Analysis of a GIX/M/1 queue with two-stage vacation policy using shift operator method

Yufei Liu, Qingqing Ye and Junnai Yan

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 19, 6732-6761

Abstract: In this paper, we investigate a GI X/M/1 queue with the two-stage vacation policy. The system will first enter a working vacation once the system becomes empty in the normal busy period, during which the service rate will be switched to a lower rate. After this working vacation, if the system is nonempty, the service rate will be switched to the normal rate immediately; otherwise, the system will enter multiple vacations during which the service rate reduces to zero until the system is nonempty after one vacation and a new normal busy period starts. The distinguishing feature of this paper is the use of a general algorithm for solving the difference equation based on the right shift operator method to obtain the queue length distribution at pre-arrival time and arbitrary time. Moreover, the sojourn time of arbitrary customer is analyzed. Finally, several typical numerical examples are provided to validate our computational algorithm.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2023.2250488 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:53:y:2024:i:19:p:6732-6761

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2023.2250488

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().