On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation

G. K. Tamrakar () and A. Banerjee ()
Additional contact information
G. K. Tamrakar: Indian Institute of Technology (BHU) Varanasi
A. Banerjee: Indian Institute of Technology (BHU) Varanasi

OPSEARCH, 2020, vol. 57, issue 4, No 12, 1337-1373

Abstract: Abstract This article considers a single server, infinite buffer, bulk service Poisson queue with single and multiple vacation. The customers are served in batches following ‘general bulk service’ (GBS) rule. The customers are arriving according to the Poisson process, and the service time of the batches follows an exponential distribution. Using bivariate probability generating function (PGF) method the steady-state joint distributions of the queue content and server content (when server is busy), and joint distribution of the queue content and type of the vacation taken by the server (when server is in vacation) have been obtained. Here by the ‘type of the vacation’ we mean the queue length at vacation initiation epoch. The information about these joint distributions may help in increasing the system performance. Finally, several numerical examples are carried out using MAPLE software to verify the analytical results.

Keywords: Bulk-service; Bivariate probability generating function; Infinite buffer queue; Single vacation; Multiple vacation (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12597-020-00446-9 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:opsear:v:57:y:2020:i:4:d:10.1007_s12597-020-00446-9

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/12597

DOI: 10.1007/s12597-020-00446-9

Access Statistics for this article

OPSEARCH is currently edited by Birendra Mandal

More articles in OPSEARCH from Springer, Operational Research Society of India
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().