STATE-DEPENDENT ROUTING ON SYMMETRICAL LOSS NETWORKS WITH TRUNK RESERVATIONS .1.

We investigate a distributed, state-dependent, dynamic routing strategy, called here aggregated-least-busy-alternative (ALBA), for circuit-switched loss networks. The networks considered are symmetric and fully connected, the offered calls form Poisson streams, and routes have at most two links. In ALBA (K), the states of each link are lumped into K (K greater-than-or-equal-to 2) aggregates, and the route of each call is determined by local information on the aggregate states of the links of the alternate routes at the time of that call's arrival. The last aggregate is always the set of states reserved for direct traffic. We give a fixed-point model for ALBA(K) for general K. The particular case of ALBA in which there is no aggregation is least-busy-alternative (LBA); ALBA(2) represents the other extreme of aggregation. We compare simulation and analytic results for LBA, and find the agreement surprisingly good. The structure of solutions computed here for LBA implies that with just a few properly designed aggregates, it is possible to closely approximate the solution (and thus the performance) of LBA. This is confirmed by results presented here on the comparative performances of LBA and ALBA(K), K = 2,3,4. We also consider an asymptotic scaling based on the fixed-point models. It is shown that there is a dichotomy in network behavior: if the offered traffic is below a threshold, then the network loss probability decreases exponentially with increasing network size, and above the threshold, performance is poor. Hence, the threshold sharply delineates ''engineered'' designs.