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Queueing Systems

, Volume 56, Issue 2, pp 79–92

First Online: 19 June 2007Received: 06 March 2006Revised: 16 May 2007

Abstract

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c-n+1, where the remaining c-n+1 is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: i the stationary workload of the queue, ii the queueing delay, i.e., the delay of a ‘packet’ a fluid particle that arrives at the queue at an arbitrary point in time, iii the flow transfer delay, i.e., the time elapsed between arrival of a flow and the epoch that all its traffic has been put into the queue, and iv the sojourn time, i.e., the flow transfer time increased by the time it takes before the last fluid particle of the flow is served. For each of these random variables we compute the Laplace transform. The corresponding tail probabilities decay exponentially, as is shown by a large-deviations analysis.

KeywordsFluid queues Flow-level analysis Sojourn times Ad hoc networks M. Mandjes’ work has been carried out partly in the Dutch BSIK-BRICKS project.

F. Roijers’ work has been carried out partly in the SENTER-NOVEM funded project Easy Wireless.

Mathematics Subject Classification 200060K25  Download to read the full article text



Autor: Michel Mandjes - Frank Roijers

Fuente: https://link.springer.com/



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