Comparison of single server queuing performance measures using fuzzy queuing models and intuitionistic fuzzy queuing models with infinite capacity

Article type: Research Article

Authors: Aarthi, S.^{; *} | Shanmugasundari, M.

Affiliations: Department of Mathematics and Statistics, College of Science and Humanities, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India

Correspondence: [*] Corresponding author. S. Aarthi, Department of Mathematics and Statistics, College of Science and Humanities, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India. E-mail: as6238@srmist.edu.in.

Abstract: This paper presents boundless capacity, one server’s fuzzy and intuitionistic fuzzy queuing models. This study’s primary objective is to demonstrate and compare the performance of a single server queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. This article demonstrates that intuitionistic fuzzy theory performs better when solving queuing problems. Furthermore, by integrating fuzzy queuing models into an intuitionistic fuzzy framework, their relevance in authentic situations is augmented. The fuzzy queuing theory model’s performance measurements are delivered as a range of values, but the intuitionistic fuzzy queuing theory model offers a broad array of values. In this context, the arrival and the service rates are both triangular (TFN) and intuitionistic triangular fuzzy numbers (TIFN). An assessment is performed to determine the evaluation criteria, employing a design protocol in which the fuzzy values are taken as-is without being turned into crisp values. As a result, in an ambiguous environment, we can use the proposed approach to pick scientific findings. In this study, we are using the TFN in an intuitionistic fuzzy environment, compensating for the degree of stability and denial so that the sum of both virtues is never higher than one. We proffered many non-normal arithmetic techniques for this sort of fuzzified integer. The envisaged compositions are intuitive and concise, as they evolved by utilising canonical algebraic mathematics. In real-world situations, this tactic is simple and straightforward to enact. The nearest interval number is then used to round a TIFN. The key advantage of this strategy is that it allows us to quickly solve a constrained unrestrained optimization model with TIFN coefficients using a multi-section heuristic. The prevailing methodologies and initiatives are destined to be relevant to different types of updated decision-making obstacles in focusing on economic equity, funding, presidency, and environmental sciences, which will be the focus of our future research. And two numerical problems are solved to showcase the sustainability of the suggested technique. In this queuing model, we predict a variety of components, including prospective queue length, expected system length, and sojourn time in both the queue and the system. The statistical analysis reveals that the quantified performance indicators of the intuitionistic fuzzy queuing model agree well with the performance measurements of the fuzzy queuing model. Even though the average correlation between the two concepts is nearly equivalent, TIFN provides a more extensive range of possibilities than TFN. Despite the fact that fuzzy set theory is used to contend with unpredictability in decision-making circumstances, it only relates to the extent of membership and lacks a model for reluctance. The fact that each asset’s affirmation and deprivation levels are comprehended is the special feature of intuitionistic fuzzy sets. As a consequence, it becomes more meticulous, suitable, and generalizable.

Keywords: Intuitionistic fuzzy queue, intuitionistic fuzzy arithmetic, sojourn time, triangular intuitionistic fuzzy numbers

DOI: 10.3233/JIFS-221367

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 3, pp. 4733-4746, 2023