Transient exponential-Erlang queues and steady-state simulation
Communications of the ACM
Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Transient behavior of the M/M/1 queue: starting at the origin
Queueing Systems: Theory and Applications
Simulation methods for queues: an overview
Queueing Systems: Theory and Applications
Some guidelines and guarantees for common random numbers
Management Science
Conjectured upper bounds on transient mean total waiting times in queuing networks
WSC '93 Proceedings of the 25th conference on Winter simulation
Control of initialization bias in multivariate simulation response
Communications of the ACM - Special issue on simulation modeling and statistical computing
A comparison of numerical techniques in Markov modeling
Communications of the ACM
Exploring exponentially weighted moving average control charts to determine the warm-up period
WSC '05 Proceedings of the 37th conference on Winter simulation
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By studying performance measures via reward structures, on-line error bounds are obtained by successive approximation. These bounds indicate when to terminate computation with guaranteed accuracy; hence, they provide insight into steady-state convergence. The method therefore presents a viable alternative to steady-state computer simulation where the output series is typically contaminated with initialization bias whose impact on the output cannot be easily quantified. The method is illustrated on capacitated queueing networks. The results indicate that the method offers a practical tool for numerically approximating performance measures of queueing networks. Results on steady-state convergence further quantify the error involved in analyzing an inherently transient system using a steady-state model.