Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Fair end-to-end window-based congestion control
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
On Stochastic Bounds for Monotonic Processor Sharing Networks
Queueing Systems: Theory and Applications
Heavy-traffic approximations for linear networks operating under α-fair bandwidth-sharing policies
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Flow-level stability of data networks with non-convex and time-varying rate regions
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Stability of Parallel Queueing Systems with Coupled Service Rates
Discrete Event Dynamic Systems
Monotonicity Properties for Multi-Class Queueing Systems
Discrete Event Dynamic Systems
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In bandwidth-sharing networks, users of various classes require service from different subsets of shared resources simultaneously. These networks have been proposed to analyze the performance of wired and wireless networks. For general arrival and service processes, we give sufficient conditions in order to compare sample-path wise the workload and the number of users under different policies in a linear bandwidth-sharing network. This allows us to compare the performance of the system under various policies in terms of stability, the mean overall delay and the weighted mean number of users. For the important family of weighted α-fair policies, we derive stability results and establish monotonicity of the weighted mean number of users with respect to the fairness parameter α and the relative weights. In order to broaden the comparison results, we investigate a heavy-traffic regime and perform numerical experiments.