Transient Effects in M/G/1 Queues: An Empirical Investigation.

摘要

This research provides numerical results for time-dependent expected server load (mean virtual waiting time) in single-server queues with Poisson arrivals and gamma distributed service times. The results are presented in tabular form to facilitate their use by practitioners involved in the study of operating systems. This research considers groups of server load processes whose parameters are selected so that the first and second moments of their net input processes are matched. An existing Laplace transform expression is employed to obtain transient expected server load at specified epochs. The tabulated results allow a comprehensive study of the error associated with using the Wiener process as an approximation of server load in queues. This study confirms that the Wiener process is always an upper bound and that the approximation is best for queues with a traffic intensity parameter near unity. The scaled results also indicate that the gamma input process and queueing process with deterministic service times provide tight lower and upper bounds, respectively, for expected server load in all queues with Poisson arrivals and gamma distributed service times.