Steady-state simulation of queueing processes: survey of problems and solutions
ACM Computing Surveys (CSUR)
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Let X(T) be an integer valued stochastic process, continuous in time, T. By a computer simulation model one can obtain from the interval (O,T) an estimate of the mean, q, of the process by the time average ri (T), where i is the initial state at time 0. One of the problems is when to stop the simulation. Before stopping the simulation we first of all have to be sure that ri (T) is an unbiased estimator for the mean value q. It can be shown that ri (T) in many cases is unbiased only for large values of T, and that this convergence is not necessarily monotonous. It can also be shown that the difference between the expected value of ri (T) and the mean value q is inversely proportional to T. Secondly, before stopping the simulation we have to be sure that the dispersion on ri (T) is small, and it can be shown that this dispersion is inversely proportional to the square root of T.