The likelihood ratio method is studied as a possible approach for sensitivity analysis of discrete event systems. A load sharing problem is considered for a multiqueue system in which customers have soft real-time constraints-if the waiting time of a customer exceeds a given random amount (called the laxity of the customer), then the customer is considered lost. A recursive optimization algorithm is formulated using likelihood ratio estimates to minimize the steady-state probability of loss with respect to the load sharing parameters, and almost sure convergence of the algorithm is proved. The algorithm can be used for online optimization of the real-time system, and does not require a priori knowledge of the arrival rate of customers to the system or the service time and laxity distributions. To illustrate the results, simulation examples are presented.
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