Traffic and Congestion Management

MSc in Urban Transport Management

UTM 511 Traffic and Congestion Management

Assignment 3

Given the cost functions of the 3 routes:

Route A: 25 + 0.15* Flow

Route B: 20 + 0.08 * Flow

Route C: 6 + 0.31 * Flow

1a) Using all-or-nothing approach, assign the trips numbering 15,000 from origin 1 to destination 2 in groups of 1,000.

No. of trips = 15,000

No. of iterations required (n) = 15,000 / 1000 = 15

Results

Final cost of Route A: 775

Final cost of Route B: 660

Final cost of Route C: 626

Maximum cost: 775 (Route A)

Minimum cost: 626 (Route C)

Average cost = (775 + 660 + 626) / 3 = 687

Maximum variation from average: I775 – 687I = 88 (Route A)

1b) Using all-or-nothing approach, assign the trips numbering 15,000 from origin 1 to destination 2 in groups of 250.

No. of trips = 15,000

No. of iterations required (n) = 15,000 / 250 = 60

Results

Final cost of Route A: 700

Final cost of Route B: 680

Final cost of Route C: 703.5

Maximum cost: 703.5 (Route C)

Minimum cost: 680 (Route B)

Average cost = (700 + 680 + 703.5) / 3 = 694.5

Maximum variation from average: I680 – 694.5I = I- 14.5I = 14.5 (Route B)

2) Comments on the different results obtained:

As seen from case 1b, when the trips are distributed in more groups of smaller proportions (with no change in the total no. of trips), the maximum cost of route is smaller than that of case 1a (703.5 < 775) while the minimum cost of route is larger than that of case 1a (680 > 626). The maximum variation from average reduces from 88 (case 1a) to 14.5 (case 1b).

The route with maximum cost and the route with minimum cost in case 1a are Route A and Route C respectively whereas the route with maximum cost and the route with minimum cost in case 1b are Route C and Route B respectively.

Hence, based on the results obtained, it can be observed that all-or-nothing approach will yield a more evenly-distributed cost among the 3 different routes when the trips are distributed in more...