Bounds on the Accuracy of the Reduced-Load Blocking Formula in Some Simple Circuit-Switched Networks

Circuit switched communication networks are considered in which each route is two links long, and each link can carry one call at a time. No symmetry assumption is made. Simple bounds, depending on the maximum call arrival rate and the maximum sum of rates at a link, are given on the blocking probabilities. An implication is that if the maximum perroute arrival rate converges to zero with a fixed bound on the sum of rates at links, then the well known reduced-load blocking approximation is asymptotically exact, uniformly over all network topologies.