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Asymptotic results for multiplexing subexponential on-off processes. (English) Zbl 0952.60098
Fluid queueing models for ATM (asynchronous transfer mode) in telecommunications are considered, where $$N$$ sources transmit fluid into the buffer during their ON periods. The buffer is emptied at rate $$c$$, and OFF periods are assumed to be exponential, ON periods to have a heavy-tailed subexponential distribution. First the tail of the activity period (the period where not all sources are idle) is determined asymptotically. Much of the rest of the paper then deals with an M/G/$$\infty$$ model obtained as limit when $$N\to\infty$$ and sources are slowed down in the appropriate way. The increase in fluid content during an activity period is studied, and the asymptotic distribution of the steady-state fluid content is determined under the more restrictive assumption of regular variation; in the general subexponential case, the results give a lower bound. A key tool is Abelian and Tauberian results for Laplace transforms.
Reviewer: S.Asmussen (Lund)

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 60G50 Sums of independent random variables; random walks
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