Applications of Perturbation Techniques to Optimal Resource Sharing in Discrete Event Systems

A large class of Discrete Event Systems (DES) may be viewed as a set of interconnected resources providing service to tasks submitted to the system. We consider the problem of optimal resource sharing in the presence of real-time constraints: a task is considered lost if its waiting time exceeds a given deadline. We derive a quasistatic distributed gradient-based algorithm and address the issue of estimating the necessary gradient information on-line with a minimum of stochastic modeling assumptions. An estimator based on Finite Perturbation Analysis is developed and compared to one obtained through the Likelihood Ratio method. Finally, we include simulation results illustratng the behavior of the algorithm using these gradient estimators.