1. Provincial Models in Gauteng
Keith Bloy

2. Contents of Presentation
Gauteng
History of PWV Consortium
Results of 3 models compared to counts
Some other aspects from studies

4. Gauteng Province 1.4 % of land area 19.7 % of population 38 % of GDP
37 % of motor vehicles

5. The PWV Consortium High economic growth in 60s & 70s
TPA decided to plan a major road network
Framework required for orderly development
Local authorities planning own roads
Need to protect corridors for the long-term
Cannot study single routes in isolation

6. PWV Consortium
PWV Consortium appointed in 1973 with Mr van Niekerk as the leader
5 Consulting engineers, 2 Town and regional planners
High growth in last the 30 years has shown the wisdom of the founders of the Consortium

7. PWV Consortium’s Models
Projective Land Use Model (PLUM)
SAPLUM used for land use projections
Transportation models

8. 1975 PWV Study 16 000 km2 544 zones Planpac/Backpac
Capacity restraint assignment

9. 1985 Update Increased to 23 900 km2 589 zones UTPS suite of programs
Equilibrium assignment

11. Vectura Study (1991) Greater emphasis on public transport
Originaly the same study area as 1985
Later enlarged to km2 and 632 zones
EMME/2
Equilibrium assignment

12. New Volume Delay Functions 1994

13. Gauteng Transportation Study (GTS)
Being developed at present
Screen line counts in 2000
Reduced study area ( km2)
828 zones

14. GTS Study Area

15. Gauteng Transportation Study
Screen line counts (2000)
80 stations

16. Comparison: Modelled vs Counts Individual Stations (80 Stations)
Study R2
Intercept
Slope
1985 Study
0.608
225.24
1.093
Vectura
0.638
133.88
1.014
Vectura-new
0.760
206.07
0.949

17. Comparison: Modelled vs Counts Screen Line Sections
Study R2
Intercept
Slope
1975 Study
0.905
14870
1.095
1985 Study
0.913
1.450
Vectura
0.937
1.186
Vectura-new
0.970
1.263

18. Comparison: Modelled vs Counts
Good agreement on screen line sections (generation & distribution models good)
New volume delay functions improved R2
Results good considering changes since 1994

19. Comparison of Trip Distribution Using UTPS & EMME/2
UTPS – Program GM (integer values)
EMME/2 – 3 Dimensional Balancing (real values)
Before function bint(x)
Basic Program, MATINT

20. Example Using bint(x) 1 2 3 4 5
Total
0.2
1.0 6
5.0

21. Example Using bint(x) 1 2 3 4 5 Total 0 +0.2 0 +0.4 1 –0.4 0 –0.2
0 0.0
1.0
0.2 6
0.8
1.8
5.0

22. Example Using bint(x) 1 2 3 4 5
Total
1.0 6
0.0
5.0

23. Example Using MATINT 1 2 3 4 5 Total 0+0.2+0.2 0+0.4+0.2 0+0.6+0.2
1.0
0.2 6
0.8
1.6
5.0

24. Example Using MATINT 1 2 3 4 5
Total
1.0 6
5.0

25. MATINT vs bint Admittedly a contrived example Actual matrices:
588 by 588 matrices
bint: column totals out by ± 32
MATINT: out by ± 1

26. Trip Distribution with a Difference
Old political system restricted where people could live
A single distribution resulted in inaccuracies
Several sub-area distributions based on known factors

27. Original distribution

28. New Distribution

29. Development of a Travel Time Matrix
Based on travel times from Vectura model
Ensure correspondence between nodes and links of Vectura and GTS models
Vectura matrix adjusted using macro and counts (560 directional counts)
10 iterations of macro, R2 = to (y = x)
New matrix assigned to Vectura network
Link travel times assigned to a user field (ul3)

30. Development of a Travel Time Matrix
Link travel times for road network from Vectura network imported into user field in GTS network (ul3)
Single trip matrix assigned to GTS network, and centroid connector travel times assigned to user field (ul3)
Volume delay functions set to user field (ul3)
Single trip matrix assigned and the resultant travel travel time matrix saved = travel time matrix

31. Development of a Travel Time Matrix
Add terminal times (based on area type and local knowledge)
Add intra-zonal travel times (1/2 travel time to nearest adjacent zone)

32. Validation of Travel Time Matrix (Measured Travel Times)
Y = X
R2 = 0.827

33. Validation of Travel Time Matrix (Measured Travel Times)
Y = X
R2 = 0.956

34. Calculate Costs of Congestion
Equilibrium assignment, calculate costs
Identify links with level of service E or F
Matrix capping using macro DEMADJ and volumes = 0.9 of capacity on selected links
Iteration: Equilibrium assignment, identify remaining links with LOS E or F, and repeat process

35. Calculate Costs of Congestion
a) Capped matrix assigned and costs calculated and subtracted from original costs: cost of congestion = R billion per year
b) Remainder matrix also assigned costs calculated using travel times from (a) and added to (a): cost of congestion = R 1035 billion

36. Minimum No of Runs for permitted errors
Travel Time Surveys
Avg Range in Speed
Minimum No of Runs for permitted errors
±2km/h
±3.5km/h
±5km/h
±6.5km/h
±8km/h
5.0 4 3 2
10.0 8
15.0 14 7 5
20.0 21 9 6
25.0 28 13
30.0 38 16 10

37. Maximum Range of Average Running Speeds for Different Numbers of Runs (km/h)
Road Types
Number of Runs 10 9 8 7 6 5
Freeway: Peak 11 12 13 15 18
Off-peak
Multi-lane : Peak
Divided Off-peak 17 21
Two-lane : Peak
Two-way Off-peak 14 16 19

38. Final Remarks
Thanks to Gautrans

39. Comparison of Trip Distribution Using UTPS & EMME/2
Three dimensional balancing
Equal time intervals of 3 minutes
Same number of trips in each interval, 10 one-minute intervals
As many one-minute intervals as possible (25)

40. Comparison of Trip Distribution Using UTPS & EMME/2
Model
Avg Tvl Time
% Intrazonals
UTPS
21.4
8.9
EMME/2 (a)
21.9
8.6
EMME/2 (b)
8.7
EMME/2 (c)

41. Comparison of Trip Distribution Using UTPS & EMME/2
Difference in cell values
EMME/2 (a)
(%of total)
EMME/2 (b)
EMME/2 (c)
82.4
82.6
85.6
± 1
95.7
96.0
98.7
± 2
97.0
97.2
99.3
± 3
97.6
97.8
99.6
± 4
98.0
98.2
99.7
± 5
98.3
98.5
99.8