The traffic situation on Mackinac Island, Michigan, where no automobiles are all
ID: 802599 • Letter: T
Question
The traffic situation on Mackinac Island, Michigan, where no automobiles are allowed (bicycles are permitted), is to be studied. Comment on how such a study could be performed using a Lagrangian approach and an Eulerian approach. Comment on the important differences in how such studies would be carried out, as well as how you'd carry out the study in practice. Please be complete, but brief (i.e. no more than half a page maximum). Part of the mark will be given for how well you can explain yourself properly in a written manner.Explanation / Answer
Lagrangian Approach:
The lagrangian approach would be made by considering each cyclist as an individual moving element and its considered that his velocity is a function of his initial position and displacement with time. As his position keeps changing, the new velocity will be a function of his new initial position, hence filling up the roads with lot of lagrangian points where velocity and distance have to measured at each and every point.
In reality, you cannot measure the velocity of each cyclist at every point on the road to finally come up with the flow rate of the traffic.
Eulerian approach:
This would involve setting up stationary points on the roads and measuring the velocity of each cyclist as they pass through this given stationary point and trying to extrapolate it to the flow of traffic. This can be done in the realistic scenario, where you can put up a speed guns at major paths and traffic points, measuring the speeds of cyclists and try to get a better idea in the traffic flow.
Hence in this case the Eularian approach is better to estimate the traffic.
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