Economical Situation of the M/M/1/k Queueing system with Encouraged Incoming and maintaining of Reneged Customers

Abstract

Today’s businesses all strive to operate smoothly and efficiently in order to meet customer demandand provide the best possible service because of the intense competition. The queuing theory is crucial in this situation. Queueing models can assist businesses in understanding their performance in advance, enabling themto plan effectively for providing seamless and effective customer service as well as long-term sustainability. Businesses entice customers to sign up for the system by offering promotions and discounts. Customers wait even longer in queue to receive services as a result of incentives like discounts.An analysis is conducted on a finite Markovian single-server queuing model with encouraged arrivals, reneging, and retention of reneged customers. Iterative derivation is used to reach the model's steady state solution. Additionally, the queueing model's performance metrics are gathered. As unique example of this model,several significant queuing models are derived. In order to develop a cost model, a model's economic analysis is presented, and a discussion of numerical representation is also included.Customers are added when they are welcomed, which changes the way theybehave in a queueing system.