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Transport modelling
Exercises part 1: generation (production and attraction)
Prof. Bruno Kochan & Dr. Muhammad Adnan
2020-2021
Practical information
 Format of the exercise sessions
 Exercises right after theory
 Explanation on exercises
 Work on exercises (individual)
 I’m available for questions
 Explanation solution exercises
 For the whole class
 Detailed solutions
 It is important to understand how to solve the exercises, not
the numerical result. Similar questions on the exam.
2
Exercises part 1: generation
 Exercise 1
 2 zones in the study area:
 From statistical analyses we know:
 Production: # work-related trips = 0.25 / inhabitant
 Attraction: # work-related trips = 1 / job
a) Calculate production and attraction of commuting trips for
both zones. Verify whether balancing is needed.
3
Exercises part 1: generation
 Exercise 1: solution
a) Production
Zone A: 1000 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡𝑠 𝑥 0.25
𝑡𝑟𝑖𝑝𝑠
𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡
= 250 𝑡𝑟𝑖𝑝𝑠
Zone B: 800 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡𝑠 𝑥 0.25
𝑡𝑟𝑖𝑝𝑠
𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡
= 200 𝑡𝑟𝑖𝑝𝑠
b) Attraction
Zone A: 240 𝑗𝑜𝑏𝑠 𝑥 1
𝑡𝑟𝑖𝑝
𝑗𝑜𝑏
= 240 𝑡𝑟𝑖𝑝𝑠
Zone B: 160 𝑗𝑜𝑏𝑠 𝑥 1
𝑡𝑟𝑖𝑝
𝑗𝑜𝑏
= 160 𝑡𝑟𝑖𝑝𝑠
4
Exercises part 1: generation
 Exercise 1: solution
c) Production and attraction in balance ?
𝑧𝑜𝑛𝑒 𝑖
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑖 =
𝑧𝑜𝑛𝑒 𝑖
𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖 ?
 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐴 + 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐵= 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴 + 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵 ?
 250 𝑡𝑟𝑖𝑝𝑠 + 200 𝑡𝑟𝑖𝑝𝑠 = 240 𝑡𝑟𝑖𝑝𝑠 + 160 𝑡𝑟𝑖𝑝𝑠 ?
 450 𝑡𝑟𝑖𝑝𝑠 ≠ 400 𝑡𝑟𝑖𝑝𝑠
 Balancing required
5
Exercises part 1: generation
 Exercise 1: solution
c) Continued…
Assume production model is most accurate:
𝑧𝑜𝑛𝑒 𝑖
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑖 = 𝑇 = 450 𝑡𝑟𝑖𝑝𝑠
𝛼 =
𝑇
𝑧𝑜𝑛𝑒 𝑖 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖
=
450 𝑡𝑟𝑖𝑝𝑠
400 𝑡𝑟𝑖𝑝𝑠
= 1.125
Attraction after balancing:
𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴
∗
= 𝛼 𝑥 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴 = 270 𝑡𝑟𝑖𝑝𝑠
𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵
∗
= 𝛼 𝑥 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵 = 180 𝑡𝑟𝑖𝑝𝑠
6
Exercises part 1: generation
 Exercise 2
 Consider 1 zone with following average HH characteristics:
7
per HH
Exercises part 1: generation
 Exercise 2 (2)
a) How many trips are generated?
Assume that income increases by 30% and within 5 years,
50% of the HH without a car will now own a car
b) How many trips are generated now?
c) Is this the best approach to tackle this type of problem?
