17/4/13

Challenge the future Delft University of Technology

CIE4801 Transportation and spatial modelling

Rob van Nes, Transport & Planning

Case study Delft, Exam questions supply modelling

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Content

• Case study Delft

• Using a model in your MSc-thesis

•  Exercises supply modelling •  Short questions •  Exam questions

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1.

Case study Delft

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Case Study: City of Delft

•  You will do a study for the city of Delft

• An increase of traffic flows through the city center is expected

•  You will develop two candidate solutions to resolve this problem: •  Electric bicycles •  Pricing, e.g. cordon

charging or parking

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Case Study: City of Delft

• The base year and future scenarios are available in OmniTRANS •  You have to determine what the future problems will be •  You have to design and implement the scenarios for the solution

candidates • Analysis techniques have to be applied to quantify the

performance of each scenario •  Congestion levels •  Selected link analysis •  Selected area analysis •  Accessibility measures

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Case Study: City of Delft

•  You have to work in couples •  Practical sessions: 3, 10 & 17 October •  You will write a report which will be graded based on:

•  Proper use of theory •  Quality of the analysis •  Quality and creativity of the solution design •  Layout and presentation

• Deadline for report: 24th of October, 16h00 •  2 hard copies!

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2.

Using a model in a MSc-thesis project

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For many MSc studies you would like to use a model

• Option 1: You can’t get any modelling data

• Option 2: There’s a model and you can get networks and OD-matrices

• Option 3: You’ve got access to the full modelling framework

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No modelling data at all

• Use other data to get an idea of the main transport characteristics •  Counts •  Household surveys, e.g. OVG/MON/OViN •  Reports on modelling studies in the same area

• Use engineering judgement •  For typical OD-pairs determine the level of service (skims of travel

times etc) and use e.g. a logit model to estimate mode choice or route choice (the parameters are your choice)

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You’ve got networks and matrices

•  You can do matrix manipulations and assignments •  Usually you’re interested in a part of the model

=> adapt the zoning system

• What’s missing is e.g. a mode choice model •  2 options

•  Determine level of service using the networks (skims) and apply a (self-made) version of the Poisson-model

•  Determine level of service and estimate a mode choice model (e.g. a Logit model having mode specific constants and parameters for the level of service of the modes)

•  In both cases select a set of relevant OD-pairs that are consistent in size

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You’ve got the full framework

• Don’t get lost in all the data and all modelling features

•  You might want to adapt the zoning system to your study goal

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3.

Supply modelling: short questions

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- Link flows and route travel times are outcomes of the traffic assignment problem. - In the all-or-nothing assignment, all OD flows are assigned to the shortest route. -  A shortest-path all-or-nothing assignment can be computed by minimizing the total travel time subject to flow conservation and nonnegativity constraints. - Outcomes of a shortest-path all-or-nothing assignment are ‘stable’ outcomes; minor changes in the network structure only result in minor changes in the assignment outcomes.

Route choice

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- In a shortest path AON assignment, the traveler chooses the objective shortest route, whereas in stochastic assignment the traveler chooses the subjective shortest route. - The logit assignment is always based on route level, whereas the probit assignment is solved on the link level. - The error term in stochastic assignment is the same for each route/link. - Nested logit models and probit models are able to deal with overlapping route alternatives.

Stochastic assignment

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- In a deterministic user-equilibrium, all route travel times for each OD pair are equal. - The solution to the DUE assignment problem is always unique. - Similar to AON assignment, the DUE assignment aims at minimizing the total network travel time. - In DUE assignment, most OD flow is assigned to the route with the lowest free-flow travel time.

DUE assignment

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Suppose we have given the following link travel time function proposed by Smock (1962): Furthermore, assume we have software for solving the deterministic user-equilibrium assignment problem. How can we compute the deterministic system-optimal assignment?

