- An outpatient clinic reported receiving on average 18 patient visits per hour and there are typically 8 patients waiting in the lobby.
a. What is probability that there are no visitors at the Clinic?
b. What is the average time a patient has to wait before they see a physician?
c. What is the average length of time each patient spends in the clinic?
d. What is the average number of patients at the Clinic?
- Customers arriving at the Tammali Falafel Express through a driver through. They place their orders at the first window then pick it up and pay at the next window. Assuming that there is a single-queue single-channel operation run by two employees, one filling the order while the other takes money from the customer. The number of cars arriving with a mean of 24 cars per hour. The average time taken to serve a car is a 1.25 minutes.
Compute the following characteristics:
a. The probability that there are no cars at the drive through at all, at any given moment.
b. The average number of cars waiting for service.
c. The average waiting time for service.
d. The average time spent by a car in the system.
e. The average number of cars in the system.
f. The probability that an arrival has to wait for service.
- At ABC University, the Registrar’s office processes students requests towards the end of the Summer. The office has one staff assisting the students. He reported that the mean number of students arriving at the counter is around 5 per hour, and the average time taken to process each request is 10 minutes. Given the Summer rush, the Registrar staff complains that he is overloaded and that many students waste their time queueing for processing their forms. Accordingly, the Senior Registrar wonders if it is cost effective to employ an extra staff for this period at the Counter. So, she checks with the Comptroller’s office who informed her that the staff is paid 5 dollars per hour and each student gets reimbursed for parking at the rate of 8 dollars per hour.
a. Determine the average number of students waiting to get their forms at the Counter (including the students being served)
b. What is the average length of time each spends at the Registrar?
c. Calculate the average cost per hour of processing the forms. This will include the cost of time lost by the students
d. Is employing an extra staff warranted?
Sample Solution