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Limits for cumulative input processes to queues. (English) Zbl 0979.60089
This is part of a series of articles devoted to obtaining approximations via limit theorems for stochastic fluid queues and stochastic fluid queueing networks with bursty input. It contains functional limit theorems for a cumulative input process associated with on-off sources, where the on-periods and off-periods may have heavy-tailed probability distributions. It also has results for cumulative busy-time and idle-time processes. Under independence assumptions, the limiting processes are reflected stable processes or more generally reflected Lévy processes. However, the general limit theorems apply without the independence assumptions.

MSC:
60K25 Queueing theory (aspects of probability theory)
60F17 Functional limit theorems; invariance principles
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