aspg-21-1920-1791475344 20261008160224 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 3 P. Yasodai Department of Mathematics, Holy Cross College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India W. Ritha Department of Mathematics, Holy Cross College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India This article examines an Erlangian queuing model in a neutrosophic fuzzy environment. The inter-arrival rates and service rates are trapezoidal neutrosophic fuzzy numbers integrated into the Erlangian queuing model. The membership functions of the performance metrics of the corresponding queuing model have been outlined using parametric programming techniques in accordance with the (σ, β, γ)- cuts and Zadeh's extension principle. The neutrosophic fuzzy queues are converted into a family of crisp queues using this principle. The applicability of the provided approach for various cutting possibilities is highlighted by concrete examples. 2023 115 125 1920 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210311 https://www.americaspg.com/journal/21/article/1920 https://www.americaspg.com/storage/91688468915.pdf