Please answer using stochastic operations principles
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 distr...
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...
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...
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...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all day and at the wash line, the cars can be cleaned at the rate of one every 4 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the: (a) average time a car spends in the service system. (b) average number of cars in line. (c) average time a...
Customers arrive at a bank that has 1 teller and they wait in line on a first-come, first-sorved basis. Customers arrive according to a Poisson process with a rate of 14.5 per hour. It takes on average 4 minutes for a customer to be served by the tellor. No customer leaves without going through service with the teller. The standard deviation of the service time is 2 minutes. What is the average time a customer spends waiting in line? (Enter...
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...
customers arrive at an average of 30 per hour. A single server in the store serves customers, taking 1.5 minutes on average to serve each customer. Inter-arrival times and service times follow the exponential distribution. What is the expected fraction of time that the server will be busy? On average, how many people will there be in the store? On average, how long will someone be in the store? What is the probability that there will be more than 2...
Cars arrive at the Dariette, a drive through restaurant, at a rate of 15 cars per hour. What is the probability that 10 or fewer cars arrving in the next hour
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
A Fast Food drive-through Restaurant with a single check-out counter opens six days a week, but its heaviest day of business is on Saturdays. Customers arrive at an average rate of 20 per hour on Saturdays. Customers can be provided service at the rate of one every two minutes. Assuming Poisson arrivals and exponential service times, find: The average number of customers in line The average time a car waits before being served The average time a customer spends in...