Proof of a fundamental result in self-similar traffic modeling
ACM SIGCOMM Computer Communication Review
A heavy-traffic analysis of a closed queueing system with a GI/\infty service center
Queueing Systems: Theory and Applications
On–off fluid models in heavy traffic environment
Queueing Systems: Theory and Applications
A flow-based model for internet backbone traffic
Proceedings of the 2nd ACM SIGCOMM Workshop on Internet measurment
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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The paper deals with the fluid limits of some generalizedM/G/∞ queues under heavy-traffic scaling. Thetarget application is the modeling of Internet traffic at the flowlevel. Our paper first gives a simplified approach in the case ofPoisson arrivals. Expressing the state process as a functional ofsome Poisson point process, an elementary proof for limit theoremsbased on martingales techniques and weak convergence results isgiven. The paper illustrates in the special Poisson arrivals casethe classical heavy-traffic limit theorems for theG/G/∞ queue developed earlier by Borovkov andby Iglehart, and later by Krichagina and Puhalskii. In addition,asymptotics for the covariance of the limit Gaussian processes areobtained for some classes of service time distributions, which areuseful to derive in practice the key parameters of thesedistributions.