Incorporating Energy Considerations in

Multimodal Transportation Systems

Incorporating Energy Considerations in

Multimodal Transportation Systems

Sam Labi, 2009

Lili Du, Srinivas PeetaSchool of Civil Engineering &

NEXTRANS CenterPurdue University

Peng Wei, Dengfeng Sun School of Aeronautics and Astronautics,

Purdue University

2011 TSL Asilomar Workshop

OutlineOutline Motivation Preliminaries

– Research statement– Interactions between Traffic Demand and Supply– Intermodal Network

Mathematical Model Solution Methodology Case Study and Preliminary Results Future Work

Energy CrisisEnergy Crisis

Oil provides about 40% of the world’s energy

Non-renewable energy source

Limited storage on earth Energy security has

gained attention around the world

World Resources Institute’s Program on Climate, Energy and Pollution

U.S Oil DemandU.S Oil DemandU.S. Energy Information Administration www.eia.doe.gov

The use of petroleum products as vehicle fuels is classified as “Transportation” use; transportation system accounts for 65% of the nation’s gasoline consumption

Long Distance Passenger Transport Service Mode Energy Consumption Efficiency

Long Distance Passenger Transport Service Mode Energy Consumption Efficiency

For passenger transportation, the order of energy efficiency is “Rail” > “Road” > “Air”

James Strickland, 2009

Rail

Road

Air

Study ObjectivesStudy Objectives Study the interurban passenger trips in the multimodal

transportation systems aiming to reduce the system energy consumption considering the interactions between policy makers, multimodal traffic facility suppliers, and traffic demand.

Develop a mathematical model whose optimal solution provides the support/insights for the system policy makers to strengthen energy sustainability in a multimodal transportation system in the context of long-term planning.

Interactions between Traffic Demand and SupplyInteractions between Traffic Demand and Supply Given a multimodal network, G Link traffic service described

by waiting time, travel time, fare, service frequency

Link traffic service leads to intermodal path traffic supply

Traffic supply further leads to traffic flow distribution among modes.

Traffic flow distribution influences energy consumption

G

Ec

w

t

H

c

r

W

C

T

R

Ω

G: multimodal network; Ω: distribution of travel demand; E: energy consumption;t/c/w/ r: travel time/fare/waiting time/service frequency;T/C/W/R: corresponding path value; H: intermodal paths.

Energy consumption will impact the network as well as the traffic supply in the long-term.

Intermodal NetworkIntermodal Network

private auto transit airrail

o s

1 2

43

Nodes: cities or mode transfer ports Directed links: the connections

between cities/transfer ports– Multiple modes: private auto, transit,

rail, and air– Links differentiated by modes instead

of physical network– Aggregated link supply level

Interurban traffic demand – Deterministic single O-D– Business and non-business trips

Energy consumption per link, δ

w: waiting time; t: travel time; c: fare; r: service frequency; p: seat capacity δ :gasoline consuming

Policy MakerMake policy to minimize energy consumption

SupplierAdjust fare and service frequency to seek profit for relevant modes

DemandMaximize trip satisfaction

S-D: Ridership Elasticity

Main Idea Parameters

Variables

Bi-Level ProgramBi-Level Program

The First Level of the Bi-Level ProgramThe First Level of the Bi-Level ProgramMin Energy consumption Supply-Demand (S-D) relations

Adjust fare based on S-D relation, the suppliers’ profit goals and the associated constraints

Adjust service frequency based on S-D relation, the suppliers’ profit goals and the associated constraints

Other constraints of the decision variables; and the conversion from path flow (x) to link flow (y); x comes from the second level

Considerations for suppliers

The objective of system

policy makers

The Second Level of the Bi-Level ProgramThe Second Level of the Bi-Level Program

Max trip satisfaction

Flow conservation

Variable constraintsStatic travel time Static waiting time

Link capacity

Mathematical Model

Linear utility function used to measure the preference of travelers for an intermodal path

Constant link travel time and waiting time, do not factor traffic congestion directly

Two classes of traffic demand: Business (B) and non-business (NB)

Travelers’ preferences

Network related

constraints

Solution MethodologySolution Methodology

• Bi-level model, NP hard• First level, nonlinear mixed integer

program• Second level, linear program

• Substituting the second level by its KKT conditions

Model Computational Complexity

Solution Method

• Bi-level program => one level nonlinear program (Mathematical Program with Complementarity Constraints, MPCC))

• Branch and Bound algorithms to address integer variables

The same as previous model

Linear relaxation

KKT conditions

Mathematical Program with Complementarity Constraints (MPCC)

Mathematical Program with Complementarity Constraints (MPCC)

Branch and Bound AlgorithmBranch and Bound Algorithm

zli, sli

zli=0sli=1

zli=1sli=0

zli=0sli=0

F1=MPCC F2=MPCC F3=MPCC

Update LB and candidate solution (z*,s*) if F1, F2 or F3 provides integer solution

l=1

i=2l=l+1

z*,s*

i=i+1LB

LB…..

