Problem 5 (10 points) Consider a queuing system, M/M/1 with one server and parameters such that customer arrivals are described by a Poisson process with X = 3 per hour, and service times are independent exponentially distributed with l = 5 minutes. 1. Derive the average queue length. E [X(), assuming that the process X = {X(t): 12 0} follows the stationary distribution. 2. Evaluate expected busy time. Solution