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Heavy-Traffic Optimality of a Stochastic Network under Utility-Maximizing Resource Control

Heng-Qing Ye·David D. Yao
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Abstract

We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job classes in a head-of-the-line processor-sharing mechanism. The allocation of the service capacities is a real-time control mechanism: in each network state, the control is the solution to an optimization problem that maximizes a general utility function. Whereas this resource control optimizes in a ``greedy'' fashion, with respect to each state, we establish its asymptotic optimality in terms of (a) deriving the fluid and diffusion limits of the network under this control, and (b) identifying a cost function that is minimized in the diffusion limit, along with a characterization of the so-called fixed point state of the network.

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Heng-Qing Ye, David D. Yao. 2006-01-05. Heavy-Traffic Optimality of a Stochastic Network under Utility-Maximizing Resource Control. https://arxiv.org/abs/math/0601088

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