Article ID: | iaor20164228 |
Volume: | 41 |
Issue: | 4 |
Start Page Number: | 1161 |
End Page Number: | 1207 |
Publication Date: | Nov 2016 |
Journal: | Mathematics of Operations Research |
Authors: | Ye Heng-Qing, Yao David D |
Keywords: | combinatorial optimization, scheduling, networks, service, queues: applications |
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