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This paper is dedicated to the presentation of the single-channel waiting line systems with Poisson arrivals and exponential service times. They represent stages of customer flow management processes. Waiting systems are stochastic mathematical models and they represent the describing base of the waiting phenomena, service processes, prioritization, etc. Mathematical models of queuing theory present interest in modeling, designing and analyzing of nowadays information networks. Increasing trend of their development and emergence of new network technologies, impose new requirements regarding the development of new mathematically waiting models. In this paper I merely present the single-channel waiting line model, at Bole international Airport, Addis Ababa, Ethiopia.