A family-practice medical clinic employs a receptionist (R), a nurse clinician (NC), and a physician (MD). The receptionist has been trained to screen patients with regard to whether they should see the NC or the MD. There are, of course, some errors, so the NC sees some patients who must then go to the MD. Currently, the waiting lines at the R, NC and MD are managed independently with a first-come, first-served priority at each queue. The information below shows the rates and flows of patients and servers. (15pts) λ = arrival rate of patients = 30 per hour p1 = fraction who go to nurse clinician = 2/3 p2 = fraction of NC patients who must also see the physician = 0.15 μS = service rate of the receptionist-screener = 40 per hour μD = service rate of the MD = 15 per hour μN = service rate of the NC = 30 per hour a. Calculate the arrival rate of patients for the NC and the MD. b. Calculate the average idle time for the receptionist R, NC and MD. c. Calculate the average number of patients waiting in each of the queues. d. Calculate the average waiting time in each of the R, NC, and MD queues: Calculate the average time in the entire system for each of the three patient paths: R to NC, R to MD, and R to NC to MD:

Just need part D and E