Diffusion Approximations for a Circuit Switching Network with Random Alternative Routing

In this paper I shall consider a model for the simplest kind of dynamic routing in a circuit-switched network, namely Random Alternative Routing: if a call cannot be carried on a first-choice route, then a second-choice route is chosen at random from a fixed set of alternatives. This kind of routing can give rise to several modes of behaviour. For example, the simple model I shall consider can exhibit bistability; the system fluctuates between a low-blocking state, where calls are accepted readily, and a high-blocking state, where the likelihood of a call being accepted can be quite low. I shall describe a method which enables one to assess the stability of the two states. In particular, it allows one to obtain qualitative estimates of the time for which these states persist.