Reference no: EM13371550
Consider a 1.25 mile stretch of a roadway of homogeneous geometric features. Assume all incoming flow is coming from the upstream section and that all traffic continues downstream of the section under consideration. In other words, there are no entrances or exits along this 1.25 mile stretch of roadway. This roadway has a speed limit of 50 mi/hr, jam density of 180 veh/mi, and a maximum flow of 3,000 veh/hr. Initially, traffic is flowing undisturbed at 80% of capacity: q = 2,400 veh/hr. Then, a partial lane blockage lasting 2 minutes occurs 1/3 of the distance from the end of the roadway. The blockage effectively restricts flow to 20% of the maximum. Clearly, a queue is going to build and dissipate. We wish to predict the evolution of the traffic density on the road before, during, and after the incident; both upstream and downstream of it.
Use a flow-based macroscopic approach, implement a first-order continuum model (LWR) with the following equilibrium speed-density relation:
u = 50[1 - k/180]1.5
where u is the average speed in mi/hr and k is the density in vehicles per lane-mile.
Write a Netlogo program that implements the LWR model using the discretization technique explained in class. Use a 6-second time step (i.e. each tick is 1/600th of an hour).
The user interface should allow users to input the following parameters.
? Segment length (mile)
- Simulation time interval (seconds)
- Two scenarios for traffic loading o Scenario 1: uniform loading rate over a 10-minute period with the following rates: 2400 veh/hr, 1800 veh/hr, and 1200 veh/hr.
o Scenario 2: triangular loading profile, over a 10-minute period, with a peak rate of 3000 veh/hr, occurring 5 minutes after the start of the loading period.
The user interface should also present the traffic densities along the roadway during each time step.
Suppose that the incident occurs at minute 3, discuss the effect of the different traffic loading patterns on the queue length and the time it takes for the queue to end (from the time the incident started). Support your discussion with printouts of the "cell" densities at each time step (6 seconds) and the values of maximum-queue-length and incident-to-clearance.