transportation and spatial modelling: lecture 2
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1 CIE4801: Trip generation and networks
17/4/13
Challenge the future Delft University of Technology
CIE4801 Transportation and spatial modelling
Rob van Nes, Transport & Planning
Trip generation and networks
2 CIE4801: Trip generation and networks
Content
• Trip generation • Definitions • 3 methods • Special issues
• Networks • Defining a network • Shortest path
3 CIE4801: Trip generation and networks
1.
Trip generation Definitions
4 CIE4801: Trip generation and networks
Introduction to trip generation Trip production / Trip attraction
Trip distribution
Modal split
Period of day
Assignment
Zonal data
Transport networks
Travel resistances
Trip frequency choice
Destination choice
Mode choice
Time choice
Route choice
Travel times network loads
etc.
5 CIE4801: Trip generation and networks
What do we want to know?
6 CIE4801: Trip generation and networks
Ambiguous definitions?
• Definition 1 • Production: person related • Attraction: activity related
• Definition 2 • Production: departures • Attraction: arrivals
7 CIE4801: Trip generation and networks
A
A B
B
from:
to:
Introduction to trip generation
8 CIE4801: Trip generation and networks
Trips or tours?
• Trip
• Tour Home Activity 1
Activity 2
Home Activity
Origin Destination
Destination Origin
9 CIE4801: Trip generation and networks
Travel characteristics Netherlands (MON)
Trips per person per day
0.00.51.01.52.02.53.03.54.04.5
1978 1983 1988 1993 1998 2003 2008
trips
Average speed
0510152025303540
1978 1983 1988 1993 1998 2003 2008
km/h
our
Distance travelled per person per day
051015202530354045
1978 1983 1988 1993 1998 2003 2008
dist
ance
[km
]
Time travelled per person per day
0102030405060708090
1978 1983 1988 1993 1998 2003 2008
time
[min
]
10 CIE4801: Trip generation and networks
Key figures passenger transportation Netherlands (MON)
• Number of trips per person per day: 2.9
• Travel time per person per day: 70 minutes (1 a 1.5 hour)
• Average trip length: 11 km
• 50% of trips is shorter than 3 km
• 1.5% of trips is longer than 100 km
Travel time budget!
11 CIE4801: Trip generation and networks
Trip purpose (Netherlands) Trips and tripkilometres
12 CIE4801: Trip generation and networks
Dominant definition in this course
Given: A map with zones and zonal data
Determine: • The number of trips departing at each zone (production) • The number of trip arriving at each zone (attraction)
From:
zone 1 … zone i … …
total attraction
zone
1
…
zone
j
…
…
tota
l pr
oduc
tion To:
13 CIE4801: Trip generation and networks
Possible factors traveller production
Factors affecting the production: • income • car ownership • household structure • family size • value of land • residential density
personal household zone
Which definition for production is used?
14 CIE4801: Trip generation and networks
Possible factors traveler attraction
Factors affecting the attraction: • office space • retail space (shops) • employment levels
And which for attraction?
15 CIE4801: Trip generation and networks
Possible classifications
Trip purpose • compulsory / mandatory trips
– working trips – education trips
• discretionary / optional trips – shopping trips – social / recreational trips
Time of day • peak period • off-peak period
Person type • income level • car ownership • household size
16 CIE4801: Trip generation and networks
2.1
Trip generation Method 1
17 CIE4801: Trip generation and networks
Regression models
k kk
Y Xβ=∑
Y Endogenous (explained) variable e.g. number of trips produced by a zone or household Exogenous (explanatory) variables e.g. number of inhabitants, household size, education Parameters
kX
kβ
1 20.91 1.44 1.07Y X X= + +
number of trips number of workers number of cars
(linear regression)
18 CIE4801: Trip generation and networks
Regression models
Y
XiX
iY
iεα
β
Least squares: minimize ( )22 ˆi i i
i iY Yε = −∑ ∑
i iY Xα β= +
19 CIE4801: Trip generation and networks
Regression models
1 20.91 1.41 1.07Y X X= + +
Linear regression:
2
1 2
2
0.84 if 01.41 1.59 if 1
3.98 if 2
XY X X
X
=⎧⎪
= + =⎨⎪ ≥⎩
Nonlinearity problem: The parameter for is not constant.
