A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Steady-state simulation of queueing processes: survey of problems and solutions
ACM Computing Surveys (CSUR)
The asymptotic efficiency of simulation estimators
Operations Research
Asymptotic formulas for Markov processes with applications to simulation
Operations Research
Using permutations in regenerative simulations to reduce variance
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on modeling and analysis of stochastic systems
Central Limit Theorems for Permuted Regenerative Estimators
Operations Research
Approximating Martingales for Variance Reduction in Markov Process Simulation
Mathematics of Operations Research
Overlapping batch means: something for nothing?
WSC '84 Proceedings of the 16th conference on Winter simulation
TRANSIENT SIMULATION VIA EMPIRICALLY BASED COUPLING
Probability in the Engineering and Informational Sciences
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
Perwez Shahabuddin, 1962--2005: A professional appreciation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
| Hi-index | 0.00 |
We propose nonstandard simulation estimators of expected time averages over finite intervals [0, t], seeking to enhance estimation efficiency. We make three key assumptions: (i) the underlying stochastic process has regenerative structure, (ii) the time average approaches a known limit as time t increases and (iii) time 0 is a regeneration time. To exploit those properties, we propose a residual-cycle estimator, based on data from the regenerative cycle in progress at time t, using only the data after time t. We prove that the residual-cycle estimator is unbiased and more efficient than the standard estimator for all sufficiently large t. Since the relative efficiency increases in t, the method is ideally suited to use when applying simulation to study the rate of convergence to the known limit. We also consider two other simulation techniques to be used with the residual-cycle estimator. The first involves overlapping cycles, paralleling the technique of overlapping batch means in steady-state estimation; multiple observations are taken from each replication, starting a new observation each time the initial regenerative state is revisited. The other technique is splitting, which involves independent replications of the terminal period after time t, for each simulation up to time t. We demonstrate that these alternative estimators provide efficiency improvement by conducting simulations of queueing models.