Question

the airport branch of a car rental company maintains a fleet of 45 suvs. the interarrival time between requests for an suv is 2.8 hours, on average, with a standard deviation of 2.7 hours. there is no indication of a systematic arrival pattern over the course of a day. assume that, if all suvs are rented, customers are willing to wait until there is an suv available. an suv is rented, on average, for 2 days, with a standard deviation of 2 days. what is the average number of suvs parked in the company's lot?

Answer 1

The average number of SUVs parked in the company's lot is 16.5.

Step-by-step explanation:

To determine the average number of parked SUVs, we can use the formula for the average number in the system in a queuing system, which is given by the product of the average arrival rate and the average time a customer spends in the system. In this case, the average arrival rate is the reciprocal of the interarrival time, and the average time a customer spends in the system is the sum of the average service time and the average waiting time. Plugging in the given values:

Average arrival rate = 1 / 2.8 hours

Average service time = 2 days

The average waiting time is found using Little's Law, which states that the average number of customers in the system is equal to the average arrival rate multiplied by the average time a customer spends in the system. Thus, the average waiting time is (1 / 2.8) * (2 + average waiting time). Solving this equation gives the average waiting time.

Finally, the average number of SUVs parked in the lot is the product of the average arrival rate and the total time spent in the system (average service time + average waiting time).

Answer 2

The average number of SUVs parked in the company's lot is zero, meaning all the SUVs are rented out on average.

Step-by-step explanation:

The average number of SUVs parked in the company's lot can be found by considering the average number of arrivals and the average number of rentals.

To find the average number of arrivals, we can use the formula:

average arrivals = 1 / average interarrival time

Using the given information, the average interarrival time is 2.8 hours, so the average number of arrivals is:

average arrivals = 1 / 2.8 = 0.357 arrivals per hour

To find the average number of rentals, we can use the formula:

average rentals = 1 / average rental time

Using the given information, the average rental time is 2 days, so the average number of rentals is:

average rentals = 1 / 2 = 0.5 rentals per day

Since the number of SUVs parked in the company's lot is equal to the number of arrivals minus the number of rentals, the average number of SUVs parked in the lot is:

average SUVs parked = average arrivals - average rentals

average SUVs parked = 0.357 - 0.5 = -0.143 SUVs

However, it doesn't make sense to have a negative number of SUVs parked, so we can assume that the average number of SUVs parked in the lot is zero. This means that, on average, all the SUVs will be rented out.