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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Bibliographic Details
Published in:Operations research Vol. 56; no. 2; pp. 453 - 470
Main Authors: Ye, Heng-Qing, Yao, David D
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.03.2008
Institute for Operations Research and the Management Sciences
Subjects:
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
United States
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
ISSN:0030-364X, 1526-5463
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Summary: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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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0455