parameter and to further study the problem when the cost function is nonlinear, deriving simple distribution-free cost sensitivity estimates and analyzing why the cμ-rule may fail in this case.