Highway Engineering

(1) Trip makers choose a route connecting their origin and destination on the
basis of which one gives the shortest travel time
(2) Trip makers know the travel times on all available routes between the origin
and destination.

If these two assumptions are made, a rule of route choice can be assembled which
states that trip makers will select a route that minimises their travel time between
origin and destination. Termed Wardrop’s first principle, the rule dictates that, on
the assumption that the transport network under examination is at equilibrium,
individuals cannot improve their times by unilaterally changing routes (Wardrop,
1952). If it is assumed that travel time is independent of the traffic volume along
the link in question, all trips are assigned to the route of minimum time/cost as
determined by the ‘all-or-nothing’ algorithm illustrated in Example 2.7.

Forecasting Future Traffic Flows 35

Example 2.7 – The ‘all-or nothing’ method of traffic assignment

The minimum time/cost paths for a six-zone network are given in Table 2.14,

with the average daily trip interchanges between each of the zones given in

Table 2.15.

Using the ‘all-or-nothing’ algorithm, calculate the traffic flows on each link

of the network.

Solution

For each of the seven links in the network, (1-2, 1-4, 2-3, 2-5, 3-6, 4-5, 5-6),

the pairs contributing to its total flow are:

Link 1-2: flows from 1-2, 2-1, 1-3, 3-1, 1-5, 5-1, 1-6, 6-1

Link 1-4: flows from 1-4, 4-1

Link 2-3: flows from 1-3, 3-1, 1-6, 6-1, 3-4, 4-3, 2-3, 3-2, 3-5, 5-3

Link 2-5: flows from 1-5, 5-1, 2-4, 4-2, 4-3, 3-4, 2-5, 5-2, 2-6, 6-2, 3-5, 5-3

Link 3-6: flows from 1-6, 6-1, 3-6, 6-3

Link 4-5: flows from 4-2, 2-4, 4-5, 5-4, 4-3, 3-4, 4-6, 6-4

Link 5-6: flows from 4-6, 6-4, 2-6, 6-2, 5-6, 6-5

The link flows can thus be computed as:

Link flow 1-2: 250 + 300 + 150 + 100 + 100 + 150 + 75 + 150 = 1275

Link flow 1-4: 125 + 200 = 325

Link flow 2-3: 100 + 150 + 75 + 150 + 50 + 100 + 275 + 325 + 125

+ 100 = 1450

Link flow 2-5: 150 + 100 + 150 + 200 + 50 + 100 + 400 + 300 + 150 + 150 +

125 + 100 = 1975

Link flow 3-6: 75 + 150 + 240 + 180 = 645

Link flow 4-5: 150 + 200 + 350 + 250 + 50 + 100 + 125 + 225 = 1450

Link flow 5-6: 125 + 225 + 150 + 150 + 200 + 175 = 1025

Figure 2.2 illustrates these 2-way daily link volumes.

Contd