0( ) exp( / )a a a a at q t q C=

Run the DUE assignment software using the following adapted (marginal) link travel time function: *

0 0

0

( ) ( ) ' ( )exp( / ) ( / )exp( / )(1 ( / ))exp( / )

a a a a a a a

a a a a a a a a

a a a a a

t q t q t q qt q C t q C q Ct q C q C

= + ⋅

= +

= +

Deterministic system optimal

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- The only difference between the objective function of an AON assignment and a DSO assignment is, that in the latter case the link travel times depend on the link flows. - In a DUE assignment, adding new links to a network can make the individual travel time higher. - In a DSO assignment, adding new links to a network can make the total network travel time higher. - In case all routes in a network have identical travel time functions and are non-overlapping, the DUE solution is equal to the DSO solution.

DUE and DSO

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4.

Supply modelling: exam questions

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Given the following travel time function in OmniTRANS:

Which parameter values should be chosen for an AON, stochastic, DUE and SUE assignment?

0 0( ) 1 , (0, )aa a a a

a

qt q t N tC

β

α⎡ ⎤⎛ ⎞⎢ ⎥= + + Θ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

z z :

α β Θ

Stoch: 0 0 >0

DUE: >0 >0 0

SUE: >0 >0 >0

AON: 0 0 0

1: assignment types

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Consider the following network.

Determine approximate route shares for the 3 different routes using the probit model, assuming that all links have equal average travel time. You may use the following list of random standard normally distributed numbers.

1.16 0.63 0.08 0.35 -0.70 1.70 0.06 1.80 0.26 0.87 -1.45 -0.70 1.25 -0.64 0.58 -0.36 -0.14 -1.35 -1.27 0.98 -0.04 -0.80 -0.77 0.86 -0.06 0.51 0.40 0.76 0.40 -1.34 0.38 1.13 0.73 -2.38 -0.27 -0.32 0.32 -0.51 -0.00 1.61 0.85 0.27 -0.92 -0.07 0.15 -0.56 -0.34 0.42 1.56 -2.44

a b

c d e

2: stochastic assignment

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a b c d e a+b a+c d+e 1.16 0.63 0.08 0.35 -0.70 1.79 1.24 -0.35 1.70 0.06 1.80 0.26 0.87 1.76 3.50 1.13 -1.45 -0.70 1.25 -0.64 0.58 -2.15 -0.20 -0.06 -0.36 -0.14 -1.35 -1.27 0.98 -0.50 -1.71 -1.29 -0.04 -0.80 -0.77 0.86 -0.06 -0.84 -0.81 0.80 0.51 0.40 0.76 0.40 -1.34 0.91 1.27 -0.94 0.38 1.13 0.73 -2.38 -0.27 1.51 1.11 -2.65 -0.32 0.32 -0.51 0.00 1.61 0.00 -0.83 1.61 0.85 0.27 -0.92 -0.07 0.15 1.12 -0.07 0.08 -0.56 -0.34 0.42 1.56 -2.44 -0.90 -0.14 -0.88

30% 30% 40%

Since all links and routes have equal average travel time, we only need to consider the error terms.

2: stochastic assignment

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Consider a network with 3 non-overlapping routes. Assume that the travel times are given by The total travel demand is 40 cars. (a) Determine the user-equilibrium flows graphically (b) Determine the user-equilibrium flows analytically

1 1 1

2 2 2

3 3 3

( ) 10 2( ) 20( ) 40

t q qt q qt q q

= +

= +

= +

3: DUE

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1t 2t3t

q3 = 2 q2 = 22 40q

42

(a)

3: DUE

q1 = 16

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(b) 1 1 2 2

2 2 3 3

1 2 3

( ) ( )( ) ( )

40

t q t qt q t qq q q

=⎧⎪

=⎨⎪ + + =⎩

1 2

2 3

1 2 3

10 2 2020 40

40

q qq q

q q q

+ = +⎧⎪

+ = +⎨⎪ + + =⎩

11 22

3 212 2 22

5

20

( 5) ( 20) 40

q q

q q

q q q

⎧ = +⎪⎪

= −⎨⎪

+ + + − =⎪⎩

1

2

3

16222

qqq

=⎧⎪

=⎨⎪ =⎩

3: DUE

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a b

c d e

f g

Consider a network in which all links are identical. The total travel demand from A to B is 1000 vehicles. (a) What are the link flows when performing a stochastic assignment? (b) What happens to these link flows in a stochastic equilibrium assignment?

