Utility-maximizing resource control: Diffusion limit and asymptotic optimality for a two-bottleneck model

Utility-maximizing resource control: Diffusion limit and asymptotic optimality for a two-bottleneck model

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Article ID: iaor20104778
Volume: 58
Issue: 3
Start Page Number: 613
End Page Number: 623
Publication Date: May 2010
Journal: Operations Research
Authors: ,
Keywords: networks, queues: theory, allocation: resources
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.

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