On-line routing of random calls in networks

We consider a random sequence of calls between nodes in a complete network with link capacities. Each call first tries the direct link. If that link is saturated, then the `first-fit dynamic alternative routing algorithmʹ sequentially selects up to d random two-link alternative routes, and assigns the call to the first route with spare capacity on each link, if there is such a route. The `balanced dynamic alternative routing algorithmʹ simultaneously selects d random two-link alternative routes; and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated. We determine the capacities needed for these algorithms to route calls successfully, and find that the second `balancedʹ algorithm requires a much smaller capacity. Our results strengthen and extend the discrete-time results presented in [10].