Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance

Srinivas R. Chakravarthy (), Shruti and Alexander Rumyantsev
Additional contact information
Srinivas R. Chakravarthy: Kettering University
Shruti: Birla Institute of Technology and Science Pilani
Alexander Rumyantsev: Karelian Research Centre of RAS

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1551-1579

Abstract: Abstract In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongoing service. The service time is independent on the batch size. First, we employ the classical embedded Markov renewal process approach to study the model. Secondly, under the assumption that the services are of phase type, we study the model as a continuous-time Markov chain whose generator has a very special structure. Using matrix-analytic methods we study the model in steady-state and discuss some special cases of the model as well as representative numerical examples covering a wide range of service time distributions such as constant, uniform, Weibull, and phase type.

Keywords: Queueing; Stochastic processes; Batch arrivals; Group clearance; Matrix-analytic method; 60J27; 60K25 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-020-09828-4 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_s11009-020-09828-4

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

DOI: 10.1007/s11009-020-09828-4

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 ().