A small clinic has one doctor on duty administering vaccines. Patients are served on a first-come-first- served basis (no appointments) and the patients form a single line to wait for their vaccination. The doctor takes, on average 3 minutes to serve a patient (exponentially distributed). On average, 16 patients arrive per hour (Poisson distributed). Assume the clinic is open continuously, and that there is unlimited space for patients to wait.

a) (2 points) Is this an M/M/1 system? Explain why or why not (including additional assumptions, if necessary).

For parts b, c, d, and e assume that it is an M/M/1 system for purposes of calculating the answers...

b) (2 points) What are the values of mu and lambda for this system?

c) (2 points) On average, what is the total time a patient spends at the clinic?

d-1) (2 points) What is the average number of patients waiting in line?

d-2) (2 points) What is probability that there will be exactly one patient at the clinic?

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p=4 1-1-4 P=1-4 -((-4) W v=-1- W-1 = = -2 TRC s = dL AD hQ Q HLTD = L * Hd D = * u(-2) = P Some Formulas Iza -1-24- -2 TRC--1---2 = (-2) AD hQ OLTD = + S = LID +ZOLID LG = I * 0 OLTD = (14 * 0) + (1 * 0} ) SL= = 2AD h C5 C + Ce = 2AD p=4 1-1-4 P=1-4 -((-4) W v=-1- W-1 = = -2 TRC s = dL AD hQ Q HLTD = L * Hd D = * u(-2) = P Some Formulas Iza -1-24- -2 TRC--1---2 = (-2) AD hQ OLTD = + S = LID +ZOLID LG = I * 0 OLTD = (14 * 0) + (1 * 0} ) SL= = 2AD h C5 C + Ce = 2AD