Fast simulation of overflow probabilities in a queue with Gaussian input

Abstract

In this article, we study a queue fed by a large number n of independent discrete-time Gaussian processes with stationary increments. We consider the many-sources asymptotic regime, that is, the buffer-exceedance threshold B and the service capacity C are scaled by the number of sources ( B ≡ nb and C ≡ nc ).We discuss four methods for simulating the steady-state probability that the buffer threshold is exceeded: the single-twist method (suggested by large deviation theory), the cut-and-twist method (simulating timeslot by timeslot), the random-twist method (the twist is sampled from a discrete distribution), and the sequential-twist method (simulating source by source).The asymptotic efficiency of these four methods is analytically investigated for n → ∞. A necessary and sufficient condition is derived for the efficiency of the single-twist method, indicating that it is nearly always asymptotically inefficient. The other three methods, however, are asymptotically efficient. We numerically evaluate the four methods by performing a detailed simulation study where it is our main objective to compare the three efficient methods in practical situations.