Performance evaluation of an importance sampling technique in a Jackson network

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The standard approach, which simulates the system using an a priori fixed change of measure suggested by large deviation analysis, has been shown to fail in even the simplest network settings. Estimating probabilities associated with rare events has been a topic of great importance in queueing theory, and in applied probability at large. In this article, we analyse the performance of an importance sampling estimator for a rare event probability in a Jackson network. This article carries out strict deadlines to a two-node Jackson network with feedback whose arrival and service rates are modulated by an exogenous finite state Markov process. We have estimated the probability of network blocking for various sets of parameters, and also the probability of missing the deadline of customers for different loads and deadlines. We have finally shown that the probability of total population overflow may be affected by various deadline values, service rates and arrival rates.