Abstract
This paper deals with an MX/G/1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p(0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q(= 1 – p). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability function and related reliability indices of this model. Finally, some numerical examples are presented for illustrative purpose.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.