Math Help Forum: computer models

A student organization is planning a car wash. A shopping center has granted
permission to use a portion of its parking lot with the understanding that no more than 24 meters of
driveway length will be used. The students expect the 8 meter-long cars to arrive at the car wash one
every 10 minutes on the average, and the car-washing team believes that it can wash a car in 5 minutes
on the average.
a). What proportion of the time will the students be able to rest?
b). How many cars will be waiting in line at the car wash on the average?

Originally Posted by Tebby

A student organization is planning a car wash. A shopping center has granted
permission to use a portion of its parking lot with the understanding that no more than 24 meters of
driveway length will be used. The students expect the 8 meter-long cars to arrive at the car wash one
every 10 minutes on the average, and the car-washing team believes that it can wash a car in 5 minutes
on the average.
a). What proportion of the time will the students be able to rest?
b). How many cars will be waiting in line at the car wash on the average?

You entitle this thread Computer Models, but you do not tell us exactly what you have been asked to do.

It looks like you are expected to construct a next event simulation for this problem. You will need to assume a distribution for the intervals between arrivals of new cars, and time to wash the current car at the head of the que (if there is one). As the available space is 24 m and the cars are 8 m the maximum que length is 3, any arrivals while the que is full must be turned away.

When a new event occurs you will need to process the time since the last event and the que length since the last event as the time that the que is a given length for all the possible lengths are the statistics you need to answer the question.

RonL