<p>In this paper, we suggest a new bi-serial queuing model that is characterized by one-time-feedback and the reneging of the customers, in order to describe the main characteristics of modern service systems. This system is composed of three similar servers, with one server in the first stage and then two servers in the second stage functioning in a bi-serial system. Once served at the first stage, the customers are directed to one of the second-stage servers depending on the service needs with a possibility of one revisit to the system via feedback. The impatience of customers is integrated with reneging whereby customers can walk out of the system when they are no longer tolerant of the delays. The associated difference-differential equations in the steady-state case are solved with the help of an analytical framework that is built on the generating functions and partial generating functions. The key finding of the paper is the clear description of the joint impact of reneging and feedback on the performance of the system. It is also found that an increase in the reneging rate although causing a decrease in the queue lengths and waiting times can also cause a decrease in the system throughput and the number of completed services, which is an important performance trade-off. Moreover, the effects of the arrival rates, service rates and feedback probabilities on the queue lengths and the total performance of the system are also studied systematically. Numerical and graphical findings show that reneging and feedback interact in a nonlinear fashion, which is beneficial to the design and optimization of bi-serial queuing networks to achieve the goal of enhancing the efficiency of operations and customer satisfaction.</p>