Scrutinization of a Neutrosophic Fuzzy Erlangian Queuing Model Using a Parametric Programming Technique

P. Yasodai ^* , W. Ritha

Department of Mathematics, Holy Cross College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India.

Emails: yasodairajendran@gmail.com; ritha_prakash@yahoo.co.in

Abstract

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.

Keywords: Fuzzy Sets; Membership Functions, Neutrosophic Fuzzy Erlangian Queuing Model; Trapezoidal Neutrosophic fuzzy number; Parametric Programming, (σ, β, γ)-cuts, Zadeh’s Extension Principle; Queue length; Waiting time.