IFM/IFEk/1 Queuing Model with Erlang Service under Heptagonal and Octagonal Intuitionistic Fuzzy Numbers

Objectives: This research identifies the steps involved in determining the membership and non-membership functions of significant State execution proportions in Erlang services and models α-cut operations. Additionally, we applied the DSW Algorithmic Rule to intuitionistic fuzzy heptagonal and octagonal numbers. In this case, the inter-entry rate is Poisson and exponential, both of which have an intuitionistic Erlang nature. The main objective of this research is to evaluate the performance of a single server queuing model in terms of fuzzy and intuitionistic queuing theory. Fuzzy and intuitionistic fuzzies are the characteristics of the entering and exiting rates, respectively. Using a predetermined technique, an approach is carried out to assess the process metrics, taking the fuzzy numbers at face value without converting them into crisp values. Methods: We use the -cut method in IFM/IFEk/1 Single Server Queuing Model in FCFS with Erlang service. By applying increasing and decreasing entrance costs, the Poisson process is used to manage the arrival rates while delivering the input. Intuitionistic fuzzy queuing models are used to extend the queuing model. Findings: We noticed that the model indicated that performance can be enhanced by adding more factors. Comparing this procedure to fuzzification, accuracy is better. Shopkeepers, dealers, and companies will all benefit from the suggested model's assistance in precisely identifying the best performance metrics for the awaiting system. Novelty: Using an intuitionistic fuzzy queue, this research presents a novel method of assessing the M/Ek/1 queuing model in Erlang services. The computation of -cut intervals is an arithmetic procedure for intuitionistic fuzzy numbers. This novel approach assesses the on-server performance of an Erlang queuing model by extending fuzzy into intuitionistic fuzzy. The fuzzy waiting theory modeling evaluation metrics are given as a range of values, in contrast to the intuitionistic model, which offers a wide range of values. Applications: Several emails arrive at a network device in a sequential manner according to a Poisson arrival process, and each email's execution time is random. When mail arrives, it is queued and processed in the order that it arrives if the network server is busy. Using fuzzy queuing theory, the emails are "customers" and the network is the "server". The single server mathematical framework is a simple tool that can be used to restore the fuzzy queuing model. The parameters are all uncertain. Keywords: Queuing Theory, Heptagonal and Octagonal Fuzzy Numbers, Heptagonal and Octagonal Intuitionistic Fuzzy Numbers, Erlang Service, DSW Algorithm, Performance Measures