Question

For the first four hours of the day, the arrival rate at the gas station is 18 vehicles per hour. the gas station is capable of serving 16 vehicles per hour. assume that the system is empty at the start and that no vehicle who arrives leaves without being served. what is the average wait time for vehicles during this time period (in hours)?

Answer 1

The average wait time for vehicles during the first four hours is 2 hours.

Step-by-step explanation:

To find the average wait time for vehicles during the first four hours, we need to calculate the average number of vehicles in the system at any given time. The arrival rate is 18 vehicles per hour, and the service rate is 16 vehicles per hour. The average number of vehicles in the system can be calculated using Little's Law: Average Number of Vehicles = Arrival Rate * Average Wait Time. Rearranging the formula, Average Wait Time = Average Number of Vehicles / Arrival Rate.

For the first four hours, the average arrival rate is 18 vehicles per hour. The average number of vehicles in the system can be calculated as follows:

1. Calculate the average number of arrivals in the first four hours: 18 vehicles/hour * 4 hours = 72 vehicles
2. Calculate the average number of vehicles in the system at any given time: 72 vehicles / 2 = 36 vehicles

Finally, calculate the average wait time: Average Wait Time = 36 vehicles / 18 vehicles/hour = 2 hours.