Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation
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 all...
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| Published in: | Operations research Vol. 56; no. 2; pp. 453 - 470 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Linthicum, MD
INFORMS
01.03.2008
Institute for Operations Research and the Management Sciences |
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| ISSN: | 0030-364X, 1526-5463 |
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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 resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation 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 allocation scheme, 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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| AbstractList | 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 resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation 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 allocation scheme, 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. 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 resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation 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 allocation scheme, 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. Subject classifications: stochastic processing network; concurrent resource occupancy; utility-maximizing resource allocation; fluid limit; diffusion limit; resource pooling; heavy-traffic optimality; Lyapunov function. Area of review: Stochastic Models. 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 resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation 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 allocation scheme, 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. [PUBLICATION ABSTRACT] |
| Audience | Trade |
| Author | Yao, David D Ye, Heng-Qing |
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| Keywords | utility-maximizing resource allocation heavy-traffic optimality Utility function Resource allocation Asymptotic optimality Resource sharing resource pooling Real time diffusion limit Optimization fluid limit stochastic processing network Fixed point theorem Heavy traffic Cost function concurrent resource occupancy Lyapunov function |
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| SubjectTerms | Applied sciences Brownian motion Computer networks concurrent resource occupancy Cost functions diffusion limit Exact sciences and technology fluid limit heavy-traffic optimality Hyperlinks Information networks Integers Learning models (Stochastic processes) Lyapunov function Markov analysis Minimization of cost Network servers Operational research. Management science Optimal solutions Queueing networks Real time Resource allocation resource pooling Safety and security measures Stochastic models stochastic processing network Studies Transmission Control Protocol/Internet Protocol (Computer network protocol) Utility functions utility-maximizing resource allocation Workloads |
| Title | Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation |
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