Dr. Xuesong Zhou

High-speed Passenger Trains on Freight Tracks: Modeling Issues on

Capacity Analysis, Train Timetabling and Real-Time Dispatching

Assistant ProfessorDepartment of Civil and Environmental Engineering

Univ. of Utahzhou@eng.utah.edu

In collaboration with Dr. Muhammad Babar Khan (Pakistan), Dr. Lingyun Meng (China)

Prepared for NEXTRANS Seminar Series, Purdue University

on May 11, 2010

Definitions

High-speed passenger rail – 152 mph or faster for upgraded track– 183 mph or faster for new track

In China, high-speed conventional rail lines operate at top speeds of 220 mph, and one maglev line reaches speeds of 270 mph.

Reference: http://en.wikipedia.org/wiki/High-speed_rail

http://en.wikipedia.org/wiki/High-speed_rail�http://en.wikipedia.org/wiki/High-speed_rail�http://en.wikipedia.org/wiki/High-speed_rail�

High-Speed Trains

E5 Series Shinkansen in Japan

World speed record holding (357mph) TGV

German designed third generation ICEonCologne-Frankfurt high-speed rail line

First High-speed Service Train

The Italian ETR 200 in 1939

It achieved the world mean speed record in 1939, reaching 127 mph near Milan

The Acela Express, currently the only high-speed rail line in the U.S., with a top speed of 150 mph

http://en.wikipedia.org/wiki/Acela_Express�

North American Railroad Network

5 major US railroads after years of consolidations:CSX, UP, CR, NS, BNSF

(Planned) High-Speed Rail System in United States

High-speed railway plans in China

17,000 mile national high-speed rail system will be built in 4 phases, for completion by 2030.

Chicago Hub Network

•France has a population distribution similar to that in the Midwest.•French experiences with TGV trains and other high-speed systems could conceivably be duplicated in the U.S.

• The total cost was projected at $68.5 billion in 2009 dollars, • Only 54% was projected to need public financing if a public-private partnership was pursued. •The public funds could be recovered from revenues in about 15 years.

If implemented, the plans could return Chicago to a status it had in the 1930s and 1940s

Reference: http://en.wikipedia.org/wiki/Chicago_Hub_Networkhttp://www.midwesthsr.org/docs/SNCF_Midwest.pdf

http://en.wikipedia.org/wiki/Chicago_Hub_Network�http://www.midwesthsr.org/docs/SNCF_Midwest.pdf�

Operational High-Speed Lines in Europe

High-Speed Lines in East Asia

Concepts of the two modesOperation Mode I (Dedicated Line)

Operation Mode II (High-speed passenger trains running on

freight tracks)

+

What We Need to Do in United States?

1. Building Infrastructure– Class I Railroad mileage shrank from 210K to

94K, from 1956 to 2007– Railroad ton-miles tripled from 589 billion to

1.772 trillion (thanks to technological advance)

2. Building Education Infrastructure for Railroad Transportation Engineering Employment dropped from 1 million to 167K

3. Building New Tracks for Research…Reference: Barkan, C.P.L. 2008. Building an Education Infrastructure for Railway Transportation Engineering: Renewed Partnerships on New Tracks, TR News 257: 18-23, Transportation Research Board of the National Academies, Washington, DC.

http://ict.uiuc.edu/railroad/CEE/pdf/Events/REES08/Barkan 2008 TR News 257 18-23.pdf�http://ict.uiuc.edu/railroad/CEE/pdf/Events/REES08/Barkan 2008 TR News 257 18-23.pdf�

Railroad Planning and Operations

Service Network Design

Traffic OD Demand Estimation

Socio-economic data, interview samples

InfrastructureResources

(yards and terminals)

Traffic OD Demand Matrix

Blocking Plan Line Plan

Train Scheduling

Route and Frequency Settings

Locomotive, Car and Crew Scheduling

Train Timetables

Resources and Policies

Train Dispatching, empty car distribution

Train DispatchingEmpty Car Distribution

Yard and Terminal Management

Railroad Network Capacity

Line capacity– Single or double-track -> meet-pass plans – Signal control type -> minimal headways – Locomotive power -> speed, acceleration/deceleration time loss – Train schedules -> overall throughput

Node capacity (yards, terminals / sidings)– Track configuration– Locomotive power-> car processing time– Yard make-up plans, terminal operating plans

