1. Explain the divergences between discrete-event simulation and Monte Carlo simulation. Provide an example of at least one situation from a health care arena when discrete-event simulation would be preferred and one when Monte Carlo simulation would be preferred.
2. Suppose we know that the average number of customers present in a queuing system is 10 and the average number of customers waiting in line is 4. Given that the average number of arrivals entering the system per hour is 20, determine the average time a customer spends in the system and the average time a customer spends in line. Be sure to provide appropriate units for your answer.
3. Each Tuesday, the new residents at an inpatient rehabilitation clinic must visit the medication lab and have all of their existing medications inventoried when they arrive. The interarrival times of patients to the medication lab follow a uniform distribution with an upper bound of 45 minutes and a lower bound of 30 minutes. The service times to have their medication logged follow a normal distribution with a mean of 20 minutes and a standard deviation of 5 seconds.
Using Excel, determine queuing and service statistics for the 40 patients who visit the medication lab over a one-day period. The columns of data you will need to generate include patient ID, interarrival time, arrival time, service start time, wait time, service time, service completion time, time in system, and server idle time.
4. Calculate the following summary statistics for question 9:
a. Number of patients who wait
b. Probability of waiting
c. Average wait time
d. Maximum wait time
e. Percentage of time server is busy
f. Number waiting > 1 minute
g. Probability of waiting > 1 minute
h. Average number of patients in line