Cross-entropy-based adaptive optimization of simulation parameters for Markovian-driven service systems

Markov fluid models represent a general description of the process of service request arrivals to service systems. The solution of performance analysis problems incorporating them often calls for a simulation approach, for which a reference methodology is Importance Sampling. However, in this case the appropriate choice of the biasing conditions is a problem in itself. In this paper an iterative method based on the cross-entropy is proposed for this choice. The equations are given that allow to derive the biasing conditions from the simulation itself. The application of the proposed method to three different sample cases, referring to one transient scenario (finite time horizon and prescribed initial conditions) and two stationary cases, shows that the method is quite accurate and that during the path towards overflow the buffer fills mostly in the first phases.