-> overall throughput

OD Demand -> Routes-> Blocks-> Trains

Station

Block

a b c d

Dab+Dac+Dad

Blocking Plan 1Dac+Dad+Dbc+Dbd

Dad+Dbd+Dcd

DadDab+Dac Dac+Dbc+Dbd Dbd+Dcd

a

b

c

d

a

b

c

d

b

c

daBlocking Plan 2

Candidate blocks

b c d100a

bc

100 500150 200

50

destination

origin

Train scheduleTime

Term

inal

sa

b

c

d

Background on Train Scheduling

Planning Applications– Satisfy passenger and

freight traffic demand– Minimize the overall

operational costs

Real-time ApplicationsAdjust the daily and hourly train operation schedules– Improve on-time performance

and reliability

Important role in railroad management: Determine the level-of-service of train timetables Serve as the basis for locomotive and crew

scheduling

Sequential scheduling– Stage 1: Line planning – Determine the routes, frequencies, preferred departure times, and

stop schedules

– Stage 2: Schedule generation Construct the arrival and departure times for each train at

passing stations Job-shop scheduling formulation and branch-and-bound

solution algorithm (Szpigel, 1973)» Minimize a weighted sum of train delays (Kraft, 1987)

Multi-criteria scheduling (e.g. Higgins and Kozan, 1998)» Mainly focus on the supply side, such as fuel costs for locomotives, labor

costs for crews» Simplify multiple objectives as a weighted linear combination

Line Planning Timetabling Rolling stock schedulingCrew

schedulingDemand

estimation

Railway Planning Process

Train Scheduling on Beijing-ShanghaiHigh-Speed Passenger Railroad in China

Around 900 miles High-speed trains (200 mile/h)

– Provide direct service for inter-city travel in this corridor

Medium-speed trains (150 mile/h)– Run on both high-speed line and

adjacent regular rail lines in order to Serve the large volume of traffic

passing through this corridor

Reduce connecting delay for interline travel

Illustration

From Shanghai to Xuzhou 17 segments, 385 miles Morning period (6:00 am-

12:00 am) 24 high-speed trains and

12 medium-speed trains

Preferred departure time interval for high-speed trains is 30 minutes

Part I: Balancing Two Conflicting Objectives

Two conflicting objectives– (High-speed trains) Expect a “perfect” schedule with high

frequency and even departure time intervals– (Medium-speed trains) Reduce total travel time

Operational policies– High-speed trains hold higher priority, i.e. medium-speed trains have

to yield to high-speed trains, if possible conflict exists– A “perfect” high-speed train timetable might result in extremely long

waiting times for medium-speed trains Need for

– Obtain non-dominated solutions for bicriteria scheduling problem

– Retrieve the trade-offs between two conflicting objectives

Reference: Zhou, X. and Zhong, M. (2005) Bicriteria Train Scheduling for High-Speed Passenger Railroad Planning Applications. European Journal of Operational Research Vol 167/3 pp.752-771.

Challenge I

Challenge II:Model Acceleration and Deceleration Time Losses

Acceleration and deceleration time losses High-speed trains: 3 minutes Medium-speed trains: 2 minutes

section k

T ime axis

station k-1

station k

station k+1

section k-1

pq(i), k-1 pq(i), k-1 1),( −kiqdτ

pq(i), kkiq

a),(τ pq(i), k

bypass station k stop at station k

Formulating Train Timetabling and Dispatching Problem

Given– Line track configuration– Minimum segment and station headways– # of trains and their arrival times at origin stations

Find– Timetable: Arrival and departure times of each train at each

station

Objectives– (Planning) Minimize the transit times and overall operational

costs, performance and reliability– (Dispatching) Minimize the deviation between actual schedules

and planned schedule

Notations

i: subscript of trainsj: subscript of sectionsu: train types , 0: high-speed train, 1: medium-speed train

: pure running time for train type u at section k without acceleration and deceleration times: acceleration time loss at the upstream station of section k with

respect to train type u: deceleration time loss at the downstream station of section k with respect to train type u

: minimum headway between train types u and v entering/leaving section k: scheduled minimum stop time for train i at station k: preferred departure time for train i at its origin, i.e. the preferred release time for job i.

kup ,ku

a,τ

kud

,τ

kvueh ,, kvulh ,,

kis ,

id~

Decision Variables

: departure time for train i at its origin: interdeparture time between train i and train i+1: entering time for train i to section k: leaving time for train i from section k

: actual acceleration time for train i at the upstream station of section k

: actual deceleration time for train i at the downstream station of section k

: total travel time for train i

: 0 or 1, indicating if train i enters section k earlier or later than train j, respectively

: 0 or 1, indicating if train i bypasses/stops at the upstream station of section k, respectively

: 0 or 1, indicating if train i bypasses/stops at the downstream station of section k, respectively

id

iye

kix ,l

kix ,

dkiB ,

akiB ,

kjiB ,,

iC

dkit ,

akit ,

Model Acceleration and Deceleration Time Losses

Multi-mode resource constrained project scheduling approach Activity (i, k) :the process of train i traveling section k and the

project is a sequence of K activities Two sets of renewable resources are entering times and leaving

times for each section the minimum headway constraints define the consumption of

resources by each activity Processing time of activity (i, k) with train type u=q(i) in mode m

