The Annals of Applied Probability

Network stability under max–min fair bandwidth sharing

Maury Bramson

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Abstract

There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massoulié and Roberts [Telecommunication Systems 15 (2000) 185–201], that represents the randomly varying number of flows present in a network. The weighted α-fair and weighted max–min fair bandwidth sharing policies are among important policies that have been studied for this model. Stability results are known in both cases when the interarrival times and service times are exponentially distributed. Partial results for general service times are known for weighted α-fair policies; no such results are known for weighted max–min fair policies. Here, we show that weighted max–min fair policies are stable for subcritical networks with general interarrival and service distributions, provided the latter have 2+δ1 moments for some δ1>0. Our argument employs an appropriate Lyapunov function for the weighted max–min fair policy.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 3 (2010), 1126-1176.

Dates
First available in Project Euclid: 18 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1276867309

Digital Object Identifier
doi:10.1214/09-AAP649

Mathematical Reviews number (MathSciNet)
MR2680560

Zentralblatt MATH identifier
1208.60087

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B15: Network models, stochastic

Keywords
Bandwidth sharing max–min fair stability

Citation

Bramson, Maury. Network stability under max–min fair bandwidth sharing. Ann. Appl. Probab. 20 (2010), no. 3, 1126--1176. doi:10.1214/09-AAP649. https://projecteuclid.org/euclid.aoap/1276867309


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