Study of Transient and Steady State Solution of M/G/1 Queue with Two Phase Repairs

Abstract

We study a single server M/G/1 queueing system with Poisson input subject to random breakdowns. The server provides service to all arriving customers on a first come first served basis and service times follow general distribution. The system may breakdown at random and it must be sent to repair process immediately. Further the repair process involves two phases of repairs with different general repair time distributions. The supplementary variable technique is applied to find explicitly probability generating function of the number in the system and the corresponding steady state results are computed explicitly.