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- Title
On the fluid limit of the M / G /∞ queue.
- Authors
Christine Fricker; M. Jaïbi
- Abstract
  The paper deals with the fluid limits of some generalized M/G/∞ queues under heavy-traffic scaling. The target application is the modeling of Internet traffic at the flow level. Our paper first gives a simplified approach in the case of Poisson arrivals. Expressing the state process as a functional of some Poisson point process, an elementary proof for limit theorems based on martingales techniques and weak convergence results is given. The paper illustrates in the special Poisson arrivals case the classical heavy-traffic limit theorems for the G/G/∞ queue developed earlier by Borovkov and by Iglehart, and later by Krichagina and Puhalskii. In addition, asymptotics for the covariance of the limit Gaussian processes are obtained for some classes of service time distributions, which are useful to derive in practice the key parameters of these distributions.
- Subjects
LIMIT theorems; STOCHASTIC processes; GAUSSIAN processes; MARTINGALES (Mathematics); DISTRIBUTION (Probability theory); PROBABILITY theory; ASYMPTOTIC distribution; POINT processes; POISSON processes; INTERNET users; STOCHASTIC convergence; QUEUING theory
- Publication
Queueing Systems, 2007, Vol 56, Issue 3/4, p255
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-007-9041-x