…..

…..

…..

l=L

z*,s*

i=I

LB

zli+sli≤1, i=2,3,4, l=1…L; zliϵ0,1; sliϵ0,1;

……

……

Initial Check new candidate nodes

Stop, if all the candidate nodes are checked

Case StudyCase Study• Study intercity trips from Lafayette to Washington D.C. with the

daily O-D traffic demand equal to150.

• Investigate the system optimal traffic flow distributions

considering energy consumption under different traffic demand

compositions (business trips and non-business trips).

• Investigate the optimal traffic flow distributions considering

system energy consumption under various road traffic conditions.

Test NetworkTest Network

Private auto (P) Transit (T) Air (A)Rail (R)

Lafayette

Indianapolis

IAD

BWI

DCPitts

DCA

• One O-D: Lafayette to Washington D.C.• Traffic demand, 150

• Four traffic modes: private auto, transit, rail, and air• Nine links, and twenty two intermodal paths differentiated by links and modes

1

23

4

5 9

6

8

7

Utility FunctionUtility Function

NB B

ar 0.0399 0.0006

ac ‐0.046 ‐0.00256

at ‐0.00193 ‐0.046

aw ‐0.0066 ‐0.0157Reference Koppelman (1990)

NB: relatively high weight to travel costB: relatively high weight to travel time

0.00.10.20.30.40.50.60.70.80.91.0

(150, 0) (125,25) (100,50) (75, 75) (50, 100) (25, 125) (0,150)

Perc

enta

ge

Intercity Traffic Demand (B, NB)

Auto, Auto, Auto Transit, Air, RailAuto, Air, Transit Auto, Air, Rail

0.00.10.20.30.40.50.60.70.80.91.0

(150, 0) (125,25) (100,50) (75, 75) (50, 100) (25, 125) (0,150)Pe

rcen

tage

Intercity Traffic Demand (B, NB)Transit, Air, TransitTransit, Air, Rail

System Optimal Traffic Demand Distributed among Intermodal Paths

System Optimal Traffic Demand Distributed among Intermodal Paths

Only Considering Traveler Preferences Considering Energy Consumption

Preliminary Results

• Without energy considerations, intermodal paths that include auto are used often by B and NB• With energy considerations, intermodal paths including transit and rail are highly recommended

Auto

Energy ConsumptionEnergy ConsumptionPreliminary Results

600800

10001200140016001800200022002400260028003000

(150,0) (125,25) (100, 50) (75,75) (50, 100) (25, 125) (0, 150)

Ene

rgy

Con

sum

ptio

n

Intercity Traffic Demand (B,NB)

EC_optEC_org

• System energy consumption is significantly reduced by shifting travelers from the intermodal paths that include auto to the intermodal paths that include transit and rail.

Ticket Price Adjustment for Each Mode on Individual Link

Ticket Price Adjustment for Each Mode on Individual Link

Reducing the system energy consumption leads to:• Transit systems may reduce fares so that more traffic demand can be shifted to

transit systems• Rail and air may increase fares to sustain the current service level

-20

-10

0

10

20

30

40

50

(150,0) (125,25) (100, 50) (75,75) (50, 100) (25, 125) (0, 150)Tick

et P

rice

Adj

ustm

ent

Intercity Traffic Demand (B,NB)

Transit(Lafayette to Indy)Transit(Indy to Pitts)Transit(BWI toDC)Transit(IAD to DCTransit(DCA to DC)Transit(Pitts to DC)Rail(BWI To DC)Airplane(Indy to BWI)Airplane(Indy to IAD)Airplane(Indy to DCA)

Preliminary Results

Preliminary Results

3

4

5

6

7

8

t0 1.25t0 1.5t0 1.75t0 2t0

Travel TimePath 5

Path 6

Path 10

Path 14

230

240

250

260

Path 5 Path 6 Path 10 path 14

Energy Consumption

• Experiments: increase road traveltime to 1.25, 1.5, 1.75, and 2 timesof the original value t0

• Check the system optimal solution• 4 paths are included• Paths 5 (1-2-6), 10 (1-3-7), and 14

(1-4-8): Transit, Air, and Transit• Path 6 (1-2-6): Transit, Air, and Rail

• Path 14 has the lowest travel time; Path 10 consumes the least fuel; Path 5 and Path 6 are relatively cheap; trade-offs exist between Paths 5, 6, 10, and14.

