Optimizing the Performance of Multi-server Heterogeneous Queueing Systems with Dynamic Customer Behaviour

Asmita Tamuli, Dhruba Das () and Amit Choudhury
Additional contact information
Asmita Tamuli: Dibrugarh University
Dhruba Das: Dibrugarh University
Amit Choudhury: Gauhati University

Sankhya B: The Indian Journal of Statistics, 2024, vol. 86, issue 2, No 3, 366-414

Abstract: Abstract This article addresses the pressing issue of customer impatience and dissatisfaction with queueing systems, a critical aspect of modern businesses. It delves into specific aspects of customer behavior, viz., reverse balking, reneging, and retention of reneged customers, which significantly influence queue dynamics. A novel finite-buffer two-server heterogeneous queueing model is introduced, taking into account reverse balking, and position-dependent reneging (reneging till the beginning of service i.e., $$R\_BOS$$ R _ B O S and reneging till the end of service i.e., $$R\_EOS$$ R _ E O S ) along with the retention of reneged customers. The probability distribution of the number of customers in the system is ferret out and the key performance measures are derived along with sensitivity analysis. Extending the analysis, this study tackles a cost optimization problem using an algorithm based on the Quasi-Newton Method (QNM) to achieve optimal solutions for both the server that optimize the cost function. A numerical example is provided to illustrate the practical implications and benefits of the proposed optimization approach for the queueing model.

Keywords: Reverse balking; Reneging; Cost optimization; Customer impatience; Heterogeneous server; Position-dependent reneging; 60K25; 90B22 (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/s13571-024-00340-0 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:sankhb:v:86:y:2024:i:2:d:10.1007_s13571-024-00340-0

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13571

DOI: 10.1007/s13571-024-00340-0

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().