The Geo / G a, Y /1/ N Queue Revisited

Mohan Chaudhry and Veena Goswami ()
Additional contact information
Mohan Chaudhry: Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, Kingston, ON K7K 7B4, Canada
Veena Goswami: School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar 751 024, India

Mathematics, 2022, vol. 10, issue 17, 1-17

Abstract: We not only present an alternative and simpler approach to find steady-state distributions of the number of jobs for the finite-space queueing model G e o / G a , Y / 1 / N using roots of the inherent characteristic equation, but also correct errors in some published papers. The server has a random service capacity Y , and it processes the jobs only when the number of jobs in the system is at least ‘ a ’, a threshold value. The main advantage of this alternative process is that it gives a unified approach in dealing with both finite- and infinite-buffer systems. The queue-length distribution is obtained both at departure and random epochs. We derive the relation between the discrete-time Geo/ G a , Y /1/N queue and its continuous-time analogue. Finally, we deal with performance measures and numerical results.

Keywords: batch service; roots; discrete-time queue; discrete renewal theory; finite buffer capacity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/17/3142/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/17/3142/ (text/html)

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:gam:jmathe:v:10:y:2022:i:17:p:3142-:d:904026

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().