A Queueing-Inventory System with Modified Delayed Vacation under Bernoulli Schedule

Qingzhe Xu (), Jianjun Li (), Liwei Liu () and Lixue Guo ()
Additional contact information
Qingzhe Xu: Nanjing University of Science and Technology
Jianjun Li: Nanjing University of Science and Technology
Liwei Liu: Nanjing University of Science and Technology
Lixue Guo: Nanjing Agricultural University

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 4, 1-22

Abstract: Abstract In this paper, we consider a queueing-inventory system with modified delayed vacation under Bernoulli schedule. If the inventory is empty upon completion of the service, the server will take the modified delayed vacation. During the modified delayed vacation period, if the replenishment is completed, the customer will still be served as normal. After this period, the server will take Bernoulli schedule, where the server reverts to normal work with probability $$q(0\le q\le 1)$$ q ( 0 ≤ q ≤ 1 ) or takes multiple vacations with probability $$1-q$$ 1 - q . The customers arrive according to a Poisson process. Upon customer arrival, if the inventory is not empty, the customer accepts the service and leaves the system carrying a product. The service time, lead time, modified delayed vacation time and multiple vacations time are all assumed to be exponentially distributed. We derive the stability condition of the system and the matrix geometric solution of steady-state probabilities using an algorithm. Then performance measures of the system are derived. Finally, numerical results are presented to demonstrate the impact of system parameters on performance measures and the expected cost function.

Keywords: Queueing-inventory system; QBD; Bernoulli schedule; (s; S) policy; 60K25; 60K30; 90B22 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-024-10117-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10117-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-024-10117-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().