THE M/M/1/K_b INTERDEPENDENT QUEUEING MODEL INCLUDES REVERSE BALKING WITH FEEDBACK AND CONTROLLABLE ARRIVAL RATES

Abstract

Objective: Some research in the queueing theory literature describes batch-delivery systems instead of only individualised one-on-one support. This study initially presents adjustable arrival percentages and interdependency in a system like these arrival and service procedures in order to determine the likelihood and characteristics of the system for queuing. It also validated the results that were attained.Methods: With Poisson as the default assumption (that there is only one arrival for every Poisson occurrence), it is expected that the input will regulate the by varying arrival rates in speed and duration. The service is trustworthy and authorised for exact results. We are just using one server for the duration of this service. Re-entering the queue to enhance the outcome is what feedback does. Service is started when the number of customers approaches or beyond the capacity that is set aside All of the probability in a stable state are found by a recursive technique.Findings: Our utilisation feedback in M/M/1/K_b model the properties and solutions of steady-state are determined and examined. The reneged customer and feedback customer, respectively, will have probabilities p_1 and p_2. Anticipated client volume and wait duration are contingent upon interdependencies, service frequency, rapid arrival frequency, and delayed arrival frequency. Based on every criteria, every outcome has been confirmed.Novelty: There are some works related to a feedback queueing system, but this will is new approach of finding the best result for the required model with controllable arrival rates along with Mutual dependability of arrival and procedure for services