Explicit Solution to a Robust Queueing Control Problem

We consider the robust optimal control of a law of large numbers approximation of a stochastic network. The robust control problem is formulated as a di®erential game, with one player choosing the policies that determine service and routing assignments, and the other choosing quantities such as the arrival and service rates, subject to constraints. The cost to be minimized by the ̄rst player and maximized by the second is the time till the origin is reached. An explicit formula is given for the value function, and some of its basic properties are studied.