Inferring finite-time performance in the M/G/1 queueing model
Jacobs, Patricia A.
Gaver, Donald Paul
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A single server is approached by a stream of Poisson arrivals with known arrival rate. The service times are assumed to be independent identically distributed with unknown distribution. One has available a finite sample of service times obtained by observing the system. A nonparametric approach is taken towards estimating the expected waiting time encountered by a new arriving customer at a finite time t, EWt both for stable and unstable systems. The estimator uses approximations to EWt and an empirical version of the well known Laplace transform of EWt for the M/G/1 queue. Empirical transform; Laplace transform of the virtual waiting of the M/G/1 queue; Exponential approximation; Brownian motion with drift. (jes)