Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP (a,b) / 1 / ∞ $^{\text {(a,b)}}/1/\infty $ Queueing System

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

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1461-1488

Abstract: Abstract This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions at other various time epochs are also derived based on prearrival epoch probabilities. A simple approach has been developed to compute the waiting-time distribution of an arriving customer. We also carried out closed-form analytical expression for the service batch size distribution of an arriving customer. Some numerical results are provided in the form of tables for a variety of interarrival-time distributions and model parameters to understand the system behaviour.

Keywords: Queueing; General bulk-service rule; Matrix-geometric method; Service batch size distribution; Waiting time distribution; 60K25; 90B22; 68M20 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-020-09823-9 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:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09823-9

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

DOI: 10.1007/s11009-020-09823-9

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 ().