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Queueing Systems 46, 159176, 2004 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.

Summary: Queueing Systems 46, 159­176, 2004
2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Explicit Solution for a Network Control Problem in the
Large Deviation Regime
RAMI ATAR and ADAM SHWARTZ {atar;adam}@ee.technion.ac.il
Department of Electrical Engineering, Technion ­ Israel Institute of Technology, Haifa 32000, Israel
PAUL DUPUIS dupuis@dam.brown.edu
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence,
RI 02912, USA
Received 23 October 2002; Revised 14 August 2003
Abstract. We consider optimal control of a stochastic network, where service is controlled to prevent
buffer overflow. We use a risk-sensitive escape time criterion, which in comparison to the ordinary escape
time criteria heavily penalizes exits which occur on short time intervals. A limit as the buffer sizes tend
to infinity is considered. In [2] we showed that, for a large class of networks, the limit of the normalized
cost agrees with the value function of a differential game. In this game, one player controls the service
discipline (who to serve and whether to serve), and the other player chooses arrival and service rates in the
network. The game's value is characterized in [2] as the unique solution to a Hamilton­Jacobi­Bellman
Partial Differential Equation (PDE). In the current paper we apply this general theory to the important case
of a network of queues in tandem. Our main results are: (i) the construction of an explicit solution to the
corresponding PDE, and (ii) drawing out the implications for optimal risk-sensitive and robust regulation


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


Collections: Engineering