ECON 85 Operations Research ASSIGNMENT NO. 9 (Queueing Theory) 1. The jobs to be performed on a particular machine arrive according to a Poisson input process with a mean rate of two per hour. Suppose that the machine breaks down and will require 1 hour to be repaired. What is the probability that the number of new jobs that will arrive during this time is: (25 points) a) Zero b) two c) five or more? 2. Consider a queuing system with a Poisson input and exponential service times. Suppose there is one server and the expected service time is exactly one minute. Compare Ls for the cases where the mean arrival rate is 0.5, 0.9 and 0.99 customers per minute, respectively. Do the same for Lq, Ws, Wq and P(W>5) or the probability of waiting time in the system. (25 points)