Bulk Queue Model With Optional Service and Service Interruption

In the present article, we investigate a queuing system in which units arrive in random batch sizes according to a Poisson process, while service is provided to individual units on a one-by-one basis. The service mechanism comprises a mandatory service phase followed by an optional service phase, undertaken according to the unit’s requirements. The server may stop functioning as a result of an unpredictable breakdown while offering any one of the services. Once the service is interrupted due to a server failure, the initiation of repair activities may be delayed owing to the unavailability of repair personnel or the required repair facilities. Following this delay, the server undergoes multiple essential repair phases before being restored to an operative state. The current non-Markovian model is investigated by employing a supplementary variable approach, and the time-independent behavior and different performance parameters of the system are discussed by means of a probability-generating function. By defining the suitable parameters, some exceptional cases are also described. Finally, the validity of the obtained analytical results is demonstrated through a numerical example.