Sojourn time distribution in a multiprogrammed computer system

We present a method for calculating the moments and the distribution of sojourn time in a multiprogrammed computer system. We assume that the CPU and I/O subsystem can be represented by a general state-dependent server who works according to the processor sharing discipline. Further, at most m jobs may be simultaneously receiving service. Thus, m is the multiprogramming level of the system. The arrival of jobs occurs according to a Poisson process, and the arrivals must wait in a waiting area if m jobs are already receiving service. The method presented may be useful in designing the multiprogramming level needed to meet certain objectives on the characteristics of the sojourn time.