How Machine Learning is Innovating Today's World

24New Approach on M/M/c/K Queueing Models via Single Valued Linguistic Neutrosophic Numbers and Perceptionization Using a Non-Linear Programming Technique

Antony Crispin Sweety C.^1* and Vennila B.²

¹Avinashilingam Institute for Home Science and Higher Education for Women, Tamil Nadu, India

²Sri Eshwar College of Engineering, Coimbatore, Tamil Nadu, India

Abstract

The framework deals with the novel idea of the neutrosophic M/M/c/K queueing model. The number of consumers that can enter the system is limited in the classic M/M/c/K model to K, and these individuals arrive adopting a Poisson process with rate λ, the parameter μ represents the service time of the customers that are distributed exponentially, and there are c servers in the system to serve the arriving customers. In the neutrosophic M/M/c/K queue, the arrival and departure rate are considered as a single valued neutrosophic number where T is the truth value, I is indeterminacy, and F is falsity. The performance measures of the neutrosophic M/M/c/K model that include both the average number of customers and mean waiting time in the queue as well as in the system are derived. Further, the performance measures of the unstable NM/NM/c/K queueing model subject to different rates of entry, service, breakdown, and repairs are analyzed. Moreover, calculation and comparison of hexagonal, heptagonal, and octagonal neutrosophic numbers are done. To illustrate the significance of the suggested paradigm, a numerical example is ...