This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method.
|Name||Memorandum Faculty of Mathematical Sciences|
|Publisher||University of Twente, Department of Applied Mathematics|