A queueing model with balking, server vacation and working breakdown

This paper focuses on a single server queueing model that includes customer's balking, server vacation, and working breakdown. When there is no customer in the system or the system becomes empty, the server goes on a vacation and returns back when one or more customer available in the system. The server resumes service to the customers accumulated during its vacation period. There is always the possibility of a server breakdown while providing services to the customers, which may result in slower service rate. Slower service rate is considered as working breakdown state of the server or a defective mode of service. If the server is providing normal or defective service, customers may balk. For the system states, some practicable performance measures such as average number of customers in the system, average total cost function, and system throughput have been established for the various system states.