G-2007-54
On the Viscosity Solutions of Hybrid HJB Equations Arising in Loss Network System Control
, , and BibTeX reference
In Z. Ma, P.E. Caines, and R.P. Malhamé,
``Control of Loss Network Systems: Call Admission and Routing Control",
(submitted to SIAM J. Control and Optimization), the call admission control (CAC) and routing
control (RC) problems for loss network systems were formulated as
optimal stochastic control (OSC) problems. The HJB equation for loss
network OSC problems is an array of first order PDEs which are
coupled with each other by sets of integral coefficients. In the
case where the value function is a set of continuously differentiable functions, V is a
classical solution to the associated loss network HJB PDEs. But, in
general, the smoothness of V or uniqueness of the classical
solutions to the HJB PDEs may not hold. In this paper we develop the
viscosity solutions to the HJB PDEs and show that, under mild
conditions, the value function V is continuous and, further,
subject to mild conditions any continuous value function is the
unique viscosity solution to the HJB PDEs.
Published July 2007 , 36 pages