Problem
Jobs arrive to a single server according to a Poisson process with rate 3 per hour. Service times are exponentially distributed with mean 1/μ hours.
1. Find μ so that the steady-state probability that there is more than 1 customer in the system is .25.
2. Now assume that μ = 5. The server gets a bonus of $1 per job that does not have to wait in the queue before entering service. Calculate the expected bonus per hour that the server makes.