Performance Evaluation of an Erlang Loss System with Server Failures and a Single Repair Facility

Loss models of fixed capacity constitute a fundamental tool in teletraffic theory, with the classical Erlang loss model being widely used for dimensioning purposes. However, practical communication systems often experience time-varying capacity due to server failures and repairs, which significantly affects Call Blocking Probabilities (CBP). This paper studies an Erlang loss system where busy servers may fail. Failed servers are repaired by a single shared repair facility, while in-service calls are lost upon server failure. Three different approaches for determining CBP are examined. The first one provides exact results through the solution of a 2D Markov chain but becomes computationally demanding for large systems. The second one, known as the performability method, offers a simple approximation but allows failures of idle servers. The third approach employs state aggregation and restricts failures to busy servers. Through analytical comparisons, we evaluate the accuracy of the two approximate methods against the exact solution. Results show that the third approach consistently outperforms the performability method.