Analysis of Two-Way Communication in $$M_1^X, M_2/G_1,G_2/1$$ M 1 X, M 2 / G 1, G 2 / 1 Retrial Queue Under the Constant Retrial Policy

Rashmi Km () and S. K. Samanta ()
Additional contact information
Rashmi Km: National Institute of Technology Raipur
S. K. Samanta: National Institute of Technology Raipur

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 4, 1-32

Abstract: Abstract This article analyzes an $$M_1^X, M_2/G_1,G_2/1$$ M 1 X , M 2 / G 1 , G 2 / 1 retrial queue with two-way communication under constant retrial policy. A server handles both inbound and outbound calls. The inbound calls arrive in batches according to a compound Poisson process. The server makes an outbound call that follows the Poisson process during its inactive period. The service duration of inbound and outbound calls follows two different arbitrary distributions, while retrial time follows an exponential distribution. Using the supplementary variable technique, the system of differential-difference equations is developed to directly compute the distribution of orbit length at random epoch. The execution of the waiting time distribution for an arbitrary call of an incoming batch constitutes the most challenging task in this study. We also conduct a comprehensive cost analysis to minimize the overall cost of system operation. Furthermore, a variety of performance metrics and numerical findings validate the proposed methodology.

Keywords: Differential-difference equation; Retrial queue; Roots approach; Supplementary variable technique; Two-way communication; Waiting time distribution; 90B22; 60K25; 68M20 (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/s11009-024-10119-5 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_s11009-024-10119-5

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

DOI: 10.1007/s11009-024-10119-5

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 ().