How large delays build up in a GI/G/1 quqe
Queueing Systems: Theory and Applications
Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
Stability and performance analysis of networks supporting elastic services
IEEE/ACM Transactions on Networking (TON)
Impact of fairness on Internet performance
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Performance modeling of elastic traffic in overload
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Convex Optimization
The Fluid Limit of an Overloaded Processor Sharing Queue
Mathematics of Operations Research
Assessing the efficiency of resource allocations in bandwidth-sharing networks
Performance Evaluation
ACM SIGMETRICS Performance Evaluation Review
Rate stability and output rates in queueing networks with shared resources
Performance Evaluation
Fixed-point approximations of bandwidth sharing networks with rate constraints
ACM SIGMETRICS Performance Evaluation Review - Special Issue on IFIP PERFORMANCE 2011- 29th International Symposium on Computer Performance, Modeling, Measurement and Evaluation
Fluid models of congestion collapse in overloaded switched networks
Queueing Systems: Theory and Applications
Dynamic server allocation for unstable queueing networks with flexible servers
Queueing Systems: Theory and Applications
Short communication: Network iso-elasticity and weighted α-fairness
Performance Evaluation
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Bandwidth-sharing networks as considered by Massoulie and Roberts provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Under mild assumptions, it has been established that a wide family of so-called @a-fair bandwidth-sharing strategies achieve stability in such networks provided that no individual link is overloaded. In the present paper we focus on @a-fair bandwidth-sharing networks where the load on one or several of the links exceeds the capacity. Evidently, a well-engineered network should not experience overload, or even approach overload, in normal operating conditions. Yet, even in an adequately provisioned system with a low nominal load, the actual traffic volume may significantly fluctuate over time and exhibit temporary surges. Furthermore, gaining insight into the overload behavior is crucial in analyzing the performance in terms of long delays or low throughputs as caused by large queue build-ups. The way in which such rare events tend to occur, commonly involves a scenario where the system temporarily behaves as if it experiences overload. In order to characterize the overload behavior, we examine the fluid limit, which emerges from a suitably scaled version of the number of flows of the various classes. The convergence of the scaled number of flows to the fluid limit is empirically validated through simulation experiments. Focusing on linear solutions to the fluid-limit equation, we derive a fixed-point equation for the corresponding asymptotic growth rates. It is proved that a fixed-point solution is also a solution to a related strictly concave optimization problem, and hence exists and is unique. We use the fixed-point equation to investigate the impact of the traffic intensities and the variability of the flow sizes on the asymptotic growth rates. The results are illustrated for linear topologies and star networks as two important special cases. Finally, we briefly discuss extensions to models with user impatience.