Driver's Donuts is a bakery and coffee shop that depends on morning com- muters for 80%...

 

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Driver's Donuts is a bakery and coffee shop that depends on morning com- muters for 80% of its daily business. During the morning rush from 5:30 a.m. to 8:30 a.m., an average of 35 cars arrive at the Driver's Donuts drive- through lane every hour, to purchase donuts and coffee through a single store window. The employee who staffs that window can serve each car in an average of 90 seconds, although this speed is partially due to the fact that a second employee talks to the car behind the one being served, inputting that car's order so that the window employee knows the order and its cost when the second car arrives at the window. Without that assistance, it takes the window employee an average of 2 minutes to serve any car, which is the practice outside of the morning rush hours, as customer traffic in the drive-through lane drops to an average of four cars an hour. Assuming that Driver's Donuts drive-through lane meets the assumptions of the M/M/1 model, answer the following questions. Questions 1. On average, how many cars are in the drive-through lane during the morning rush? (This includes any car being served). During the morning rush, how much time does the average Driver's Donuts customer spend in the drive-through lane? 2. If a car arrived between 1:00 p.m. and 2:00 p.m., how much time could the cus- tomer expect to spend in the drive-through lane? What is the probability that the customer would find no other cars in the lane, and be able to pull up to the window immediately? 3. If a customer arrives at the drive-through lane during the morning rush, what is the probability that the customer will have to wait until a Driver's Donuts employee takes their order? Driver's Donuts is a bakery and coffee shop that depends on morning com- muters for 80% of its daily business. During the morning rush from 5:30 a.m. to 8:30 a.m., an average of 35 cars arrive at the Driver's Donuts drive- through lane every hour, to purchase donuts and coffee through a single store window. The employee who staffs that window can serve each car in an average of 90 seconds, although this speed is partially due to the fact that a second employee talks to the car behind the one being served, inputting that car's order so that the window employee knows the order and its cost when the second car arrives at the window. Without that assistance, it takes the window employee an average of 2 minutes to serve any car, which is the practice outside of the morning rush hours, as customer traffic in the drive-through lane drops to an average of four cars an hour. Assuming that Driver's Donuts drive-through lane meets the assumptions of the M/M/1 model, answer the following questions. Questions 1. On average, how many cars are in the drive-through lane during the morning rush? (This includes any car being served). During the morning rush, how much time does the average Driver's Donuts customer spend in the drive-through lane? 2. If a car arrived between 1:00 p.m. and 2:00 p.m., how much time could the cus- tomer expect to spend in the drive-through lane? What is the probability that the customer would find no other cars in the lane, and be able to pull up to the window immediately? 3. If a customer arrives at the drive-through lane during the morning rush, what is the probability that the customer will have to wait until a Driver's Donuts employee takes their order?

Answer rating: 100% (QA)

we will use the MM1 queuing model Average number of cars in the drivethrough lane during the morning ... View the full answer