Effective bandwidths at multi-class queues
Queueing Systems: Theory and Applications
Effective bandwidths for the multi-type UAS channel
Queueing Systems: Theory and Applications
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
End-to-end congestion control for the internet: delays and stability
IEEE/ACM Transactions on Networking (TON)
Bandwidth sharing: objectives and algorithms
IEEE/ACM Transactions on Networking (TON)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
On performance bounds for balanced fairness
Performance Evaluation - Internet performance symposium (IPS 2002)
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We consider a multi-class single server queueing network as a model of a packet switching network. We discuss how such networks perform a proportionally fair optimization when congested. We discuss the connections between product form queueing networks, insensitivity and proportional fairness. We prove that stationary throughput of a closed multi-class single server queueing network converges to a proportionally fair allocation as the number of packets across routes increases. We then let the rate packets enter different routes of the network be controlled by congestion windows, which record the number of sent but not yet acknowledged packets on each route of the network. By considering a sequence of such congestion windows we allow the network to become congested. We show that these networks maximize aggregate utility subject to the networks capacity constraints. To perform this analysis we require our utility functions to satisfy an exponential concavity assumption. This family of utility functions includes the weighted α-fair family of utilities for parameter α 1.