8
Exercises part 1: generation
 Exercise 2: Solution
a) 180 𝐻𝐻 𝑥 6
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻 𝑑𝑎𝑦
+ 80 𝐻𝐻 𝑥 8
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻 𝑑𝑎𝑦
+ 40𝐻𝐻 𝑥 11
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻 𝑑𝑎𝑦
=
2160 𝑡𝑟𝑖𝑝𝑠
b) 90 𝐻𝐻 𝑥 6
𝑡𝑟𝑖𝑝𝑠
𝑑𝑎𝑦
+ 170 𝐻𝐻 𝑥 8
𝑡𝑟𝑖𝑝𝑠
𝑑𝑎𝑦
+ 40𝐻𝐻 𝑥 11
𝑡𝑟𝑖𝑝𝑠
𝑑𝑎𝑦
= 2340 𝑡𝑟𝑖𝑝𝑠
c) Good approach ? No because of income change that
cannot be taken into account
9
per HH
Exercises part 1: generation
 Exercise 3
 Data from a HH travel survey for 3 zones
10
Exercises part 1: generation
 Exercise 3 (2)
 Two production models were estimated:
1. Linear regression model
𝑦 = 0.2 + 0.5𝑥1 + 1.1𝑍1
where 𝑦 = average number of trips per HH during rush hour
𝑥1 = number of employed HH members
𝑍1 =
1 if income > 70,000
0 otherwise
2. Category analysis model
# employed HH
members
Income
Low High
1 or less 0.8 1.0
2 or more 1.2 2.3
11
Cell value =
average
number of
trips / HH
Exercises part 1: generation
 Exercise 3 (3)
 Given the current (observed) production and assuming
unaltered zone characteristics:
a) Which model performs best?
12
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
1. Linear regression model
𝑦 = 0.2 + 0.5𝑥1 + 1.1𝑍1
where 𝑦 = average number of trips per HH during rush
hour
𝑥1 = number of employed HH members
𝑍1 =
1 if income > 70,000
0 otherwise
13
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
Zone I: 𝑦 = 0.2 + 0.5 𝑥 1
𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑
𝐻𝐻
+ 1.1 𝑥 0 = 0.7
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻
Zone II: 𝑦 = 0.2 + 0.5 𝑥 2
𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑
𝐻𝐻
+ 1.1 𝑥 0 = 1.2
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻
Zone III: 𝑦 = 0.2 + 0.5 𝑥 2
𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑
𝐻𝐻
+ 1.1 𝑥 1 = 2.3
𝑡𝑟𝑖𝑝𝑠
𝐻𝐻
14
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
Zone I: #𝐻𝐻 =
20000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠
2
𝑝𝑒𝑟𝑠𝑜𝑛𝑠
𝐻𝐻
= 10000 𝐻𝐻
Zone II: #𝐻𝐻 =
60000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠
3
𝑝𝑒𝑟𝑠𝑜𝑛𝑠
𝐻𝐻
= 20000 𝐻𝐻
Zone III: #𝐻𝐻 =
100000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠
2.5
𝑝𝑒𝑟𝑠𝑜𝑛𝑠
𝐻𝐻
= 40000 𝐻𝐻
15
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
Zone I: #trips = 0.7
trips
HH
x 10000 𝐻𝐻 = 7000 𝑡𝑟𝑖𝑝𝑠
Zone II: #trips = 1.2
trips
HH
x 20000 𝐻𝐻 = 24000 𝑡𝑟𝑖𝑝𝑠
Zone III: #trips = 2.3
trips
HH
x 40000 𝐻𝐻 = 92000 𝑡𝑟𝑖𝑝𝑠
16
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
2. Category analysis model
17
# employed HH
members
Income
Low High
1 or less 0.8 1.0
2 or more 1.2 2.3
Cell value =
average
number of
trips / HH
Exercises part 1: generation
 Exercise 3: Solution
 Data from a HH travel survey for 3 zones
Zone I: #trips = 0.8
trips
HH
x 10000 𝐻𝐻 = 8000 𝑡𝑟𝑖𝑝𝑠
Zone II: #trips = 1.2
trips
HH
x 20000 𝐻𝐻 = 24000 𝑡𝑟𝑖𝑝𝑠
Zone III: #trips = 2.3
trips
HH
x 40000 𝐻𝐻 = 92000 𝑡𝑟𝑖𝑝𝑠
18
Exercises part 1: generation
 Exercise 3: Solution
 Category analysis scores best (smallest difference with
observations)
 Not by definition the best approach !
19
Linear
regression
Category
analysis
Observed
Zone I 7000 trips 8000 trips 8200 trips
Zone II 24000 trips 24000 trips 24300 trips
Zone III 92000 trips 92000 trips 92500 trips
Questions ?

