A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Discrete-time conversion for simulating finite-horizon Markov processes
SIAM Journal on Applied Mathematics
The asymptotic efficiency of simulation estimators
Operations Research
A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
A new variance-reduction technique for regenerative simulations of Markov chains
Proceedings of the 29th conference on Winter simulation
Exploiting multiple regeneration sequences in simulation output analysis
Proceedings of the 30th conference on Winter simulation
On the small-sample optimality of multiple-regeneration estimators
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
Improving standardized time series methods by permuting path segments
Proceedings of the 33nd conference on Winter simulation
SIMULATION OF PROCESSES WITH MULTIPLE REGENERATION SEQUENCES
Probability in the Engineering and Informational Sciences
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
The semi-regenerative method of simulation output analysis
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Exploiting regenerative structure to estimate finite time averages via simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotic Variance Of Passage Time Estimators In Markov Chains
Probability in the Engineering and Informational Sciences
Permuted Standardized Time Series for Steady-State Simulations
Mathematics of Operations Research
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We propose a new estimator for a large class of performance measures obtained from a regenerative simulation of a system having two distinct sequences of regeneration times. To construct our new estimator, we first generate a sample path of a fixed number of cycles based on one sequence of regeneration times, divide the path into segments based on the second sequence of regeneration times, permute the segments, and calculate the performance on the new path using the first sequence of regeneration times. We average over all possible permutations to construct the new estimator. This strictly reduces variance when the original estimator is not simply an additive functional of the sample path. To use the new estimator in practice, the extra computational effort is not large since all permutations do not actually have to be computed as we derive explicit formulas for our new estimators. We examine the small-sample behavior of our estimators. In particular, we prove that for any fixed number of cycles from the first regenerative sequence, our new estimator has smaller mean squared error than the standard estimator. We show explicitly that our method can be used to derive new estimators for the expected cumulative reward until a certain set of states is hit and the time-average variance parameter of a regenerative simulation.