Routing traffic in telephone networks

Telephone calls arriving at a switching center must be assigned to any one of the outgoing trunks which has idle links. With probability 1-??i the call may be lost due to congestion in subsequent trunks along the route, and with probability ??i the call is successful, and then the links along the route remain busy for an exponential holding time. If the ??i do not depend on the routing policy, then assigning the call to the trunk with largest such ??i minimizes the expected number of lost calls. When ??i does depend upon the policy, a suboptimal policy combining overflow and load sharing is proposed.