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

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:
2010

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Abstract

We study a stochastic network that consists of two servers shared by two classes of jobs. Class 1 jobs require a concurrent occupancy of both servers while class 2 jobs use only one server. The traffic intensity is such that both servers are bottlenecks, meaning the service capacity is equal to the offered workload. The real-time allocation of the service capacity among the job classes takes the form of a solution to an optimization problem that maximizes a utility function. We derive the diffusion limit of the network and establish its asymptotic optimality. In particular, we identify a cost objective associated with the utility function and show that it is minimized at the diffusion limit by the utility-maximizing allocation within a broad class of “fair” allocation schemes. The model also highlights the key issues involved in multiple bottlenecks.