A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue

Abstract

This paper presents a decomposition technique for the service station reliability in a discrete-time repairable ${\text{Geom}}^X$/G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the structures of the service station indices are also found. Finally, special cases and numerical examples validate the derived results and show that our analytic technique is applicable to reliability analysis of some complex discrete-time repairable bulk arrival queueing systems.