Analytic perturbation analysis for DEDS with discontinuous sample-path functions

This paper considers a new Analytic Perturbation Analysis (APA) approach for Discrete Event Dynamic Systems (DEDS) with discontinuous sample-path functions with respect to control parameters. The performance functions for DEDS usually are formulated as mathematical expectations, which can be calculated only numerically. APA is based on new analytic formulas for the gradients of expectations of indicator functions; therefore, it is called analytic perturbation analysis. The gradient of performance function may not coincide with the expectation of a gradient of sample-path function (i.e., the interchange formula for the gradient and expectation sign may not be valid). Estimates of gradients can be obtained with one simulation run of the models. The approach is demonstrated with three examples: a simple "shut down" problem, a multiclass queuing network, and a failure probability of inspected mechanical components. Numerical simulations are performed for the second example.