| This thesis considers multi-class queueing network systems with fixed routing. With the control as one player and the arrival and service rates as the other, the problem can be formulated as a differential game in which the law of large number limit of risk sensitive control problem serves as a special case. Representations of the value function are developed by studying the geometric properties of the associated Hamiltonians. A set valued optimal feedback control is discovered. Also provided is the method of its construction by the representation and the projected Isaacs equations. Not only guarantees certain level of performance, the optimal feedback control also preserves robust stability over some ranges of rate perturbation. |