2X
# trips per household # workers per household # cars per household
1
2
YXX
=
=
=
Regression with dummy variables:
1
1 2
0.84 1.410.75 3.14
Y XD D
= + +
+ +
1 1D = if 1 car, 0 otherwise if 2 or more cars, 0 otherwise
2 1D =1X
Y
X2 ≥ 2X2 = 1X2 = 0
20 CIE4801: Trip generation and networks
Example for 24-hour model
T r i p purpose
Regression formula
Work 0.9 * working population + 0.9 * jobs
Business 0.5 * working population
Education 0.2 * households + 1.9 * students
Shopping 1.0 * households + 15.6 * retail jobs
Other 3.5 * households
Total 6.5 * households + 2.9 * jobs
Note that in this case it is assumed that production equals attraction
21 CIE4801: Trip generation and networks
2.2
Trip generation Method 2
22 CIE4801: Trip generation and networks
Cross-classification models
Classify households in homogenous groups e.g. number of people in household, number of cars, and combinations
all households
trip rate trip rate
group 1 group 2
group 3
group 4
23 CIE4801: Trip generation and networks
Cross-classification models
Advantages: • groupings are independent of zone system • relationships do not need to be linear • each group can have a different form of relationship
Disadvantages: • no extrapolation beyond the calibrated groups • large samples are required (at least 50 obs. per group) • what is the best grouping?
24 CIE4801: Trip generation and networks
Cross-classification models
household size
1 person 2 persons 3 persons ≥
0 cars 1 car 2 cars ≥
20, 0.2n µ= = 10, 0.5n µ= = 0, ?n µ= =
85, 0.5n µ= = 150, 0.9n µ= = 20, 1.5n µ= =
25, 0.7n µ= = 40, 1.2n µ= = 30, 2.0n µ= =
130, 0.5n µ= = 200, 0.9n µ= = 50, 1.8n µ= =
30, 0.3n µ= =
255, 0.8n µ= =
95, 1.3n µ= =
25 CIE4801: Trip generation and networks
Cross-classification models
130, 0.5n µ= = 200, 0.9n µ= = 50, 1.8n µ= =
household size
1 person 2 persons 3 persons ≥
0 cars 1 car 2 cars ≥
30, 0.3n µ= =
255, 0.8n µ= =
95, 1.3n µ= =
0.9µ =
0.6−
0.1−
0.4+
0.4− 0.0 0.9+
0.0 0.3 1.2
0.4 0.8 1.7
0.9 1.3 2.2
Multiple Class Analysis (MCA)
0.2 0.5 ?
0.5 0.9 1.5
0.7 1.2 2.0
26 CIE4801: Trip generation and networks
Cross-classification models
household size
1 person 2 persons 3 persons ≥
0 cars 1 car 2 cars ≥
0.0 0.3 1.2
0.4 0.8 1.7
0.9 1.3 2.2
Zone i having 253 households yields
50
25
10
30 1
70
44
10
13
Trip production of zone i: 188
27 CIE4801: Trip generation and networks
2.3
Trip generation Method 3
28 CIE4801: Trip generation and networks
Discrete choice models
Binary logit Alternative 0: do not make a trip Alternative 1: make one or more trips 1 ...V =
0 0V =
Probability of making at least one trip:
11
0 1 1
exp( ) 1exp( ) exp( ) 1 exp( )
VpV V V
µµ µ µ+ = =
+ + −
How many trips on average does a person make?
29 CIE4801: Trip generation and networks
Discrete choice models
Stop/repeat-model
person
0 trips ≥1 trips
binary logit 1p +0p
1 trip ≥2 trips
binary logit 2p +1p
2 trips ≥3 trips
binary logit 3p +2p
etc…
Possible attributes: • Houshold
characteristics • Driving license • Car ownership • Gender • Age • Education • Income
30 CIE4801: Trip generation and networks
3.
Trip generation Special issues
31 CIE4801: Trip generation and networks
Special issues
• What about external zones?
• Modelling all trips or a single mode?
• Segmentation?
