Performance Evaluation of an Erlang Loss System with Server Failures

Abstract

Loss models of fixed capacity constitute a fundamental tool in teletraffic theory, with the classical Erlang loss model being widely used for dimensioning purposes. In practical communication systems, however, server failures and repairs introduce time-varying capacity, significantly affecting call blocking probabilities (CBPs). This paper studies an Erlang loss system where busy servers may fail. Failed servers are repaired by either a shared or a non-shared repair facility, while in-service calls are lost upon server failure. Three approaches for determining CBP in the shared and non-shared repair cases are examined. The first provides exact results by solving a 2D Markov chain but becomes computationally demanding for large systems. The second, known as the performability method, offers a simple approximation but allows failures of idle servers. The third approximate approach employs state aggregation while restricting failures to busy servers. These approximate solutions offer computational efficiency, but they cannot ensure consistently accurate performance. To circumvent this limitation, we propose a novel method for the exact and efficient determination of CBPs. Analytical comparisons show that: (1) the third approach consistently outperforms the performability method and (2) the proposed method outperforms the approximate methods in both the shared and the non-shared repair cases.