A Utility-based Dynamic Demand Estimation Model that ...cpb-us-e1.wpmucdn.com/sites.northwestern......

www.mobilab.lu

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

www.mobilab.lu

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;

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

Traffic Zone A

Observations

Traffic Zone C

Traffic Zone B

1

3

2 4

Introduction (2):Traffic Prediction and Dynamic OD Estimation

Simulation

www.mobilab.lu

▪ 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

www.mobilab.lu

▪ 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]

www.mobilab.lu

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

www.mobilab.lu

▪ 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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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.

www.mobilab.lu

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:

www.mobilab.lu

▪ 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

www.mobilab.lu

▪ 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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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;

www.mobilab.lu

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;

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

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:

www.mobilab.lu

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:

www.mobilab.lu

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:

www.mobilab.lu

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

www.mobilab.lu

Utility-Based OD Estimation (5):Properties

Capacity

Ttoll

Capacity

Ttoll

Tend

Tend

TendTtoll

www.mobilab.lu

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

www.mobilab.lu

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

www.mobilab.lu

Utility-Based OD Estimation (5):Properties

Trip-Based Case:

Traffic Zone A

Counting Station

Traffic Zone B

1 2

Real Demand Estimated Demand

www.mobilab.lu

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;

www.mobilab.lu

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