Combining importance sampling and temporal difference control variates to simulate Markov Chains
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Efficient simulation of buffer overflow probabilities in jackson networks with feedback
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling simulations of phase-type queues
Winter Simulation Conference
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The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the probability along the most likely paths to the rare event. Traditionally, insights from large deviations theory are used to identify the distribution emphasizing these most likely paths. In this paper we develop an intuitivecyclic approach for selecting such a distribution. The key idea is to select a distribution under which the event of interest is no longer rare and the probability of occurrence of a cycle in any sample path remains equal to the original probability of that cycle. We show that only an exponentially twisted distribution can satisfy thisequiprobable cycle condition. Using this approach we provide an elementary derivation of the asymptotically optimal change of measure for level crossing probability for Markov-additive processes. To demonstrate its ease of use for more complex stochastic systems, we apply it to determine the asymptotically optimal change of measure for estimating buffer overflow probability of a single-server queue subject to server interruptions.