Abstract
An M/M/1 queue with working vacation state has been considered. If the system is in busy state, it functions as a single server Markovian queue. When it is on vacation, again it functions as a single server Markovian queue but with different arrival and service rates. In addition, during busy period, the arrival and service are generated by K distinct randomly varying environments. The server takes vacation whenever there are no one in the system. But, the vacationing server serves at a lower rate as an arrival occur. The vacation policy is multiple vacation policy and the vacation period follows negative exponential. For this model using Matrix-Geometric method the probability distribution of number of customers in the queue in steady state has been obtained. Some illustrative examples are also provided.
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.