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This paper presents a framework for analyzing time complexity of rare events estimators for queueing models. In particular it deals with polynomial and exponential time switching regenerative (SR) estimators for the steady-state probabilities of excessive backlog in the GI=GI=1 queue, and some of its extensions. The SR estimators are based on large deviation theory and exponential change of measure, which is parametrized by a scalar t. We show how to find the optimal value w of the parameter t, which leads to the optimal exponential change of measure (OECM), and we find conditions under which the OECM generates polynomial time estimators. We, finally, investigate the "robustness" of the proposed SR estimators, in the sense that we find how much one can perturb the optimal value w in the OECM such that the SR estimator still leads to dr...
In this paper we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level; finally, the tilting parameter just found is used to estimate the overflow probability of interest. We recognize three distinct properties of the method which together explain why the method works well; we conjecture that they hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.
In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.
common random numbers;antithetic random numbers;importance sampling;control variates;conditioning;stratied sampling;splitting;quasi Monte Carlo
In this paper we propose a fast adaptive Importance Sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First we estimate the minimum Cross-Entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level; finally, the tilting parameter just found is used to estimate the overflow probability of interest. We recognize three distinct properties of the method which together explain why the method works well; we conjecture that they hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.
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