Performance Optimization of a Class of Discrete Event Dynamic Systems Using Calculus of Variations Techniques

We explore an approach involving the use of calculus of variations techniques for discrete event dynamic system (DEDS) performance optimization problems. The approach is motivated by the observation that such problems can be described by separable cost functions and recursive dynamics of the same form as that used to describe conventional discrete-time continuous-variable optimal control problems. Three important difficulties are that DEDS are generally stochastic, their dynamics typically involve max and min operations, which are not everywhere differentiable, and the state variables are often discrete. We demonstrate how to overcome these difficulties by applying the approach to a transportation problem, modeled as a polling system, where we are able to derive an explicit and intuitive analytic expression for an optimal control policy.