The Discrete-Time GI/Geo/1 Queue with Single Geometric Vacation

Abstract We consider the discrete-time GI/Geo/1 queueing system in which the server takes exactly one geometric vacation each time the system empties. We derive the probability generating functions of the stationary queue length and the stationary FCFS sojourn time. The results are then compared with corresponding continuous-time counterparts. The results are also compared with those of the GI/Geo/1 queue with multiple geometric vacations.