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The paper presents a detailed study of a computer-controlled queuing system with a Poisson distribution input, first-come first-served queue discipline, single server with general service times and switching network through which the establishment of connection between customer in the queue and the idle server is subject to blocking. A generating function for the probability of queue size and a necessary and sufficient condition for the existence of statistical equilibrium for the queue size are obtained. Also, the Laplace-Stieltjes transform of waiting-time distribution is presented. Finally, the average queue size and the average waiting time are reported.