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Transport_Modelling__2_Production_and_Attraction_Exercises.pptx

  • 1. Transport modelling Exercises part 1: generation (production and attraction) Prof. Bruno Kochan & Dr. Muhammad Adnan 2020-2021
  • 2. Practical information  Format of the exercise sessions  Exercises right after theory  Explanation on exercises  Work on exercises (individual)  I’m available for questions  Explanation solution exercises  For the whole class  Detailed solutions  It is important to understand how to solve the exercises, not the numerical result. Similar questions on the exam. 2
  • 3. Exercises part 1: generation  Exercise 1  2 zones in the study area:  From statistical analyses we know:  Production: # work-related trips = 0.25 / inhabitant  Attraction: # work-related trips = 1 / job a) Calculate production and attraction of commuting trips for both zones. Verify whether balancing is needed. 3
  • 4. Exercises part 1: generation  Exercise 1: solution a) Production Zone A: 1000 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡𝑠 𝑥 0.25 𝑡𝑟𝑖𝑝𝑠 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡 = 250 𝑡𝑟𝑖𝑝𝑠 Zone B: 800 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡𝑠 𝑥 0.25 𝑡𝑟𝑖𝑝𝑠 𝑖𝑛ℎ𝑎𝑏𝑖𝑡𝑎𝑛𝑡 = 200 𝑡𝑟𝑖𝑝𝑠 b) Attraction Zone A: 240 𝑗𝑜𝑏𝑠 𝑥 1 𝑡𝑟𝑖𝑝 𝑗𝑜𝑏 = 240 𝑡𝑟𝑖𝑝𝑠 Zone B: 160 𝑗𝑜𝑏𝑠 𝑥 1 𝑡𝑟𝑖𝑝 𝑗𝑜𝑏 = 160 𝑡𝑟𝑖𝑝𝑠 4
  • 5. Exercises part 1: generation  Exercise 1: solution c) Production and attraction in balance ? 𝑧𝑜𝑛𝑒 𝑖 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑖 = 𝑧𝑜𝑛𝑒 𝑖 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖 ?  𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐴 + 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐵= 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴 + 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵 ?  250 𝑡𝑟𝑖𝑝𝑠 + 200 𝑡𝑟𝑖𝑝𝑠 = 240 𝑡𝑟𝑖𝑝𝑠 + 160 𝑡𝑟𝑖𝑝𝑠 ?  450 𝑡𝑟𝑖𝑝𝑠 ≠ 400 𝑡𝑟𝑖𝑝𝑠  Balancing required 5
  • 6. Exercises part 1: generation  Exercise 1: solution c) Continued… Assume production model is most accurate: 𝑧𝑜𝑛𝑒 𝑖 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑖 = 𝑇 = 450 𝑡𝑟𝑖𝑝𝑠 𝛼 = 𝑇 𝑧𝑜𝑛𝑒 𝑖 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖 = 450 𝑡𝑟𝑖𝑝𝑠 400 𝑡𝑟𝑖𝑝𝑠 = 1.125 Attraction after balancing: 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴 ∗ = 𝛼 𝑥 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐴 = 270 𝑡𝑟𝑖𝑝𝑠 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵 ∗ = 𝛼 𝑥 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝐵 = 180 𝑡𝑟𝑖𝑝𝑠 6
  • 7. Exercises part 1: generation  Exercise 2  Consider 1 zone with following average HH characteristics: 7 per HH
  • 8. Exercises part 1: generation  Exercise 2 (2) a) How many trips are generated? Assume that income increases by 30% and within 5 years, 50% of the HH without a car will now own a car b) How many trips are generated now? c) Is this the best approach to tackle this type of problem? 8
  • 9. Exercises part 1: generation  Exercise 2: Solution a) 180 𝐻𝐻 𝑥 6 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 𝑑𝑎𝑦 + 80 𝐻𝐻 𝑥 8 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 𝑑𝑎𝑦 + 40𝐻𝐻 𝑥 11 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 𝑑𝑎𝑦 = 2160 𝑡𝑟𝑖𝑝𝑠 b) 90 𝐻𝐻 𝑥 6 𝑡𝑟𝑖𝑝𝑠 𝑑𝑎𝑦 + 170 𝐻𝐻 𝑥 8 𝑡𝑟𝑖𝑝𝑠 𝑑𝑎𝑦 + 40𝐻𝐻 𝑥 11 𝑡𝑟𝑖𝑝𝑠 𝑑𝑎𝑦 = 2340 𝑡𝑟𝑖𝑝𝑠 c) Good approach ? No because of income change that cannot be taken into account 9 per HH
