Abstract
In this chapter a stochastic hybrid systems framework is established for the formulation of call admission control (CAC) and routing control (RC) problems in networks. The hybrid state process of the underlying system is a piecewise deterministic Markovian process (PDMP) evolving deterministically between random event instants at which times the state jumps to another state value. The random events in the system correspond to the arrival of call requests or the departure of connections. The resulting NETCAD stochastic state space systems framework permits the formulation and analysis of centralized optimal stochastic control with respect to specified utility functions. The NETCAD framework permits the formulation and analysis of centralized optimal stochastic control with respect to specified utility functions; in particular, this entails the derivation of the Hamilton-Jacobi-Bellman equation for optimally controlled NETCAD systems.
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