Dynamic routing and admission control for virtual circuit networks

The dynamic joint routing and admission control problem in multiple class multiple source-destination virtual circuit networks is considered. A nonlinear dynamic queueing model for virtual circuit networks that considers the dynamic interaction among the virtual circuit and packet processes is introduced. Then a multi-objective cost function of rejecting and maintaining virtual circuits, as well as of delaying and servicing packets is defined. The combined problem is formulated as an optimal control problem. Necessary optimality conditions are provided by Pontryagin's maximum principle. Sufficient optimality conditions based on the convexity of the Hamiltonian function are also given. For the finite horizon, the optimal controls can be found after numerically solving a Two-Point Boundary-Value Problem. For the longrun stationary equilibrium, the state-dependent routing and admission controls are derived.This work was supported by the National Science Foundation under Grant DMC-8452002 together with matching funds from AT&T Information Systems.