Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model

Abstract

In this paper first, we review two extensions of the Erlang multi-rate loss model (EMLM), whereby we can assess the call-level quality-of-service (QoS) of ATM networks. The call-level QoS assessment in ATM networks remains an open issue, due to the emerged elastic services. We consider the coexistence of ABR service with QoS guarantee services in a VP link and evaluate the call blocking probability (CBP), based on the EMLM extensions. In the first extension, the retry models, blocked calls can retry with reduced resource requirements and increased arbitrary mean residency requirements. In the second extension, the threshold models, for blocking avoidance, calls can attempt to connect with other than the initial resource and residency requirements which are state dependent. Secondly, we propose the connection-dependent threshold model (CDTM), which resembles the threshold models, but the state dependency is individualized among call-connections. The proposed CDTM not only generalizes the existing threshold models but also covers the EMLM and the retry models by selecting properly the threshold parameters. Thirdly, we provide formulas for CBP calculation that incorporate bandwidth/trunk reservation schemes, whereby we can balance the grade-of-service among the service-classes. Finally, we investigate the effectiveness of the models applicability on ABR service at call set-up. The retry models can hardly model the behavior of ABR service, while the threshold models perform better than the retry models. The CDTM performs much better than the threshold models; therefore we propose it for assessing the call-level performance of ABR service. We evaluate the above-mentioned models by comparing each other according to the resultant CBP in ATM networks. For the models validation, results obtained by the analytical models are compared with simulation results.