On a Geo/G/1 Queue with Disastrous and Non-disastrous Failures

Abstract

This paper considers a Geo/G/1 queue system with disastrous and non-disastrous failures. In the discussed system, once the server suffers from a disastrous failure, all customers in the system are lost at once and the server is immediately sent to a repair facility for fixing. During the repair period of a disastrous failure, arrival customers are blocked and turned away till the server has been repaired. The server may also encounter a non-disastrous failure. During the repair time of a non-disastrous failure, arriving customers are allowed to join the system and in the meanwhile a disastrous failure may occur. By using supplementary variable technique, some system characteristics such as the idle period and the busy cycle are derived. The system size and the expected sojourn time are also obtained. Finally, some numerical examples and results are presented.