Dynamic Routing in Stochastic

This paper reviews some current work on routing in loss and queueing networks. We describe two classes of bound on the performance of any dynamic routing scheme, together with some open questions concerning whether the bounds can be approached under certain limiting regimes. The rst class of bound is particularly appropriate for networks in heavy traac, where the key feature of a good routing scheme is its eeective utilization of various pooled resources identiied by a uid version of the routing problem. The second class of bound is particularly appropriate for highly connected networks, with many alternative paths. Again, a network ow representation is central, but this time involving a collection of Markov decision processes, one for each resource of the network. Despite their simplicity, the bounds are able to identify the great variety of qualitatively distinct behaviour expected of a good dynamic routing scheme, depending on a network's size, connectivity, asymmetry and degree of overload.