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Transient behavior of the \(M/G/1\) workload process. (English) Zbl 0833.90042
The authors describe the time-dependent moments of the workload process in the M/G/1 queue. The \(k\)th moment as a function of time can be characterized in terms of a differential equation involving lower moment functions and the time-dependent server-occupation probability.
For general initial conditions it is shown that the first two moment functions can be represented as the difference of two nondecreasing functions, one of which is the moment function starting at zero. Results for the covariance function of the stationary workload process are also obtained.
It is interesting that the various time-dependent characteristics can be described directly in terms of the steady-state workload distribution.

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