Another queuing model illustrates service demand from a finite population of users. The underlying assumption is that if a significant fraction of these users are already waiting for service, then the arrival rate of further service demands decreases until more of the users are serviced and returned to the calling community. Models of this class are referred to as Machine Repairman models, because the calling population can be viewed as a set of machines where individual machines occasionally breakdown and need repair.

The @PFS (Poisson Finite Source) function computes the expected number of customers either in repair or waiting for repair, given the number of customers, number of repairmen, and the limiting load of the queue. The following model illustrates the use of the @PFS function to model a computer timesharing system. Each of the incoming ports can be thought of as a customer. Usually, the number of incoming ports is limited, thus the finite source assumption is appropriate.