Monte Carlo Simulation

Hello all,

I am trying to complete a monte carlo simulation in relation to a traffic lane closure.

"Consider traffic on I-5 proceeding north from Santa Clara. At a particular location on I-5, traffic data have been collected during the afternoon rush hours; data on traffic volumes were
collected on the free flowing part of I-5 upstream of a reduction in the number of lanes, and also at the point just after the reduction in lanes. These data were analyzed and at the free flowing location, the sample mean was 90 cars/minute and the sample standard deviation was 30 cars/minute. At the point where the number of lanes is reduced by one, the sample mean was 75 cars/minute and the standard deviation was 20 cars/minute."

I am having trouble relating the two means and standard deviations in the model. I have been able to do the simulation with just one (mean and std dev), but adding the second throws a wrench in it.

Any help is greatly appreciated.

The second half of the question.

"Assume that the number of cars at both points in any minute is statistically independent of the number of cars at those points in the preceding minute. Construct a simulation model of cars on the highway and the queue that forms at the point where the highway narrows. Assume that the rush hour lasts 60 minutes. Assume that the queue length at the beginning of the rush hour is zero. Calculate the average arrival rate, average departure rate, average queue length, and maximum queue length for a 60-minute rush hour. Make the simulation long enough—for example, you may simulate ten 60-minute rush hours, or 100 60-minute rush hours, or 1,000 60-minute rush hours—so that these averages do not vary significantly every time the spreadsheet recalculates."

The columns I have setup are:

Period, Queue at beginning of period, Arrivals, Departures Queue at end of period,