P T AR

Lafayette

Indy

IAD

BWI

DCPitts

DCA

1

4

6

5

7

89

23

120

140

160

Path 5 Path 6 Path 10 Path 14

Fare

0%

20%

40%

60%

80%

100%

(150, 0) (125,25) (100,50) (75, 75) (50, 100) (25, 125) (0,150)

Traffic Flow Distribution among Paths (1.5 t0)

Path 5

Path 6

Path 10

Path 14

0%

20%

40%

60%

80%

100%

(150, 0) (125,25) (100,50) (75, 75) (50, 100)(25, 125) (0,150)

Traffic Flow Distribution among Paths (1.25 to)

Path 5

Path 6

Path 10

Path 14

(B, NB)

Preliminary Results

• As road traffic becomes more congested, path 6/14 has more/less flow, and paths 10 and 5 get relatively less flow.

• Need to consider traveler’s preferences and multimodal network structure, though energy consumption is the main concern.

0%

20%

40%

60%

80%

100%

(150, 0) (125,25) (100,50) (75, 75) (50, 100) (25, 125) (0,150)

Traffic Flow Distribution among Paths (1.75 t0)

Path 5

Path 6

Path 10

Path 14

0%

20%

40%

60%

80%

100%

(150, 0) (125,25) (100,50) (75, 75) (50, 100) (25, 125) (0,150)

Traffic Flow Distribution among Paths (2t0)

Path 5

Path 6

Path 10

Path 14

(B, NB)

(B, NB)(B, NB)

SummarySummary• Mathematical model which provides technical support for system

policy makers so that they can develop efficient plans to reduce energy consumption in multimodal transportation systems in the long-term planning context.

• System energy consumption can be significantly reduced by shifting traffic demand to the more energy-efficient intermodal paths.

• Air, combined with other traffic modes such as transit and rail, can result in energy-efficient intermodal paths.

• Improving energy efficiency in a multimodal transportation system entails the systematic consideration of modal energy efficiency, traveler preferences, and network structure.

Future WorkFuture Work• Perform a more comprehensive case study

over a large network• Test the impact of gasoline price on the system

energy consumption• Test the interactions between different modes

under network structural changes

Input Data Based on Survey (1/2)Input Data Based on Survey (1/2)Link Mode p0 δ c0($) t0(h) r0 w0(h)

1 1 1 5 15 1 N 01 2 40 3 20 1.9 6 0.3332 4 100 240 100 1.667 1 1.53 4 120 230 110 1.1 2 1.54 4 120 235 120 1.333 2 1.55 1 1 25 70 8.333 N 05 2 80 18 100 11.667 1 0.56 1 1 8 35 0.667 N 06 2 40 7 20 0.833 10 0.256 3 90 4 10 0.5 12 0.3337 1 1 6 25 0.583 N 07 2 40 5 15 0.667 8 0.258 1 1 5 10 0.333 N 08 2 60 3 5 0.333 8 0.3339 1 1 20 35 5 N 09 2 60 10 50 6.667 1 0.333

Input Data Based on Survey (1/2)Input Data Based on Survey (1/2)Link Mode θ ζ η br ur bc uc

1 1 N N N 0.001 N 10 401 2 0.4 0.2 0.2 1 8 15 352 4 0.4 0.9 0.9 1 2 80 1503 4 0.4 0.9 0.9 1 3 90 1504 4 0.4 0.9 0.9 1 3 100 1605 1 N N N 0 N 40 905 2 0.6 0.2 0.2 0 2 90 1506 1 N N N 0 N 30 406 2 0.4 0.2 0.2 1 12 18 356 3 0.5 0.5 0.5 1 16 5 207 1 N N N 0 N 20 357 2 0.2 0.2 0.2 1 10 10 208 1 N N N 0 N 5 208 2 0.2 0.2 0.2 1 12 1 109 1 N N N 0 N 30 609 2 0.6 0.2 0.2 0 2 45 60

Lagrangian, KKT ConditionsLagrangian, KKT Conditions Lagrangian function

KKT Conditions