Call admission and routing controls for loss (circuit-switched) networks with semi-
Markovian, multi-class call arrivals and general connection durations, were formulated as optimal
stochastic control problems in [12, 13]. Each of the resulting so-called (network) hybrid HJB equations
corresponds to a collection of coupled first-order partial differential equations for which, when it
exists, the continuously differentiable value function is a solution to the associated hybrid HJB
equations. In general, the smoothness of the value functions and uniqueness of the solutions to
the hybrid HJB equations may not hold. In this paper, viscosity solutions to a general class of
hybrid HJB equations are developed and under mild conditions it is shown that the value function is
continuous and, further, any continuous value function is the unique viscosity solution to the hybrid
HJB equations.