Calculate the length of queue at the bottleneck

Reference no: EM132208529

Question: Let us consider the bottleneck model discussed in the class. Let us give specific values for the parameters in the model. In particular, assume that ?? = 1, ?? = 0.5, ?? = 2, ?? ∗ = 8, ?? = 200, and ?? = 50. Using the formula sheet provided, solve the following problems:

a) Draw a curve for cumulative arrivals at the bottleneck and that for cumulative exits from the bottleneck. In drawing the graph, be specific about the intercepts, slopes, and definition of the axis.

b) Calculate the length of queue at the bottleneck at time 7.

c) Calculate the travel time of the commuter who joins the queue at time 7.

d) Compute the cost per person in equilibrium (??¯) and the total cost for all (??(??)).

e) Draw the graph illustrating the relationship between arrival time at work and the travel time cost.

f) Draw a graph illustrating the relationship between arrival time at work and the time-early-orlate cost.

g) Draw a graph illustrating the length of queue by time.

h) Compute the total travel time costs for all commuters.

i) Derive the time-varying socially optimal toll, and illustrate using a graph

Reference no: EM132208529

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