  • 10. Exercises part 1: generation  Exercise 3  Data from a HH travel survey for 3 zones 10
  • 11. Exercises part 1: generation  Exercise 3 (2)  Two production models were estimated: 1. Linear regression model 𝑦 = 0.2 + 0.5𝑥1 + 1.1𝑍1 where 𝑦 = average number of trips per HH during rush hour 𝑥1 = number of employed HH members 𝑍1 = 1 if income > 70,000 0 otherwise 2. Category analysis model # employed HH members Income Low High 1 or less 0.8 1.0 2 or more 1.2 2.3 11 Cell value = average number of trips / HH
  • 12. Exercises part 1: generation  Exercise 3 (3)  Given the current (observed) production and assuming unaltered zone characteristics: a) Which model performs best? 12
  • 13. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones 1. Linear regression model 𝑦 = 0.2 + 0.5𝑥1 + 1.1𝑍1 where 𝑦 = average number of trips per HH during rush hour 𝑥1 = number of employed HH members 𝑍1 = 1 if income > 70,000 0 otherwise 13
  • 14. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones Zone I: 𝑦 = 0.2 + 0.5 𝑥 1 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 𝐻𝐻 + 1.1 𝑥 0 = 0.7 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 Zone II: 𝑦 = 0.2 + 0.5 𝑥 2 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 𝐻𝐻 + 1.1 𝑥 0 = 1.2 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 Zone III: 𝑦 = 0.2 + 0.5 𝑥 2 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 𝐻𝐻 + 1.1 𝑥 1 = 2.3 𝑡𝑟𝑖𝑝𝑠 𝐻𝐻 14
  • 15. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones Zone I: #𝐻𝐻 = 20000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 2 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 𝐻𝐻 = 10000 𝐻𝐻 Zone II: #𝐻𝐻 = 60000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 3 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 𝐻𝐻 = 20000 𝐻𝐻 Zone III: #𝐻𝐻 = 100000 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 2.5 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 𝐻𝐻 = 40000 𝐻𝐻 15
  • 16. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones Zone I: #trips = 0.7 trips HH x 10000 𝐻𝐻 = 7000 𝑡𝑟𝑖𝑝𝑠 Zone II: #trips = 1.2 trips HH x 20000 𝐻𝐻 = 24000 𝑡𝑟𝑖𝑝𝑠 Zone III: #trips = 2.3 trips HH x 40000 𝐻𝐻 = 92000 𝑡𝑟𝑖𝑝𝑠 16
  • 17. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones 2. Category analysis model 17 # employed HH members Income Low High 1 or less 0.8 1.0 2 or more 1.2 2.3 Cell value = average number of trips / HH
  • 18. Exercises part 1: generation  Exercise 3: Solution  Data from a HH travel survey for 3 zones Zone I: #trips = 0.8 trips HH x 10000 𝐻𝐻 = 8000 𝑡𝑟𝑖𝑝𝑠 Zone II: #trips = 1.2 trips HH x 20000 𝐻𝐻 = 24000 𝑡𝑟𝑖𝑝𝑠 Zone III: #trips = 2.3 trips HH x 40000 𝐻𝐻 = 92000 𝑡𝑟𝑖𝑝𝑠 18
  • 19. Exercises part 1: generation  Exercise 3: Solution  Category analysis scores best (smallest difference with observations)  Not by definition the best approach ! 19 Linear regression Category analysis Observed Zone I 7000 trips 8000 trips 8200 trips Zone II 24000 trips 24000 trips 24300 trips Zone III 92000 trips 92000 trips 92500 trips

Editor's Notes

  1. Work at own pace on the exercises
  2. Ps
  3. Ps
  4. Calculate number of trips according to both models Compare estimation to the given rush hour trips per zone