(0=no-stop and 1=stop)

Apply the algorithm proposed by Patterson et al. (1989) for solving multi-mode resource constrained project scheduling problem

=++=+=+

=

=

111001

00

),,(

,,,

,,

,,

,

mifpmifpmifp

mifp

kmupt

kud

kua

ku

kua

ku

kud

ku

ku

ττττ section k

xlj,k

xej,k

section k-1

T ime axis

station k+1

station k-1

station k

hlq(j),q(i), k

xli,k

pt(q(j),m,k)

j i

heq(j),q(i), k

xei,k

xlj,k-1

hlq(i),q(j), k

heq(i),q(j), k

Integer Programming Formulation

Allowable adjustment for departure time: (2N constraints)

Interdeparture time: (Nh -1 constraints for high-speed trains)

Departure time: (N constraints)

Total travel time: (N constraints)

Dwell time: (N*(K-1) constraints)

Travel time on sections: (N×K constraints)

Acceleration time: (N×K constraints)

Deceleration time: (N×K constraints)

Iigddgd iiiii ∈∀+≤≤−~~

1 \{ }i i i h hy d d i I N+= − ∀ ∈

Iidx iei ∈∀=1,

IixxC eil

Kii ∈∀−= 1,,

}1{\,,1,, =∈∀∈∀≥− − kVkIisxx kil

kie

ki

VkIittpxx dkiakikiq

eki

lki ∈∀∈∀++=− ,,,),(,,

1},1{\, 1,1,,, ==∈∀∈∀−≥× −ai

lki

eki

aki BkVkIixxMB VkIiBt kiq

aaki

aki ∈∀∈∀×= ,),(,, τ

1},{\,* ,,1,, ==∈∀∈∀−≥ +dKi

lki

eki

dki BKkVkIixxMB

VkIiBt kiqddkidki ∈∀∈∀×= ,),(,, τ

Integer Programming Formulation (Cont’)

Minimum headway: (N× (N-1) ×K× 4 constraints)

VkIjijihxxorhxxeither kjqiqeekie

kjkiqjqee

kje

ki ∈∀∈≠∀≥−≥− ,,,),(),(,,),(),(,,VkIjijihxxorhxxeither kjqiqll ki

lkjkiqjq

llkj

lki ∈∀∈≠∀≥−≥− ,,,),(),(,,),(),(,,

VkIjIijiMBhxx kjiiqjqee

kje

ki ∈∀∈∈≠∀×−−≥− ,,,)1( ,,)(),(,,

VkIjIijiMBhxx kjijqiqee

kie

kj ∈∀∈∈≠∀×−≥− ,,,,,)(),(,,

VkIjIijiMBhxx kjiiqjqll

kjl

ki ∈∀∈∈≠∀×−−≥− ,,,)1( ,,)(),(,,

VkIjIijiMBhxx kjijqiqll

kil

kj ∈∀∈∈≠∀×−≥− ,,,,,)(),(,,

To model the above “either-or” type constraints

Illustration of a Double-Track Train Schedule

section k

section k-2

xlj,k

xej,k

section k-1

di section 1

hlq(j),q(i),k-1

T ime axis

ii gd −~

ii gd +~

id~

station k+1

station 1

station k-2

station k-1

station kxlj,k-1

dj

......

heq(i),q(j),k

Utility Function for High-speed Trains Passengers

– Represent passengers’ preference information as a multi-attribute utility function

– U= –0.0099 (In-vehicle travel time) –0.0426 (Out-of-vehicle waiting time)

– Calibrated by the study for high-speed rail in the Toronto-Montreal corridor (KPMG Peat Marwick, Koppelman, 1990)

– In-vehicle travel time: Out-of-vehicle waiting time

» Function of variance of inter-departure times for given # of trains

Objectives

First Objective:Minimize the variation of inter-departure times for high-speed trains

i.e. Minimize the expected waiting time from a passenger arriving at the terminal to the departure time of the next high-speed trainIf assuming passengers independently and randomly arrive at the terminal,

(Random incidence theorem described by Larson and Odoni, 1981)Second objective:

Minimize the total travel time for medium-speed trains

∑−

=

−==1

1

21 )()(

hN

iii yyYVarZMin

∑+=

=N

Nii

h

CZMin1

2

Branch-and-Bound Solution Algorithm

Step 1: (Initialization)Create a new node, in which contains the first task of all trains. Set the

departure time for this train and insert this node into active node list(L).

Step 2: (Node selection)Select an active node from L according to a given node selection rule.

Step 3: (Stopping criterion)If all of active nodes in L have been visited, then terminate.

Step 4: (Conflict set construction)Update the schedulable set in the selected node.Insert these tasks and task t(i,j) into the current conflict set.

i j

i j

h

ij

h

Conflict

Additional delay

i first

j first

Branch-and-Bound Algorithm for Generating Non-dominated Solutions

Step 1: (Initialization) Create a root node into the active node list. i=0.

