Response-time distribution for a processor-sharing system.

We consider the response time for jobs in a processor-sharing system with a Poisson arrival process and exponentially distributed required service time, i.e. an M/M/1 - PS queue. The response time W is the sum of the delay and the required service time. We derive an integral representation for the equilibrium response- time distribution Pr{W>t}, and evaluate this integral numerically for several values of the traffic intensity rho 1. We also investigate the behavior of Pr{W>t} in the heavy-traffic case when p is close to 1.