Every 15 minutes a patient arrives the health center and first go to registration desk, it takes 10 minutes on average to register. There is only one clerk at the registration desk who works 8 hours per day. Assume arrivals are Poisson distributed and service times are exponentially distributed.
a. What percentage of time is this clerk Idle?
b. What is the average time the patients spent at the registration desk?
c. How much time on average, does a patient spend waiting in line?
d. How long is the (waiting) line, on average?
e. What is the probability that an arriving patient just before entering the Health center will find at least one other patient waiting in line?
f. If the health center decides to hire one more clerk for the same task and with the same service time, what is the average time the patientsspent at the registration desk? Compare it with your answer b). What would be the utilization of each clerk?
g. If health center buys a software, service time reduces to 6 minutes. Assume service time is constant. How does this change your answer to b)?
h. Suppose that each clerk works with a wage of $35 per hour and software costs to health center $50 per hour. Health center should be charged by $100/hour for holding each patient in the system. What is the daily operational cost of this system for the following scenarios: • One clerk • Two clerks • One software Which one is the best scenario in terms of total cost?