2025, Vol. 6, Issue 1, Part B
Fuzzy mathematical modeling and analysis of multi-server queuing system
Author(s): Rekha and Shaweta Sharma
Abstract: The objective of this study is to develop a fuzzy multi-server queuing model that incorporates uncertainties in real-world queuing systems, addressing the limitations of traditional crisp models that assume fixed values for arrival rates, service rates, and the number of servers. By integrating fuzzy logic, the study aims to enhance decision-making in dynamic environments such as hospitals, banks, and call centers. The methodology involves constructing a fuzzy M/M/C queuing model where key parameters are represented as triangular fuzzy numbers (TFNs), with the arrival rate modeled as (8, 10, 12) customers per hour, the service rate as (4.5, 5, 5.5) customers per hour, and the number of servers as (2, 3, 4). The fuzzy performance measures are computed using α-cut analysis and interval arithmetic, allowing for a comprehensive evaluation of system behavior under fluctuating conditions. A comparative analysis is conducted between crisp and fuzzy models to demonstrate the advantages of fuzzy queuing in handling variability. The results indicate that system utilization varies between (0.6, 0.67, 0.75), the expected number of customers in the system ranges from (4.8, 5.33, 5.9), and the expected waiting time fluctuates within (0.48, 0.53, 0.59) hours. These findings highlight the effectiveness of fuzzy modeling in capturing operational uncertainties and providing a more adaptive and realistic assessment of queuing dynamics. Despite increased computational complexity, the fuzzy model enhances predictive accuracy, optimizes resource allocation, and improves service efficiency, making it a robust tool for managing queuing systems in uncertain environments.
Pages: 119-123 | Views: 74 | Downloads: 33
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How to cite this article:
Rekha and Shaweta Sharma. Fuzzy mathematical modeling and analysis of multi-server queuing system. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(1): 119-123.
