Estimating the Total Population Overflow as a Rare Event in a Tandem Network

We analyze the performance of an importance sampling estimator for a rare event probability in 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.