• Role of accessibility?
• Does total of departures equal total of attractions?
32 CIE4801: Trip generation and networks
Which area do you model?
Study area
Influence area
External area
Study area
Internal Out Out
Influence area
In Through and…..
Through and…..
External area
In Through and…..
Through and…..
Study area
Cordon
Study area
Internal Out
Cordon
In Through
33 CIE4801: Trip generation and networks
Swiss model
34 CIE4801: Trip generation and networks
Segementation by trip purpose Trips and trip kilometres
35 CIE4801: Trip generation and networks
Role of accessibility?
• MON: ‘fixed’ trip rate per person per day
• Recent model estimations: small effect for some trip types
• In case of unimodal models? Substantial impact, especially for public transport
36 CIE4801: Trip generation and networks
Does trip production equal trip attraction?
120
130
100
• We have determined the trip production
80 170 50
• We have determined the trip attraction
What to do?
300
350
Trip balancing: your choice to decide which of the two is the constraint
350 93 198 59
350
37 CIE4801: Trip generation and networks
4.
Networks Defining a network
38 CIE4801: Trip generation and networks
Networks trip production / trip attraction
trip distribution
modal split
period of day
assignment
zonal data
transport networks
travel resistances
trip frequency choice
destination choice
mode choice
time choice
route choice
travel times network loads
etc.
39 CIE4801: Trip generation and networks
Constructing a transport network
Given a map of the study area, how to represent the infrastructure and the travel demand in a model?
40 CIE4801: Trip generation and networks
Network attributes
node • x-coordinate • y-coordinate
centroid node • zonal data • origin/destination
link • node-from • node-to • length • maximum speed • number of lanes • capacity
41 CIE4801: Trip generation and networks
Links and junctions
=
Junction with all turns allowed
Junction with no left turns allowed
42 CIE4801: Trip generation and networks
Define zones and select roads
43 CIE4801: Trip generation and networks
Define zones
390
389
388
383
385
384
377
379
380
382
381
378
949
363
374
452
375
373
951952
953
954
372
950
948
298
294
293
288
249281 282
310
311
312 313
314 315
316
287
322324
325
326
328
331
332
339
330
333
329
334335
323 319321
318
336337
338
340
341
342
309
944
344
305
304
308
307
317302
297
295
292
291
290288
299
300 301
296
306
303
345
346
327
343
964
943
348
349350
354
355
357
351
352
353
359
358
356 365364
371
370
361
362
368 369
365367
360
945
946947
356 955
387
470
471
959481
482
446453
454
461 458
459
460
448
449 450451
452
456
455
457
480
479
552
554
551
555 540 539
984983
528
979978
538982
981
529
985
527526
533
534
524523
537525
963
522
521
576
483
520519
518
517
516
513
514
515
509
508
507
506
505
510
511
512
577 578 579
463
464473
476
474
472475
478
468
467
465
466
469
489
957
386
490503
491
492488
484485487488
497
495
498
494
498
499
502
501
500
445
393
440
441
442
958
443
444
439961
438
587
588
504
585 962589
280
279
278
320
How do we determine zones? • base zone definitions on official spatial systems (e.g. municipalities, postal districts) • try keeping compact convex forms • more zones needed for modal split than for assignment
44 CIE4801: Trip generation and networks
Select links
4321 nodes1217 zones
826 nodes 170 zones
204 nodes 36 zones
centroidnodereal linkconnector
How many zones / nodes / links? • depends on the application • rule of thumb: include 75% of the network capacity (note: 20% of the network accounts for 80% of the travelled kilometers)
modelling =
the art of leaving things out
45 CIE4801: Trip generation and networks
Which roads should be included?
46 CIE4801: Trip generation and networks
Urban or regional model?
Regional Urban
47 CIE4801: Trip generation and networks
Example car network regional model
48 CIE4801: Trip generation and networks
Important issues
• Connecting the zones to the network:
• Single connector or multiple connectors?
• Connecting to which type of node/link?
• Choices have major consequences for the assignment to the network!
49 CIE4801: Trip generation and networks
Public transport network
• Car or bike: • Roads defined using links
• PT: Network of services • Space accessibility
• Stops, stations
• Lines
• Time accessibility
• Frequencies
• Operating hours
• Defined using access links, transfer links, in-vehicle links, ...
