Redialing policies: Optimality and success probabilities

Since callers encountering busy signals often want to redial, modern commun ication networks have been designed to provide automatic redialing. Rediali ng services commonly have two parameters: a maximum number n of retries and a total duration tau over which retries are to be made. Typically, retries are made at evenly spaced time intervals of length tau/n until either the call succeeds or n retries have failed. This rule has an obvious intuitive appeal; indeed, among the main results of this paper are proofs that tau/n- spacing is optimal in certain basic models of called-number behavior. Howev er, it is easy to find situations where tau/n-spacing is not optimal, as th e paper verifies. All of our models assume Poisson arrivals, but different assumptions are st udied for the call durations; for a given mean, these are allowed to have t he relatively high-variance exponential distribution or the zero-variance d istribution concentrated at a point. We approximate the probability of succ ess for the Erlang loss model with c > 1 trunks, and we calculate exact pro babilities of success for the c = 1 Erlang model and the model with one tru nk and constant call durations. For the latter model, we present two intrig uing conjectures, one about the optimal choice of tau when n = 1 and one ab out the optimality of the tau/n-spacing policy. In spite of their apparent simplicity, these conjectures seem difficult to resolve. Finally, we study policies that continue redialing until they succeed, balancing a short mean wait against a small mean number of retries to success.