An average of 40 cars per hour (interarrival times are exponentially distributed) are tempted to use the drive-in window at the Hot Dog King restaurant. If a total of more than 4 cars are in line (including the car at the window) a car will not enter the line. It takes an average of 4 minutes (exponentially distributed) to serve a car.
(a) What is the average number of cars waiting for the drive-in window (not including a car at the window)?
(b) On the average, how many cars will be served per hour?
(c) I have just joined the line at the drive-in window. On the average, how long will it be
before I have received my food?
An average of 40 cars per hour (interarrival times are exponentially distributed) are tempted to use...
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
An average of 10 cars/hour arrive at a car repair station with two servers. Assume that the average service for each customer is 4 minutes and both interarrival and service times are exponentially distributed. If this car repair station has a capacity of 4 cars a. Write the steady-state equations and solve them. Compare the results with those calculated in question 1 and draw a conclusion. b. What is the probability that the car repair station is idle? c. What...
Waiting lines Customers walk in at random to a deli. The interarrival times are exponentially distributed with an average of 5 minutes. The deli prepares one order at a time. The order preparation times are exponentially distributed with an average of 3 minutes. 13. What kind of waiting line model is appropriate for the deli? 14. What is the utilization? 15. What is the total amount of time a customer would expect to spend at the deli (from walking in...
Waiting lines Customers walk in at random to a deli. The interarrival times are exponentially distributed with an average of 5 minutes. The deli prepares one order at a time. The order preparation times are exponentially distributed with an average of 3 minutes. 13. What kind of waiting line model is appropriate for the deli? 14. What is the utilization? 15. What is the total amount of time a customer would expect to spend at the deli (from walking in...
An average of 90 cars per hour arrive at a single-server toll booth. The average service time for each customer is a half minute, and both interarrival times and service times are exponential. For each of the following questions, show your work, including the formula that you are using. 1) On average, how many cars per hour will be served by the server
7. The Canara Bank drive-thru teller window can serve a customer at an average of 4 minutes per customer. Service time has a negative exponential distribution. Customers arrive in their cars at a rate (Poisson distributed) of 12 per hour and form a single waiting line: a. Determine the average waiting time, the average queue length, and the probability that there is no customer in the system. b. If Canara Bank decides to open a second drive-thru teller window with...
3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the window every hour. It takes 1 minute on average to serve a customer. a. What is the average number of customers that will be in line and in service at any time? b. On average, how long will a customer spend in the system?
1. Keuka Park Savings and Loan currently has one drive-in teller window. Cars arrive at a mean rate of 10 per hour. The mean service rate is 12 cars per hour. a. What is the probability that the service facility will be idle? b. If you were to drive up to the facility, how many cars would you expect to see waiting and being serviced? c. What is the average time waiting for service? d. What is the probability an...
A quick-service restaurant has a single drive-through lane with one worker at the window. It is assumed that the worker can process an order every 3 minutes on average and that the processing (service) times are exponentially distributed. Customers arrive at the drive-through at the rate of 15 per hour. a. The worker at the drive-thru is busy ????? of time. (Enter your response rounded to two decimal places.) b. The average number of cars waiting at the drive-thru is...
1. At a fast food restaurant, the waiting time at the drive-through window has an average of 3 minutes, with a standard deviation of 0.8 minutes. i. What is the probability that a random sample of 64 cars will have an average waiting time of less than 3.25 minutes? ii. Did you use the CLT to do this problem? Explain.