MAT540 Strayer University Week 2 Queuing Analysis Systems Exercises
1. The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant)can service 10 customers per hour. Cars arrive at the regular unleaded pump at a rate of 6 perhour. Determine the average queue length, the average time a car is in the system, and theaverage time a car must wait. If the arrival rate increases to 12 cars per hour, what will be theeffect on the average queue length?
2. The First American Bank of Rapid City has one outside drive-up teller. It takes the teller anaverage of 4 minutes to serve a bank customer. Customers arrive at the drive-up window at arate of 12 per hour. The bank operations officer is currently analyzing the possibility of adding asecond drive-up window, at an annual cost of $20,000. It is assumed that arriving cars would beequally divided between both windows. The operations officer estimates that each minute’sreduction in customer waiting time would increase the bank’s revenue by $2,000 annually.Should the second drive-up window be installed?
3. All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at aweigh station. Trucks arrive at the weigh station at a rate of 200 per 8-hour day, and the stationcan weigh, on the average, 220 trucks per day.
a. Determine the average number of trucks waiting, the average time spent waiting andbeing weighed at the weigh station by each truck, and the average waiting time beforebeing weighed for each truck.
b. If the truck drivers find out they must remain at the weigh station longer than 15minutes, on average, they will start taking a different route or traveling at night, thusdepriving the state of taxes. The state of New Mexico estimates that it loses $10,000 intaxes per year for each extra minute trucks must remain at the weigh station. A new setof scales would have the same service capacity as the present set of scales, and it isassumed that arriving trucks would line up equally behind the two sets of scales. Itwould cost $50,000 per year to operate the new scales. Should the state install the newset of scales?
4. During registration at State University every semester, students in the college of business musthave their courses approved by the college advisor. It takes an average of 2 minutes to approveeach schedule, and students arrive at the adviser’s office at the rate of 28 per hour. The dean ofthe college of business is considering the addition of a second adviser in the college advisingoffice to serve students waiting to have their schedules approved. This new adviser could servethe same number of students per hour as the present adviser. Determine L, Lq, W, and Wq forthis altered advising system. As a student, would you recommend adding the adviser?
5. The Quick Wash 24-hour Laundromat has 16 washing machines. A machine breaks down every20 days (exponentially distributed). The repair service with which the Laundromat contractstakes an average of 1 day to repair a machine (exponentially distributed). A washing machineaverages $5 per hour in revenue. The Laundromat is considering a new repair service thatguarantees repairs in 0.50 day, but it charges $10 more per hour than the current repair service.Should the Laundromat switch to the new repair service
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