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This paper discusses a multi-server retrial queuing system, where the customers may leave the system due to balking and impatience. Deviated from the classical retrial queue, we use a novel model that reflects the queue state, the ambition of queuing and the urgency of requests. In particular, when customers find that a certain amount of requests were in the service area, they will enter in orbit or service area. We study the interrelation of the parameters in the model, and effect of balking, retrial, and buffer size on performance measurements in the steady-state conditions. We also study the performance of the model of the queuing transaction in the computer networks under the specific parameter settings. Simulation results are presented by using OPNET Modeler tool.