Groupe d’études et de recherche en analyse des décisions

G-2007-53

Control of Loss Network Systems: Call Admission and Routing Control

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In this paper the call admission control (CAC) and routing control (RC) problems for loss network systems are studied as optimal stochastic control (OSC) problems. The so-called pre-state process of the underlying system is a piecewise deterministic Markov process (PDMP) evolving deterministically between (random) event instants at which times the pre-state jumps to another value. The random events in the system correspond to the arrival of call requests or the departure of (active) connections. In the principal result the Hamilton-Jacobi-Bellman (HJB) equations are derived for the underlying stochastic optimal control problems; Unlike the usual single HJB scalar partial differential equation, we now have a finite collection of those, inducing coupling within a finite family of integer indexed value functions. The number of such coupled equations is equal to the number of admissible connection states within the network. Analytical expressions of optimal controls are derived for some simple loss network systems.

, 48 pages