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Transient characteristics of an $$M/M/\infty$$ system. (English) Zbl 0829.60058
Summary: Convergence results are given for transient characteristics of an $$M/M/ \infty$$ system such as the period of time the occupation process remains above a given state, the area swept by this process above this state and the number of customers arriving during this period. These results are precise in contrast to approximations derived in the framework of the Poisson clumping heuristic introduced by D. Aldous [“Probability approximations via the Poisson clumping heuristic” (1989; Zbl 0679.60013)].

##### MSC:
 60J05 Discrete-time Markov processes on general state spaces 30E15 Asymptotic representations in the complex plane 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems 60K25 Queueing theory (aspects of probability theory)
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