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