Loss Models with Dependent Service Times

Effective approximations are developed for the blocking probability in a general stationary loss model with dependence among successive service times as well as among successive interarrival times by exploiting 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 effective approximations for the separate blocking probabilities of individual arrival streams in multi-class loss models.