Approximate blocking probabilities in loss models with independence and distribution assumptions relaxed

Effective approximations are developed for the blocking probability in a general stationary loss model, where key independence and exponential-distribution assumptions are relaxed, giving special attention to dependence among successive service times, not studied before. The new approximations exploit recent heavy-traffic limits for the steady-state number of busy servers in the associated infinite-server model with the same arrival and service processes. In addition, a new heavy-traffic approximation is developed for the long-run proportion of time that all servers are busy. These new approximations are then combined to develop new approximations for the separate blocking probabilities of individual arrival streams in multi-class loss models. Simulation experiments show that these approximations are effective.