Question

Part B: Let's consider a town with a low-capacity town route (1500 vehicles per hour) and a high-capacity bypass (3000 v/h), as shown below. The bypass is longer but has higher geometric design standards. Let's assume that during morning peak, 2000 drivers approach the town and all of them want to use the shortest route, i.e. via town center. Not all drivers will be able to use this route, since it would become too congested even before its ultimate capacity. This means that many drivers would choose the bypass to avoid long queues and delays, until the network reaches equilibrium.

PLEASE SHOW WORK. WILL UPVOTE WITHIN A DAY.

Answer 1

We know the equation those are :

1. Cb=15+0.005*Vb

2. Ct=10+0.02*Vt

For equilibrium we know that both the costs would be equal

So it becomes

15+0.005*Vb=10+0.02*Vt

Now we also know that

Vb +Vt = 2000

Vb = 2000-Vt

15+0.005(2000-Vt)=10+0.02*Vt

0.015Vt=25-10

Vt=1000 vehicle

Vb =2000-1000 = 1000 vehicle

We can see that half the traffic moves through town and half through bypass

So the general equation for traffic through each road is

Traffic through town = V/2

Traffic through bypass =V/2

Where V is the total traffic volume

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