The Importance Sampling Simulation of MMPP/D/1 Queueing

概要

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We investigate an importance sampling (IS) simulation of MMPP/D/1 queueing to obtain an estimate for the survivor function P(Q > q) of the queue length Q in the steady state. In [11], we studied the IS simulation of 2-state MMPP/D/1 queueing and obtained the optimal simulation distribution, but the mathematical fundation of the theory was not enough. In this paper, we construct a discrete time Markov chain model of the n-state MMPP/D/1 queueing and extend the results of [ 11] to the n-state MMPP/D/1. Based on the Markov chain model, we determine the optimal IS simulation distribution of the n-state MMPP/D/1 queueing by applying the large deviations theory, especially, the sample path large deviations theory. Then, we carry out IS simulation with the obtained optimal simulation distribution. Finally, we compare the simulation results of the IS simulation with the ordinary Monte Carlo (MC) simulation. We show that, in a typical case, the ratio of the computation time of the IS simulation to that of the MC simulation is about 10^<-7>, and the 95% confidence interval of the IS is slightly improved compared with the MC.
一般社団法人電子情報通信学会の論文
1997-11-25