Introductory example of equilibrium assignment

The effectiveness of the equilibrium assignment is described in the example in Table 132 and Image 97. The example analyzes the relation between traffic zone "village A" and traffic zone "city X".

For simplicity, the total impedance of a route is the sum of the link impedances of the route (Impact models), i.e. the impedances of the connectors and turns are not modeled in this example. In detail, the following assumptions apply:

• The impedance of the links is determined from the current travel time tCur. The current travel time tCur is in turn calculated using the capacity restraint function BPR with a=1, b=2 and c=1.
• The access and egress times for the connectors are not considered, that is, they are set to 0 minutes.
• Turn penalties are not considered.

With regard to the traffic demand the following applies.

• The traffic demand between A-Village and X-City is 2,000 car trips during peak hour.
• Capacity and demand refer to one hour.

The example network contains three routes which connect village A and city X.

• Route 1 via nodes 10 – 11 – 41 – 40
• Route 2 via nodes 10 – 11 – 20 – 21 – 30 – 31 – 40
• Route 3 via nodes 10 – 12 – 21 – 30 – 31 – 40

Route 1 mainly uses country roads and is 26 km long. It is the shortest route. Route 2 is 30 km long. It is the fastest route because the federal road can be traversed at a speed of 100 km/h if there is free traffic flow.

Route 3 which is also 30 km long is an alternative route which only makes sense if the federal road is congested.

Image 97: Example network for equilibrium assignment

Table 132: Example network for equilibrium assignment

LinkNo	From Node	To Node	Type	Length [m]	Capacity [car units/h]	v0-PrT [km/h]
1	10	11	20 Federal road	5000	1200	100
2	11	20	20 Federal road	5000	1200	100
3	20	21	20 Federal road	5000	1200	100
4	20	40	90 Rail track	10000	0	0
5	21	30	20 Federal road	5000	1200	100
6	30	31	20 Federal road	5000	1200	100
7	31	40	20 Federal road	5000	1200	100
8	11	41	30 Country road	16000	800	80
9	40	41	30 Country road	5000	800	80
10	10	12	40 Other roads	10000	500	60
11	12	21	40 Other roads	5000	500	60

As a result, the assignment provides values of Table 133 for the three routes (PrT paths).

Table 133: Assignment results for the three PrT paths

Route	tCur	t0	Impedance	Volume (AP)
1	18min 45s	38min 20s	2300	736.431
2	18 min	38min 20s	2302	994.102
3	24 min	38min 20s	2301	269.466

The most important assignment results for links are displayed in Table 134.

Table 134: Assignment result at the links

Link	tCur	Impedance	Volume (AP)	Saturation PrT (AP)	VehicleHr(tCur)	VehKmTravelled PrT
1	9min 14s	554	1730.533	144.2 %	266h 28min 30s	8652.669
2	5min 4s	304	994,102	82.8 %	83h 49min	4970.510
3	5min 4s	304	994.1024	82.8 %	83h 49min	6317.841
5	6min 20s	380	1263.568	105.3 %	133h 13min 40s	6317.841
6	6min 20s	380	1263.568	105.3 %	133h 13min 40s	6317.841
7	6min 20s	380	1263.568	105.3 %	133h 13min 40s	6317.841
8	22min 10s	1330	736.431	92.1 %	272h 5min 45s	11782.907
9	6min 56s	416	736.431	92.1 %	85h 1min 48s	3682.158
10	12min 54s	774	269.466	53.9 %	57h 57min 19s	2694.661
11	6min 27s	387	269.466	53.9 %	28h 58min 40s	1347.331