Transient behaviour of time-varying tandem queueing networks

Anjale Ramesh () and M. Manoharan ()
Additional contact information
Anjale Ramesh: University of Calicut
M. Manoharan: University of Calicut

OPSEARCH, 2025, vol. 62, issue 1, No 5, 104-118

Abstract: Abstract Most of the large-scale service systems in real life are subject to time-varying conditions, such as arrival rates, service rates, and other factors that can affect system performance. These systems can be adequately modelled using time-varying queueing systems, where one or several parameters change over time. Analysis of transient behaviour in such time-varying queueing systems is more challenging than their steady-state analysis. This study deals with the transient analysis of Markovian queues connected in tandem, where both the service and arrival processes at each station depend on time. To begin with, we derive the transient distributional relationship between the average workload and the customer’s waiting time in a single-server non-Markovian queue with time-varying arrival and service rates. We then generalise the transient laws for single-server queues to a k-station tandem network. Furthermore, we develop an algorithm for analysing transient performance measures in a k-station tandem queueing network and conduct a numerical study based on the algorithm. Numerical study supports the effectiveness of the algorithm, and the results provide insights into the transient behaviour of tandem networks, specifically in bottleneck scenarios. The study reveals that the location of the bottleneck station in a line has a significant impact on average workload in the stations.

Keywords: Transient analysis; Tandem queues; Time-varying workload; Time-varying queues (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12597-024-00790-0 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:62:y:2025:i:1:d:10.1007_s12597-024-00790-0

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

DOI: 10.1007/s12597-024-00790-0

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 ().