Two origins, A and B, are connected to a single destination D by multiple paths.

Question

Two origins, A and B, are connected to a single destination D by multiple paths. Origin A is directly connected to destination D via link 1 and indirectly via link 2 through Origin B. Origin B is connected directly to destination D via links 3 and 4. Link 1 Origin Link 3Dest Link 2 origin B Link 4 TAD-22-tAD BD-10-2 t2= 1+2x2 All volumes are expressed in vehicles per hour (vph); all travel times are expressed in minutes (min). The estimated demand and performance functions are provided with the network (where T is OD demand volume (in vph), x is link volume (in vph), and t is travel time (in minutes, for OD pairs or links). Find the User Equilibrium flow pattern.

Explanation / Answer

* With reference to above performance and demand functions and by initial deductions or simplification we have inferred the following data which would be useful in ascertainment of user equilibrium flow pattern are as given below.

- TAD ( Route 1 OR Link 1 ) = 22-3-x1

- TAD ( Route 2 OR Link 2+Link3 ) = 22-3-2x2-x3

- TAD ( Route 3 OR Link 2+Link4 ) = 22-2-2x2-x4

Inferences - 1. TAD ( Route 2 ) < TAD ( Route 1)

2. TAD ( Route 2 ) < TAD ( Route 3)

Hence, by analysing all the given equations & analyzing the relationship between the

time(t) vs route volume (x).

-Route 1 or Link 1 is the most preferred one because of the least time( t1) & least vehicle volume ( x1) on this.

-Route 3 is the next preferred route Whereas Route 2 is the least preferred route because it take higher time ( t2 + t3) than other two routes.

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