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Available online at www.sciencedirect.com Systems & Control Letters 51 (2004) 269275

Summary: Available online at www.sciencedirect.com
Systems & Control Letters 51 (2004) 269­275
A Brownian control problem for a simple queueing system
in the Hal˙n­Whitt regime
Rami Atara;;1, Avi Mandelbauma;2, Martin I. Reimanb
aTechnion, I.I.T., Haifa 32000, Israel
bBell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA
Received 22 May 2002; received in revised form 1 January 2003; accepted 4 September 2003
We consider a formal di usion limit for a control problem of a multi-type multi-server queueing system, in the regime
proposed by Hal˙n and Whitt. This takes the form of a control problem where the dynamics are driven by a Brownian
motion. In one dimension, a pathwise minimum is obtained and is characterized as the solution to a stochastic di erential
equation. The pathwise solution to a special multi-dimensional problem (corresponding to a multi-type system) follows.
c 2003 Elsevier B.V. All rights reserved.
Keywords: Queueing networks; Stochastic control; Heavy tra c asymptotics
1. Introduction
Brownian control problems (BCPs) were proposed
by Harrison [8] as formal di usion limits for queue-
ing network control problems, to provide a basis for


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering