Abstract
This paper aims to derive the analytical solution of the truncated single-channel queue: M/M/1/N at the steady state by adding the concepts of encouraging arrivals, feedback strategy, catastrophe, and retention of reneged customers. Using the iterative method obtain the probability that there are n customers in the system, the possibility of a vacuous system, and some performance effectiveness measures. Some important queueing models are exceptional cases of this system. Some numerical values are given for the additional concepts to show the effect of the (arrival rate, and catastrophe rate) on the model so that the companies implementing this model work to reduce the harmful ones.