Path assignment for virtual circuit routing

We consider a network which routes on a virtual-circuit. Each virtual-circuit is associated with a session. Virtual-circuit is assigned to a session at the time the session is initiated. We address the dynamic case where new sessions arrive and old sessions terminate. We formulate an optimal control problem to deduce which virtual-circuit an incoming session will be assigned to. We then discuss various approximations to the problem and show that the heuristic rule, "route on the shortest marginal delay path", is close to optimal in an asympotic sense.