A simple computer system is described, which consists of a CPU and I/O unit and which works in a multiprogramming manner. The model assumes that the system works under heavy load so that the incoming queue is never empty, that the service times at the two units are exponentially distributed independent random variables, and that the number of iterations of the programs is geometrically distributed. Head of the line priority of programs which are being processed over newcomers is considered. Steady state distribution of the states of the system is numerically solved under the assumption of a finite waiting room. The suggested system is compared with one working in “batch mode” and with an equivalent multiprogramming system with a constant number of programs. The latter comparison shows that the suggested priority rule improves the expected response time without affecting the throughput and the utilizations of the CPU and the I/O unit. The model induces an interesting dependence phenomenon which is discussed at length. © 1973, ACM. All rights reserved.