A property management team recently signed a contract with an old downtown Toronto office building, and...

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A property management team recently signed a contract with an old downtown Toronto office building, and the first issue they must address is the current parking system. According to their observations, the current parking system has only one lane and one parking validation window, where one parking staff operates on a first-come, first-served basis. The parking staff can validate the parking passes and issue receipts at a rate of 40 seconds per car on average following a negative exponential distribution. Following a Poisson distribution, 86 cars will arrive at the entrance every hour on average during business hour. (a) List appropriately service rate and arrival rate first and then calculate what is the parking entrance utilization? (b) What is the average number of cars waiting in line? (c) What is the average time in minutes that a car has to spend at the parking entrance (both waiting in line and being served)? (d) What is the probability that there will be more than three cars at the parking entrance? The property management team consider replacing the manual parking entrance with automated parking system. The new parking system uses Radio-frequency identification (RFID) technology to read signal from the implanted RFID microchips in the updated parking passes at a constant rate of 98 cars per hour. Assuming the arrival rate is the same. (e) With the automated parking system, what is the average time (in minutes) of a car needs to wait in line? (f) If the goal is to reduce number of cars at the parking entrance (both waiting in line and being served) to under 5 cars, would you agree to use automated parking system? Justify your answer. A property management team recently signed a contract with an old downtown Toronto office building, and the first issue they must address is the current parking system. According to their observations, the current parking system has only one lane and one parking validation window, where one parking staff operates on a first-come, first-served basis. The parking staff can validate the parking passes and issue receipts at a rate of 40 seconds per car on average following a negative exponential distribution. Following a Poisson distribution, 86 cars will arrive at the entrance every hour on average during business hour. (a) List appropriately service rate and arrival rate first and then calculate what is the parking entrance utilization? (b) What is the average number of cars waiting in line? (c) What is the average time in minutes that a car has to spend at the parking entrance (both waiting in line and being served)? (d) What is the probability that there will be more than three cars at the parking entrance? The property management team consider replacing the manual parking entrance with automated parking system. The new parking system uses Radio-frequency identification (RFID) technology to read signal from the implanted RFID microchips in the updated parking passes at a constant rate of 98 cars per hour. Assuming the arrival rate is the same. (e) With the automated parking system, what is the average time (in minutes) of a car needs to wait in line? (f) If the goal is to reduce number of cars at the parking entrance (both waiting in line and being served) to under 5 cars, would you agree to use automated parking system? Justify your answer.