An escape time criterion for queueing networks: Asymptotic risk-sensitive control via differential games

Details An escape time criterion for queueing networks: Asymptotic risk-sensitive control via differential games An escape time criterion for queueing networks: Asymptotic risk-sensitive control via differential games

2005-01-03

arxiv.org/abs/math/0501031v1

Math. Op. Res., 28 no. 4 p. 801-835 (2003)

Mathematics

Probability

Scientific paper

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 which 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.

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