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MATHEMATICS OF OPERATIONS RESEARCH Vol. 28, No. 4, November 2003, pp. 801835
 

Summary: MATHEMATICS OF OPERATIONS RESEARCH
Vol. 28, No. 4, November 2003, pp. 801835
Printed in U.S.A.
AN ESCAPE-TIME CRITERION FOR QUEUEING NETWORKS:
ASYMPTOTIC RISK-SENSITIVE CONTROL
VIA DIFFERENTIAL GAMES
RAMI ATAR, PAUL DUPUIS, and ADAM SHWARTZ
We consider the problem of risk-sensitive control of a stochastic network. In controlling such a
network, an escape-time criterion can be useful if one wishes to regulate the occurrence of large
buffers and buffer overflow. In this paper a risk-sensitive escape time criterion is formulated, which
in comparison to the ordinary escape-time criteria penalizes exits that occur on short time intervals
more heavily. The properties of the risk-sensitive problem are studied in the large buffer limit and
related to the value of a deterministic differential game with constrained dynamics. We prove that
the game has value and that the value is the (viscosity) solution of a PDE. For a simple network,
the value is computed, demonstrating the applicability of the approach.
1. Introduction. In this paper we consider a problem of risk-sensitive control (or rare
event control) for queueing networks. The network includes servers that can offer service
to two or more classes of customers, and a choice must be made regarding which classes
to offer service at each time. We study a stochastic control problem in which this choice is
regarded as the control and where the cost is a risk-sensitive version of the time to escape

  

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

 

Collections: Engineering