50 CIE4801: Trip generation and networks
5.
Networks Shortest path
51 CIE4801: Trip generation and networks
Shortest Path algorithms
• “Oldies” • Moore (1959) • Dijkstra (1959) • Floyd-Warschall (1962)
• Still a topic for research
52 CIE4801: Trip generation and networks
Main concept for ‘tree algorithms’ (Moore and Dijkstra)
• For all nodes • Set travel time tt(x) to and set the back node bn(x) to 0
• For the origin i set time to 0 and back node to -1 • Node i is the first active node a • Select all links (a,j) and check travel times
• If tt(a)+time(a,j) < tt(j) tt(j)=tt(a)+time(a,j) and bn(j)=a and node j becomes an active node
• Node a is no longer active
• Select a new active node from the stack and repeat previous step until there are no active nodes left
• For Dijkstra: select the link having the lowest travel time and select the active node having the lowest travel time
∞
53 CIE4801: Trip generation and networks
Main concept for matrix algorithm (Floyd-Warschall)
• Create two matrices from all nodes to all nodes • tt(i,j) = t(i,j) for all links (i,j) or tt(i,j) = • bn(i,j)=i for all links (i,j)
• For every node k check travel times • If tt(i,k) + tt(k,j) < tt(i,j)
tt(i,j) = tt(i,k) + tt(k,j) and bn(i,j)=bn(k,j)
• Repeat previous step until no changes are made
∞
54 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
Shortest paths
55 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
2 0
Shortest paths
56 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
3 0 2
Shortest paths
57 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
3
3
2
Shortest paths
58 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4 4 3
2
Shortest paths
59 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4 4
5
3
2
Shortest paths
60 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
6 5
4 3
2
Shortest paths
61 CIE4801: Trip generation and networks
2 1
3
2
1 1
2
1
1
5
6
4
6 6
4 3
2
Shortest paths
62 CIE4801: Trip generation and networks
2 1
3
2
1
2
1
1
Shortest path tree Contains shortest paths to all nodes from a certain origin
Shortest paths
63 CIE4801: Trip generation and networks
1 1
4
7
2
5
8
3
6
9
2
3 4 5 6 7
8 9 10 11 12
Shortest route from node 7 to node 5: node 7 à node 4 à node 1 à node 2 à node 5 or link 8 à link 3 à link 1 à link 4
Representation of shortest paths
64 CIE4801: Trip generation and networks
1 1
4
7
2
5
8
3
6
9
2
3 4 5 6 7
8 9 10 11 12
Very compact, less practical: Back node representation
4 1 6 7 2 9 -1 7 8
node
1
node
2
node
3
node
4
node
5
node
6
node
7
node
8
node
9
route “7 à x”
Number for elements for storing all shortest routes in the network:
9 9 81N N× = ⋅ =
Representation of shortest paths
65 CIE4801: Trip generation and networks
1 1
4
7
2
5
8
3
6
9
2
3 4 5 6 7
8 9 10 11 12
link 1 0 1 0 0 1 0 0 0 link 2 0 0 0 0 0 0 0 0 link 3 1 1 0 0 1 0 0 0 link 4 0 0 0 0 1 0 0 0 link 5 0 0 1 0 0 0 0 0 link 6 0 0 0 0 0 0 0 0 link 7 0 0 0 0 0 0 0 0 link 8 1 1 0 1 1 0 0 0 link 9 0 0 0 0 0 0 0 0 link 10 0 0 1 0 0 1 0 0 link 11 0 0 1 0 0 1 1 1 link 12 0 0 1 0 0 1 0 1
rout
e 7à
1 ro
ute
7à2
rout
e 7à
3 ro
ute
7à4
rout
e 7à
5 ro
ute
7à6
rout
e 7à
8 ro
ute
7à9
Less compact, very practical: Assignment map
Number for elements for storing all shortest routes in the network:
( 1) 12 9 8 864A N N× × − = ⋅ ⋅ =
3 0 2 4 0 0 0 1 0 0 0 0
Representation of shortest paths
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