Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65444
Title: Diffusion limit of fair resource control-stationarity and interchange of limits
Authors: Ye, HQ 
Yao, DD
Keywords: Diffusion limit
Interchange of limits
Proportional fair allocation
Stationary distribution
Stochastic processing network
Uniform stability
Issue Date: 2016
Publisher: Institute for Operations Research and the Management Sciences
Source: Mathematics of operations research, 2016, v. 41, no. 4, p. 1161-1207 How to cite?
Journal: Mathematics of operations research 
Abstract: We study a resource-sharing network where each job requires the concurrent occupancy of a subset of links (servers/resources), and each link's capacity is shared among job classes that require its service. The real-Time allocation of the service capacity among job classes is determined by the so-called "proportional fair" scheme, which allocates the capacity among job classes taking into account the queue lengths and the shadow prices of link capacity. We show that the usual traffic condition is necessary and sufficient for the diffusion limit to have a stationary distribution. We also establish the uniform stability of the prelimit networks, and hence the existence of their stationary distributions. To justify the interchange of two limits, the limit in time and limit in diffusion scaling, we identify a bounded workload condition, and show it is a sufficient condition to justify the interchange for the stationary distributions and their moments. This last result is essential for the validity of the diffusion limit as an approximation to the stationary performance of the original network. We present a set of examples to illustrate justifying the validity of diffusion approximation in resource-sharing networks, and also discuss extensions to other multiclass networks via the well-known Kumar-Seidman/Rybko-Stolyar model.
URI: http://hdl.handle.net/10397/65444
ISSN: 0364-765X
EISSN: 1526-5471
DOI: 10.1287/moor.2015.0773
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