Comparative analysis of methods of residual and elapsed service time in the study of the closed retrial queuing system M/GI/1//N with collision of the customers and unreliable server

The aim of the present paper is to investigate a finite-source M/GI/1 retrial queuing system with collision of the customers where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. The method of elapsed service time and the method of residual service time are considered using asymptotic approach under the condition of unlimited growing number of sources. It is proved, as it was expected, that basic characteristics of the system, such as the stationary probability distribution of the server states and the asymptotic average of the normalized number of customers in the system are the same and do not depend on the applied method. © Springer International Publishing AG 2017