Example of link impedance calculation

Table 92 to Table 95 show an example in which link impedance consists of the current travel time and road toll. For HGV transport systems which have a higher "value of time" the influence of road tolls on link impedance is less than for car transport systems.

Table 92: Input data for link impedance calculation

Link length

10,000 m

Permitted maximum speed v0 car

130 km/h

Permitted maximum speed v0 HGV

100 km/h

Road toll for cars

€1

Road toll for HGV

€5

Capacity

3,000 car units/h

Car volume

1,000 cars/h = 1,000 car units/h

HGV volume

100 HGV/h = 200 car units/h

Value of time VOTCar

18 €/h = 0.005 €/s

Value of time VOTHGV

36 €/h = 0.010 €/s

VD function according to BPR

with a = 1, b = 2, c = 1

Table 93: Car travel times and speeds

Car travel time in unloaded network

t0 car = 10 000 • 3.6 / 130 = 277s

Car travel time in loaded network

tCur car = 277 • (1+(1 200/3 000)²) = 321s

Car speed in loaded network

vCur car = 10 000 • 3.6 / 321 = 112 km/h

Table 94: HGV travel times and speeds

HGV travel time in unloaded network

t0 HGV = 10 000 • 3.6 / 100 = 360s

HGV travel time in loaded network

tCur HGV = MAX (321s; 360s) = 360s

HGV speed in loaded network

vCur HGV = 100 km/h

HGV speed only declines if the volume is more than 1644 car units/h if:

tCur = 277 • (1+(1644/3000)²) = 360s

Table 95: Calculation of link impedance for HGVs and cars

Car impedance in loaded network

Rcar = 1 + 0.005 • 321 = 2.61 €

HGV impedance in loaded network

RHGV = 5 + 0.010 • 360 = 8.60 €