The ZU cafeteria serves on average 2000 customers a day during the lunch break (12:00-2:00 pm). It takes about 10 seconds to process a customer at the cashier. How many students on average wait in the queue (work in process)?

Students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take, on average, 4 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.   a. What percentage of time is Judy idle? (Round your answer to 1 decimal place.)     b. How much time, on average, does a student spend waiting in line? (Do not round intermediate calculations. Round your answer to 1 decimal place.)     c. How long is the (waiting) line on average? (Round your answer to 2 decimal places.)     d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=40 per hour​ (according to a Poisson​ distribution). Copying takes an average of 40 ​seconds, or μ=90 per hour​ (according to a negative exponential​ distribution). ​If the percentage of time used is 44% and the average length of the queue is 35 students and the average number is 80 then what is the average time spent waiting in the queue and the average time in the system ​ (round your response to two decimal points).

A Northwest Airlines ticket counter forecasts that 30 people per hour will need to check in. It takes an average of 1.5 minutes to service a customer. Assume that interarrival times and  service times are exponential and that all customers wait in a single line for the first avaliable agent.If we want the average time a customer spends in line and in service to be 3 minutes or less, how many ticket agents should be on duty?

United Raiders Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash resister and the operator is the server in this queuing system; the customers who line up at the counter to pay their selections form the waiting line.  Customers arrive at a rate of 24 per hour according to a Poisson distribution, and service times are on average equal to 2 minutes per customer. What is the number of customers waiting in the queue on average?

Bobby, another enterprising barber, is thinking about advertising in the local newspaper because he is idle 45 percent of the time. Currently, customers arrive, on average, every 40 minutes. What does the arrival rate need to be for Bobby to be busy 85 percent of the time?

During the evening hours, an average of 52 customers can be found in Sachi’s Sports Bar. About 40 customers arrive each hour. Using Little’s Law, how long does each customer stay at Sachi’s?

An average of 40 cars per hour (interarrival times are exponentially distributed) are tempted to use the drive in window at the Hot DogKing Restaurant.If  a total of more than 4 cars are in line (including the car at the window) a car will notenter the line. Ittakes an average of 4 minutes(exponential 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 lineat the drive-in window. On the average, how long will it be before I recieve the food?

True or False?  In a waiting line system, the average system time Wₛ must be longer than the average waiting time Wq

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