Blocking probability in a switching center with arbitrary routing policy

We model the arrival of calls at a switch where they are assigned to any one of the available idle outgoing links. A call is blocked if all links are busy. It may be lost after assignment to an idle link with a probability that depends on the link. For the case of Poisson arrivals and exponential holding times, all show that the distribution of passage time to the blocked state is independent of the assignment policy. As a consequence, the blocking probability and the law of the overflow traffic are also independent of the assignment policy.