A Stochastic Network Under Proportional Fair Resource Control---Diffusion Limit with Multiple Bottlenecks

Authors:
Heng-Qing Ye;David D. Yao
Affiliations:
Department of Logistics and Maritime Studies, Hong Kong Polytechnic University, Hong Kong;Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Venue:
Operations Research
Year:
2012

Citing 10
Cited 1

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
An invariance principle for semimartingale reflecting Brownian motions in an orthant

Queueing Systems: Theory and Applications
State space collapse with application to heavy traffic limits for multiclass queueing networks

Queueing Systems: Theory and Applications
Heavy traffic resource pooling in parallel-server systems

Queueing Systems: Theory and Applications
Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cµ-Rule

Operations Research
Stability of Data Networks: Stationary and Bursty Models

Operations Research
Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation

Operations Research
Utility-Maximizing Resource Control: Diffusion Limit and Asymptotic Optimality for a Two-Bottleneck Model

Operations Research

Interchange of limits in heavy traffic analysis under a moment condition

ACM SIGMETRICS Performance Evaluation Review

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study a multiclass stochastic processing network operating under the so-called proportional fair allocation scheme, and following the head-of-the-line processor-sharing discipline. Specifically, each server's capacity is shared among the job classes that require its service, and it is allocated, in every state of the network, among the first waiting job of each class to maximize a log-utility function. We establish the limiting regime of the network under diffusion scaling, allowing multiple bottlenecks in the network, and relaxing some of the conditions required in prior studies. We also identify the class of allocation schemes among which the proportional fair allocation minimizes a quadratic cost objective function of the diffusion-scaled queue lengths, and we illustrate the limitation of this asymptotic optimality through a counterexample.