The authors consider the probability distribution Pr(W>t) of the waiting time W in a closed processor-sharing system with CPU-switching times. The waiting time is the time needed for a particular job, called tagged job, to be served by the CPU. The switching time ∈ is the time spent by the CPU to transfer the control from one job to the next one. In this paper the authors consider two different models of this processor-sharing system: in MODEL1 a CPU discipline with switching time ∈>0 and one class of users is considered, whereas in MODEL2 a CPU discipline with switching time ∈=0 and two classes of users are considered. For these models the authors derive an asymptotic formula for Pr(W>t) using matched asymptotic expansions that hold in the heavy usage region.
