Post on 30-Jul-2020
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A Utility-based Dynamic Demand Estimation Model that Explicitly Accounts for Activity Scheduling and Duration.
Guido CANTELMO1, Francesco VITI1, Ernesto CIPRIANI2, Marialisa NIGRO2
1University of Luxembourg, 2Univeristy of Roma Tre
JULY 24 – 26, 2017
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Presentation Outline
▪ Introduction:
▪ Traffic Prediction and Dynamic OD Estimation;
▪ Utility Based OD Estimation;
▪ Utility-Based OD Estimation:
▪ Lower Level – The DTA;
▪ Upper Level – The Goal Function;
▪ Numerical Results:
▪ Trip-Based case;
▪ Tour-Based case;
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Introduction (1):Traffic Prediction and Dynamic OD Estimation
The current state of the practice for managing Transportation Systems:
Demand Model
Supply Model
Traffic state
estimation
OD estimation uses traffic information
and Big Data to calibrate the demand
model
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Traffic Zone A
Observations
Traffic Zone C
Traffic Zone B
1
3
2 4
100
1
2
3
4
100 200
100
100
100
Introduction (2):Traffic Prediction and Dynamic OD Estimation
Simulation
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Traffic Zone A
Observations
Traffic Zone C
Traffic Zone B
1
3
2 4
Introduction (2):Traffic Prediction and Dynamic OD Estimation
Simulation
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▪ Including activity information in demand estimation
▪ Trips link activities activities constrain travel behavior
▪ Trip chains scheduling of activities constrain trip
schedules
Introduction (3):Traffic Prediction and Dynamic OD Estimation
0 5 10 15 20 25
Lin
k F
low
Time of the day [hh]
Total
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▪ Including activity information in demand estimation
▪ Trips link activities activities constrain travel behavior
▪ Trip chains scheduling of activities constrain trip
schedules
Introduction (3):Traffic Prediction and Dynamic OD Estimation
0 5 10 15 20 25
Lin
k F
low
Time of the day [hh]
0 5 10 15 20 25
Lin
k F
low
Time of the day [hh]
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Main contributions / innovation:
▪ Reformulate the OD estimation problem by including utilities for
reaching a certain destination both in space and time
▪ Increase the reliability of the dynamic demand estimation by
considering departure time choice jointly with the route choice
▪ Explicitly consider activity patterns, scheduling and duration in the OD
estimation problem
▪ Test the new approach to both toy networks and realistic large scale
networks
Introduction (4):Traffic Prediction and Dynamic OD Estimation
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▪ Utility-based demand modeling and estimation
▪ Activity sequence and duration as input
▪ Activity scheduling as trade-off problem
▪ Reducing the localism in the optimization
Introduction (5):Traffic Prediction and Dynamic OD Estimation
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𝐟𝐬 = 𝑨𝒙 = 𝑩𝑷𝒙
The mathematical formulation of the Demand Estimation problem:
𝐱∗ = argmin𝐱
𝑧1 𝐝, 𝐱 𝑤1 + 𝑧2 𝒍𝐨, 𝐥𝐬 𝑤2 + 𝑧2 𝒏𝐨, 𝒏𝐬 𝑤2 + 𝑧2 𝐫𝐨, 𝐫𝐬 𝑤2 + 𝑧2 𝑫𝐨, 𝑫𝐬 𝑤2
S.t.
