Computation of the Asymptotic Bias and Variance for Simulation of Markov Reward Models
نویسندگان
چکیده
The asymptotic bias and variance are important deter minants of the quality of a simulation run In particu lar 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 re quired to obtain a statistically signi cant estimate of a measure While both of these measures can be computed analytically for simple models and measures e g the average bu er occupancy of an M G queue practical computational methods have not been developed for gen eral model classes Such results would be useful since they would provide insight into the simulation time re quired 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 e ciently 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 de ned on very large and irregular Markov reward models To illustrate this point we apply the developed algorithm to queues with complex tra c be havior di erent service time distributions and several alternative scheduling disciplines that may be typically encountered in nodes in high speed communication net works
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