Importance Sampling for a Two-Node Jackson Network with Customer Impatience until the End of Service

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. Estimating probabilities associated to rare events has been a topic of great importance in queuing theory, and in applied probability at large. We analyze the performance of an importance sampling estimator for a rare event probability in a Jackson network. The present paper 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 derive a closed form solution for the probability of missing deadline. Then the results have employed in an importance sampling technique to estimate the probability of total population overflow which is a rare event. We have also shown that the probability of this rare event may be affected by various deadline values.