Demand
Data
Link
Data
Node
Data
Route
DataOther
Data
Network Loading and Behavioral model
The DODE problem is underdetermined because:
▪ Demand Data;
▪ Traffic Data;
▪ Accurate Dynamic Network Loading
▪ Accurate Behavioral Model
DTADynamic Traffic Assignment
Data and Information
Introduction (6):Traffic Prediction and Dynamic OD Estimation
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The mathematical formulation of the Demand Estimation problem:
Utility-Based OD Estimation (1):Upper Level – The Goal Function
1. The lower level: Utility Based Departure Time Choice Model
𝑈𝑛 𝑡, 𝑟 = max𝑡,𝑟
ሻ𝑈𝑛𝐴 𝑡, 𝑟 − 𝑈𝑛
𝑇(𝑡, 𝑟 ;
Dis-
Utilit
y
Time
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The mathematical formulation of the Demand Estimation problem:
Utility-Based OD Estimation (1):Upper Level – The Goal Function
1. The lower level: Utility Based Departure Time Choice Model
𝑈𝑇 = 𝛼 𝑇𝑀 𝑡ℎ𝑑 + 𝛽 ∙ 𝑚𝑎𝑥 0; 𝑡𝑤
𝑎0 − 𝑡ℎ𝑑 − 𝑇𝑀 𝑡ℎ
𝑑 + 𝛾 ∙ 𝑚𝑎𝑥 0; 𝑡ℎ𝑑 + 𝑇𝑀 𝑡ℎ
𝑑 + 𝑡𝑤𝑎0
Travel Time Late Arrival Time Early Arrival Time
𝛽 𝛾 𝜇𝜆Pre
ferr
ed A
rriv
al T
ime
Pre
ferr
ed D
ep
art
ure
Tim
e
Dis-
Utilit
y
Time
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Utility-Based OD Estimation (2):Upper Level – The Goal Function
▪ If all the users maximize their own utility, we have a temporal distribution-
model, which provides a structure to the demand.
▪ Different parameters of the DTA model provide a different distribution, for a
certain value of N.
▪ The model capture distribution of travel times, duration and departure time.
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Utility-Based OD Estimation (3):Upper Level – The Goal Function
The Utility-Based Demand Estimation
nnn z ffvvnωdnωdnω
ˆ,...,ˆ,,...,minarg),(),...,,( 111,
*1
*
S.t.
𝐟𝟏, … , 𝐟𝒏 =max𝒕
𝑈𝑠 ሻ𝒕(𝛡, 𝒓, 𝒏 ;
The “classical” Bi-level Demand
nndd
n zn
ffvvdd ˆ,...,ˆ,,...,minarg,..., 1110,...,
*1
*
1
S.t.
),...,( )ˆ,...,ˆ( 11 nn DTA ddff
𝛡 = 𝜶,𝜷, 𝜸, 𝝉 =
Where:
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▪ The (GLS) Demand Estimation Process
orig
in …
T nT 1 T 2
Start: Time Dependent OD flows Link FlowLink Flow
nnz ffvv ˆ,...,ˆ,,..., 111
Estimate The
Error
Assignment
Estimate New
Parameters
Get New Matrix
Utility-Based OD Estimation (4):Upper Level – The Goal Function
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▪ How the different elements of the Utility Based Demand Estimation work:
orig
in …
Start
t1
t2
tn
…
Departure
Time Choice
Model
Assignment
0123456789101112131415161718192021222324
Link Flow
Link Flow
Estimate New
Parameters
nnz ffvv ˆ,...,ˆ,,..., 111
Estimate The Error
Get Time Dependent OD
Flows
𝝕𝟏 𝝕𝟐 𝝕𝒏…
Utility-Based OD Estimation (5):Upper Level – The Goal Function
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Utility-Based OD Estimation (7):Property of the model
2th Property: The observability of the variables is Higher for the
Utility-Based Approach
3th Property: The MPRE of Utility-Based OD estimation is less than or
equal to the case where the Departure time is exogenous;
1th Property: If 𝑁𝑑𝑒𝑝𝑡𝑖𝑚𝑒−𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 < 𝑁𝑡𝑖𝑚𝑒−𝑖𝑛𝑡𝑒𝑟𝑣𝑙𝑎𝑠
Then 𝑁𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠−𝑈𝑡𝑖𝑙𝑖𝑡𝑦𝐵𝑎𝑠𝑒𝑑 < 𝑁𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠−𝐶𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙
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Numerical Results (1):
Trip-Based case
Traffic Zone B
Traffic Zone A
A B C
D
TTab=2t;
TTdb=t;
TTbc=t;
The Experiment is performed:
▪ I-LTM Dynamic Traffic Assignment Model
▪ Assuming a “bad” spatial distribution of the
demand
▪ We consider ONLY trip based demand
▪ Only Link Flows are considered in the goal
function
▪ Finite Difference Gradient Based Approach
Is the model more reliable in term of spatial/temporal distribution?
