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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.

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