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The average virtual waiting time as a measure of performance. (English) Zbl 0707.60089

Let \(\{Y_ t\}\) be the virtual waiting time in the M/G/1 queue and \(M(t)=E Y(t)\). If \(\rho <1\), \(M(\infty)=\lim M(t)\) exists as \(t\to \infty\), and it is shown that \(M(\infty)-M(t)=o(e^{-\theta t})\) where the constant \(\theta\) is familiar from large deviations theory. Further, the estimation of \(\theta\) from empirical data is discussed. If \(\rho >1\), similar discussion is given for \(\bar M(\infty)-\bar M(t)\), where \(\bar M(t)=M(t)-(\rho -1)t\).
Reviewer: S.Asmussen

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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References:

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