Modelling Random Fluctuations in a Bistable Telecommunications Network

Phil Pollett

Abstract: I shall consider a model for the simplest kind of dynamic routing in a telecommunications 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 system can exhibit bistability: it 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. Bistability can have serious implications for the performance of the network, for in the high-blocking state a situation can develop where large numbers of calls use alternative routes, which generally demand greater link occupancy than do first-choice routes and, thus, new calls are likely to be blocked frequently. The high-blocking state tends to persist because, even when calls are accepted, they are allocated first-choice routes rather rarely. I shall describe a method which allows one to assess the stability of the two states by providing qualitative estimates of the time for which they persist. I shall also indicate some strategies for removing bistability.

Acknowledgement: This worked was funded by the Australian Research Council.

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Last modified: 10th July 1996