A

B

4: SUE

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(a) In a stochastic assignment, congestion effects are not taken into account. There are three routes: a → b → e c → f → g a → d → g They all have the same costs, therefore each route gets equal share. Link flows: [a,b,c,d,e,f,g] = [666,333,333,333,333,333,666]

a b

c d e

f g

A

B

A

B

333 333

333

333 333

333

333 333

333

4: SUE

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(b)  In a stochastic equilibrium assignment, congestion effects are taken into account. Links a and g will become more congested. Therefore the route a → d → g (which uses two congested links) will be used less.

Therefore, links a, d, and g will have less flow, and the other links will have a higher flow.

a b

c d e

f g

A

B

A

B

350 350

300

350 300

300

350 350

350

4: SUE

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Consider the following network with two OD pairs, (A,C) and (B,C):

Determine the link flows in a deterministic user-equilibrium.

A

B

C

1 10t =

2 2t =

4 2t =5 12t =

3 36 / 2000t q= +

5000ACT =

10000BCT =

5 DUE

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Deterministic user-equilibrium: Case I.

Case II. Case III. Case IV. Case V.

A

B

C

1 10t =

2 2t =

4 2t =5 12t =

3 36 / 2000t q= +1 2 5000f f+ =

A

B

C

1f

2f

3f

4f3 4 10000f f+ =

32 10t+ <

32 10t+ =

1 2 3 4 f f f f 0 5000 10000 0 ? ? 10000 0 5000 0 10000 0 5000 0 ? ? 5000 0 0 10000

310 2 12t< + <

32 12t+ =

32 12t+ >

32 12 :t+ = 3 3 42 6 (0 ) / 2000 12 8000, 2000f f f+ + + = ⇒ = =

5000 0

8000 2000

5: DUE

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Consider the following network with one OD pair, (A,B) :

Suppose that the travel demand from A to B is 1200. Iteratively determine the link flows in a deterministic system optimum.

A B

21

1 12( ) 63 400

qt q ⎛ ⎞= + ⎜ ⎟⎝ ⎠

22 2( ) 14

800qt q = +

6: DSO

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First, determine the marginal link cost functions: 2 2

* 1 1 11 1 1 1 1 1 1 1

2 4 1( ) ( ) ( ) 6 6 23 400 3 400 400 400

q q qt q t q t q q q⎛ ⎞ ⎛ ⎞ ⎛ ⎞ʹ′= + = + + ⋅ = +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

* 2 22 2 2 2 2 2 2 2

1( ) ( ) ( ) 14 14800 800 400q qt q t q t q q qʹ′= + = + + = +

0 0 6 14 1200 0 1 1200 0 24 14 0 1200 1/2 600 600 10.5 15.5 1200 0 1/3 800 400 14 15 1200 0 1/4 900 300 16.2 14.8 0 1200 1/5 720 480 12.5 15.2 1200 0 1/6 800 400 14 15 1200 0 1/7 857 343 15.2 14.9

1q 2q 1t 2t 1w 2w α

6: DSO

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5.

Next week: Guest lectures

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Next week

•  Lectures from practice in The Netherlands •  Dutch National Model System: Gerard de Jong (Significance, ITS Leeds) •  Base year matrix estimation (Regional Model): Peter Mijjer (4Cast) •  Regional Model application: Jan van der Waard (KIM) •  Urban transport modelling: Bastiaan Possel (Goudappel Coffeng)

• Goal of these presentations: •  Lectures focus on basic theory, practical on a simple case •  These lectures focus on models in practice and their context

•  Your task: •  Determine similarities and differences between my story and theirs •  Per practical team, send me an e-mail before Wednesday 14.00 with one

or two topics that struck you and/or requires additional discussion

Monday

Tuesday