Recently the development of the real-time environment has influenced the design and altered the concepts of computer oriented systems. A priority queuing model was developed to analyse the performance of a simple real-time computer system. The jobs come from remoted stations and form a Poisson process. Each job consists of two tasks: the communication task which is placed in the high priority queue, and a processing task which is executed by the computer on an available basis. The stationary queue length and the waiting time distributions are investigated.