Management Science
The UltraSAN modeling environment
Performance Evaluation - Special issue: performance modeling tools
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Stochastic Activity Networks: Structure, Behavior, and Application
International Workshop on Timed Petri Nets
Initial bias and estimation error in discrete event simulation
WSC '82 Proceedings of the 14th conference on Winter Simulation - Volume 2
Modeling issues in a shipping system
WSC '96 Proceedings of the 28th conference on Winter simulation
Simulating markov-reward processes with rare events
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Warm-up periods in simulation can be detrimental
Probability in the Engineering and Informational Sciences
Simulating flow level bandwidth sharing with pareto distributed file sizes
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Rethinking the initialization bias problem in steady-state discrete event simulation
Proceedings of the Winter Simulation Conference
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The asymptotic bias and variance are important determinants of the quality of a simulation run. In particular, the asymptotic bias can be used to approximate the bias introduced by starting the collection of a measure in a particular state distribution, and the asymptotic variance can be used to compute the simulation time required to obtain a statistically significant estimate of a measure. While both of these measures can be computed analytically for simple models and measures, e.g., the average buffer occupancy of an M/G/1 queue, practical computational methods have not been developed for general model classes. Such results would be useful since they would provide insight into the simulation time required for particular systems and measures and the bias introduced by a particular initial state distribution. In this paper, we discuss the numerical computation of the asymptotic bias and variance of measures derived from continuous-time Markov reward models. In particular, we show how both measures together can be efficiently computed by solving two systems of linear equations. As a consequence of this formulation, we are able to numerically compute the asymptotic bias and variance of measures defined on very large and irregular Markov reward models. To illustrate this point, we apply the developed algorithm to queues with complex traffic behavior, different service time distributions, and several alternative scheduling disciplines that may be typically encountered in nodes in high-speed communication networks.