Fluid limits for an ALOHA-type model with impatient customers

Maria Frolkova-Remerova, Serguei Foss, Bert Zwart

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Random multiple-access protocols of type ALOHA are used to regulate networks with a star configuration where client nodes talk to the hub node at the same frequency (finding a wide range of applications among telecommunication systems, including mobile telephone networks and WiFi networks). Such protocols control who talks at what time sharing the common idea "try to send your data and, if your message collides with another transmission, try resending later".
In the present paper, we consider a time-slotted ALOHA model where users are allowed to renege before transmission completion. We focus on the scenario that leads to overload in the absence of impatience. Under mild assumptions, we show that the fluid (or law-of-large-numbers) limit of the system workload coincides a.s. with the unique solution to a certain integral equation. We also demonstrate that the fluid limits for distinct initial conditions converge to the same value as time tends to infinity.
Original languageEnglish
Pages (from-to)69-101
Number of pages33
JournalQueueing Systems
Volume72
Issue number1-2
DOIs
Publication statusPublished - 1 Oct 2012

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