Abstract
We analyze a discrete-time single-server queueing system whose arrival stream is a Bernoulli process and service times are generally distributed. An extension of the N-policy is considered: the server remains idle till the queue length becomes i > 1 with probability θj. After the idle (vacation) period, the server needs a random amount of startup time before serving. Moreover, after the system is empty in a departure epoch, the service station employs a random time to close down the system, although the shutdown is interrupted and the service is resumed immediately without setup if an arrival takes place during such a period. By using the supplementary variable technique, we obtain the queue and system length distributions as well as some performance measures. We also find out the distributions and mean values of the different periods in a cycle and the waiting time. Finally, a cost model and several numerical results are presented.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
