A differential game formulation of a controlled network

Authors:
Hui-Ming Pai
Affiliations:
Department of Statistics, National Taipei University, Taipei, Taiwan 237
Venue:
Queueing Systems: Theory and Applications
Year:
2010

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Abstract

This paper considers multiclass queueing network systems with fixed routing. With the service control as one player and the arrival and service rates as the other, the problem of network regulation can be formulated as a differential game. Representations of the value function are developed by studying the geometric properties of the associated Hamiltonians and are expressed in terms of related simpler halfspace problems. Also, a method of constructing the optimal feedback controls through the representation and the projected Isaacs equations is provided. The controls so constructed give both a guaranteed level of performance and robust stability over a range of rate perturbations.