An escape-time criterion for queueing networks: asymptotic risk-sensitive control via differential games. (English) Zbl 1082.60520

Atar, Rami; Dupuis, Paul; Shwartz, Adam

Math. Oper. Res. 28, No. 4, 801-835 (2003).

Summary: 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. 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.

MSC:

60K25	Queueing theory (aspects of probability theory)
49N70	Differential games and control
90B22	Queues and service in operations research
91A23	Differential games (aspects of game theory)

Keywords:

Queueing network; stochastic control