State-dependent routing for telephone traffic: Theory and results

In the modern telephone network, it has become feasible to consider sophisticated call-routing schemes in order to minimize network blocking --- in particular, routing schemes which select a route for a call on the basis of the network 'state' at the time of call-arrival. In this paper, we construct an analytical model for such state-dependent routing in the framework of Markov decision processes, and derive a simple state-dependent routing scheme called 'separable' routing. The performance of this routing scheme in two network designs for a metropolitan network model is compared over a range of loads, by means of call-by-call simulations of traffic flow, with that of two other schemes: the 'sequential' routing used in the Dynamic Non-Hierarchical Routing (DNHR) network, and the 'Least-Loaded Routing' (LLR) proposed for the Trunk Status Map. In one case, separable routing achieves lower network blocking than the other schemes at normal load and overloads, while, in the other case, the improvement occurs only above a certain level of overload. However, a modified version of separable routing (to be presented in a future paper) achieves better performance than the other schemes in both networks over the entire range of loads.