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Robust formulation of a network control problem

A very simple model for a queueing network is one where the queue lengths are represented as a vector, and where they change in time according to a deterministic mechanism. On the boundary of the state space, constraint directions are defined that properly correct the dynamics when one or more of the queues are empty, and arrival and service rates are allowed to be functions of time. In this paper we study a model of this kind, where the goal is the optimal robust design of network controls. We define a game played between two players, each one controlling one of these sets of variables, where the cost is the time till the origin is hit. A solution to the game gives an optimal robust policy for the control of the network (through service allocations) under changes in input and service rates. The paper formulates the game, states an analytic characterization of the value function, and in the context of several examples comments on the robust properties of the service controls designed in this way.