First set of experiments: Trip-Based scenario
Destination
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Numerical Results (2):
Trip-Based case
First set of experiments:
Classical Approach Utility-Based Approach
Sim
ula
ted L
ink F
low
s
Real Link FlowsS
imula
ted L
ink F
low
sReal Link Flows
Real Demand flowStarting Demand flow
Estimated Demand flow
Classical GLS
Traffic Zone A
Dem
and F
low
Time of the day [h]
Capacity
Traffic Zone B
Dem
and F
low
Time of the day [h]
Capacity
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Numerical Results (2):
Trip-Based case
First set of experiments:
Classical Approach Utility-Based Approach
Sim
ula
ted L
ink F
low
s
Real Link FlowsS
imula
ted L
ink F
low
sReal Link Flows
Real Demand flowStarting Demand flow
Estimated Demand flow
Traffic Zone A
Dem
and F
low
Time of the day [h]
Capacity
Traffic Zone B
Dem
and F
low
Time of the day [h]
Capacity
Utility-Based GLS
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Numerical Results (2):
Trip-Based case
First set of experiments:
Classical Approach Utility-Based Approach
Sim
ula
ted L
ink F
low
s
Real Link FlowsS
imula
ted L
ink F
low
sReal Link Flows
Real Demand flowStarting Demand flow
Estimated Demand flow
Classical GLS
Traffic Zone A
Dem
and F
low
Time of the day [h]
Capacity
Traffic Zone B
Dem
and F
low
Time of the day [h]
Capacity
Utility-Based GLSClassical Approach Utility-Based Approach
Go
al F
unction
Number of Iterations
Goal F
unction
Number of Iterations
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Utility-Based OD Estimation (8):Properties
Including Activity Duration:
Counting Station
Traffic Zone A
1
Traffic Zone B
2
Traffic Zone C
3
Traffic Zone D
4
▪ Destination choice model based on the utility/dis-utility;
▪ Utility functions Accounts for scheduling and duration;
▪ Departure time choice for different legs of the trip are correlated;
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Utility-Based OD Estimation (8):Properties
Including Activity Duration:
Counting Station
Traffic Zone A
1
Traffic Zone B
2
Traffic Zone C
3
Traffic Zone D
4HomeWork
Grocery Store
Grocery Store
▪ Destination choice model based on the utility/dis-utility;
▪ Utility functions Accounts for scheduling and duration;
▪ Departure time choice for different legs of the trip are correlated;
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Numerical Results (3):
Tour-Based case
Second set of experiments: Tour-Based Case
Home Work
Gym
Gym
▪ Commuting-based demand;
▪ Only link flows are considered in the goal function;
▪ Finite Difference Gradient Based Approach;
▪ I-LTM Dynamic Traffic Assignment Model
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Numerical Results (4):
Tour-Based case
Second set of experiments:
Goa
l F
un
ctio
n (
RM
SE
)
Iteration Number
Sim
ula
ted
Lin
k F
low
s
Observed Link Flows
Classical GLS
Utility Based GLS
Classical GLS
Utility Based GLS
Scatter Link Flows Goal Function Trend
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Numerical Results (5):
Tour-Based case
Second set of experiments:
Dem
an
dF
low
(V
eh
/h)
Time of the day
Real Demand flow
Starting Demand flow
Classical GLS
Utility Based GLS
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Numerical Results (5):
Tour-Based case
Second set of experiments:
Dem
an
dF
low
(V
eh
/h)
Time of the day
Real Demand flow
Starting Demand flow
Classical GLS
Utility Based GLS
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Numerical Results (5):
Tour-Based case
Second set of experiments:
Dem
an
dF
low
(V
eh
/h)
Time of the day
Real Demand flow
Starting Demand flow
Classical GLS
Utility Based GLS
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Testing on Big sized networks
