Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX

A. Mohammed Shapique (), R. Sudhesh () and S. Dharmaraja ()
Additional contact information
A. Mohammed Shapique: IFET College of Engineering
R. Sudhesh: UCE: BIT Campus, Anna University
S. Dharmaraja: Indian Institute of Technology Delhi

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 3, 1-33

Abstract: Abstract A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high altitude platform (HAP) systems. In this system, the WiMAX mobile station (MS) switches to a close-down period for a random duration at the end of the busy period. At the end of the close-down period, if the system is non-empty, the MS switches to a functional state. Otherwise, the MS takes an ordinary vacation. The MS switches to a working vacation (WV) if the system is empty at the end of the ordinary vacation period. Jobs arriving during the WV are served at a slower service rate. Jobs may become impatient in any state of the system except during the regular busy period. Explicit expressions for the transient and steady-state probabilities of this system are obtained using continued fraction and confluent hypergeometric functions. Furthermore, performance indices such as mean, variance, average abandonment rate, and system throughput are computed. Finally, a cost-profit analysis and graphical illustrations are provided.

Keywords: Single server; Close-down period; Working vacation; Impatient customers; Transient probabilities; Confluent hypergeometric function; Incomplete gamma function (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/s11009-024-10094-x 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:3:d:10.1007_s11009-024-10094-x

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

DOI: 10.1007/s11009-024-10094-x

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 ().