The stable M/G/1 queue in heavy traffic and its covariance function
- 1 March 1977
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (1) , 169-186
- https://doi.org/10.2307/1425823
Abstract
Let X(t) be the virtual waiting-time process of a stable M/G/1 queue. Let R(t) be the covariance function of the stationary process X(t), B(t) the busy-period distribution of X(t); and let E(t) = P{X(t) = 0|X(0) = 0}.For X(t) some heavy-traffic results are given, among which are limiting expressions for R(t) and its derivatives and for B(t) and E(t).These results are used to find the covariance function of stationary Brownian motion on [0, ∞).Keywords
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