An \(M/G/1/1\) queue with unreliable server and no waiting capacity. (English) Zbl 1004.90023

Summary: An \(M/G/1\) queueing system with no waiting room is considered. The server is assumed to provide two types of services-regular and optional with the provision of server breakdown. Explicit expressions for the transient probabilities for the system being idle, busy and breakdown are obtained. The reliability and availability analysis of the system are carried out. For the specific choice of distributions and parameters involved, numerical illustrations are provided. Earlier results are deduced as special cases of this more general model.


90B22 Queues and service in operations research
90B25 Reliability, availability, maintenance, inspection in operations research