Network of Luxembourg City:
▪ 17 traffic zones
▪ 24 h of Simulation
▪ Large number of Variables (14000 OD pairs)
▪ 32 Loop Detectors vs 2744 (active) Links
Estimated Profile with standard SPSAParametric Approach:
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Testing on Big sized networks
Network of Luxembourg City:
▪ 17 traffic zones
▪ 24 h of Simulation
▪ Large number of Variables (14000 OD pairs)
▪ 32 Loop Detectors vs 2744 (active) Links
Estimated Profile with standard SPSAParametric Approach:
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Testing on Big sized networks
Network of Luxembourg City:
▪ 17 traffic zones
▪ 24 h of Simulation
▪ Large number of Variables (14000 OD pairs)
▪ 32 Loop Detectors vs 2744 (active) Links
Estimated Profile with standard SPSAParametric Approach:
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Conclusions:
Problems and challenges:
✓ A novel Utility Based Demand Estimation Model:
▪ Off-line flow based demand estimation;
▪ Reduces the localism of the DDE;
▪ Accounts for different trip purposes ;
▪ Provide a structure/Reduce the number of variables (Smoother Goal
Functions);
▪ Bring consistency in the Demand Estimation;
✓ Shortcomings:
▪ Solution Algorithms (Line Search);
▪ Exploit Analytical Relations between different activity patterns;
▪ Still computational demanding (Finite Difference Approach);
✓ Future Work:
▪ Mapping activity locations;
▪ Multimodal
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Utility-Based OD Estimation (5):Properties
Capacity
Ttoll
Capacity
Ttoll
Tend
Tend
TendTtoll
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Evidences behind the proposed approach:
▪ We need to account for temporal
and spatial demand structure;
▪ Few activities/trips carry a lot of information;
▪ It is possible to use few variables to model the mobility demand?
(Average departure time, variance,..);
Introduction (5):Regular Demand Patterns and Empirical
analysis
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Utility-Based OD Estimation (4):Properties
Trip-Based Case:
1th Property: If 𝑁𝑑𝑒𝑝𝑡𝑖𝑚𝑒−𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 < 𝑁𝑡𝑖𝑚𝑒−𝑖𝑛𝑡𝑒𝑟𝑣𝑙𝑎𝑠
Then 𝑁𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠−𝑈𝑡𝑖𝑙𝑖𝑡𝑦𝐵𝑎𝑠𝑒𝑑 < 𝑁𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠−𝐶𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙
▪ The number of Variables is usually lower.
▪ Spatial and temporal Correlation Between the variables:
GF
alpha
Perturbing the
Total Demand
GF
alpha
Perturbing the Spatial/Temporal
Distribution
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Utility-Based OD Estimation (5):Properties
Trip-Based Case:
Traffic Zone A
Counting Station
Traffic Zone B
1 2
Real Demand Estimated Demand
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Utility-Based OD Estimation (6):Properties
▪ MPRE (Maximum Possible Relative Error) is infinite;
▪ Utility Constraints the solution space of the MPRE;
Err
or
in O
D1
Error in OD2
Utility/Disutility of Travelling
OD2OD1
Real Demand
2th Property: The MPRE of Utility-Based OD estimation is less than or
equal to the case where the Departure time is exogenous;
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Utility-Based OD Estimation (7):Properties
Trip-Based Case:
▪ Small Perturbation;
▪ Similar solution at Equilibrium;
▪ Limited effect on the Goal Function;
▪ New Link Flows not observable
(limited number of counting stations);
▪ Bigger Perturbation and departure
time choice model;
▪ More likely to find a different
Equilibrium;
▪ More observability (of the variables);
Classical GLS formulation:
Utility-Based formulation:
3th Property: The observability of the variables is Higher for the
Utility-Based Approach
Counting
Station