M/G/∞ with exponentially distributed setup times

We consider an M/G/∞ model with exponentially distributed setup times. Arrivals result in an off server starting a setup. Upon completing a setup, a server begins serving a waiting customer. Upon completing service, with probability p the server becomes eligible to serve another waiting customer. Among other things, we show, in steady state, that the number of busy servers is Poisson distributed and is independent of the number of servers in setup.