Step 2: (Branching) Consider high-speed train i = i*+1, branch several nodes, each corresponding to different feasible departure time for train i. Insert new nodes into the active node list.

Step 3: (Evaluation 1) Obtain objective function Z1 by calculating variance of departure times for existing high-speed trains.

Step 4: (Evaluation 2) Obtain objective function Z2 by solving subproblem with the fixed departure times for high-speed trains.

Step 5: (Dominance Rule) Apply proposed dominance rules to compare the current node with the other existing nodes, and prune all dominated nodes. Go back to Step 2.

High-speed train 1

High-speed train 2

High-speed train 3

High-speed train 4

High-speed train 5

Subproblem 1: Determine departure time of high-speed trains

Subproblem 2: Schedule all medium-speed trains

Non-Dominated Schedules

Z1(b)Z1(a) 2nd objective

1st objectiveDominated Schedule

Non- Dominated

Schedule

Z2(a)

Z2(b)

First objective: Expected waiting time for high-speed trains at originSecond objective: Average travel time for medium-speed trains

b

a

Construction of Non-Dominated Set

Objective 2

Objective 1Case 1:The new schedule replacesall the schedules in the set

Objective 1

Objective 1 Objective 1

Case 2:The new schedule replacessome of the schedules in the set

Case 3:The new schedule isadded to the set.

Case 4:The new schedule isout of the set.

Objective 2

Objective 2 Objective 2

Illustration of Dominance RulesDecision pointPartial schedule at node a

Partial schedule at node b

station 5

station 4

station 3

station 2

station 1

station 5

station 4

station 3

station 2

station 18 1 2 3

8 1 2 39

9

Main Idea:Cut dominated partial schedule

at early as possible

Conditions for node adominating node b

(1) Same set of finished trains

(2) Z (a) < Z (b) for finished trains

(3) The starting time for each unfinished activity in node a is no later than the counterpart in node b for each feasible mode

Heuristic Algorithm

Beam search algorithm uses a certain evaluation rule to select the k-best nodes to be computed at next level

High-speed train 1

High-speed train 2

High-speed train 3

High-speed train 4

High-speed train 5

High-speed train 1

High-speed train 2

High-speed train 3

High-speed train 4

High-speed train 5

High-speed train 6

High-speed train 7

Limitation of Branch-and-Bound Algorithm

Remaining non-dominated nodes in the B&B tree still grows rapidly

0100002000030000400005000060000700008000090000

100000110000120000130000

3 4 5 6

# of high-speed trains to be considered

# of

sol

utio

ns

Possible Solutions

Non-dominatedpartial schedules

Illustration of One Non-Dominated Schedule

Evaluation Rules

Utility based evaluation rule– Represent passengers’ preference information as a multi-

attribute utility function E.g. U= –0.0099 (In-vehicle time) –0.0426 (Out-of-vehicle time)

– Calibrated by the study for high-speed rail in the Toronto-Montreal corridor (KPMG Peat Marwick, Koppelman, 1990)

Random sampling– Capture the global trade-off information associated with

the efficient frontier– Randomly sample the nodes in the non-dominated partial

solutions at the current level

Exact Algorithm (B&B) vs. Heuristic Algorithm (Beam Search)

Beam width = 50

346

348

350

352

354

356

358

360

362

0 20 40 60 80 100 120Variance of interdeparture times

Aver

age t

rave

l tim

e for

med

ium

-spe

ed tr

ains

(min

s)

Exact solutions

Utility evaluation rule

Random selection rule

Trade-Off Curves forTwo Conflicting Objectives

335

340

345

350

355

360

365

14.5 15 15.5 16 16.5 17 17.5Expected waiting time for high-speed trains (mins)

Aver

age

trave

l tim

e fo

r med

ium

-spe

ed tr

ains

(m

ins)

Exact solutions for 6 high-speed trains

Utility evaluation rule for 24high-speed trains w ith beamw idth = 50

Utility evaluation rule for 24high-speed trains w ith beamw idth = 100

20 min

2 min

1 hour optimization horizon

6 hour optimization horizon

Part II: Optimizing Slack Time Allocation

Marketing – concurrent use of critical points (e.g. stations, switches and signals)

Logistics – Costs, efficient usage of rolling-stock and personnel

Operating Constraints – passengers’ travel times, pleasant transfers

and waiting times

Slack Time ?

Reference: Muhammad, K, and Zhou, X (2010) Stochastic Optimization Model and Solution Algorithm for Robust Double-Track Train-Timetabling Problem. IEEE Transactions on Intelligent Transportation Systems. Vol. 11. No. 1. pp. 81 – 89

Model Formulation

J1

J4

1

2

3

4

Time

Stat

ion

(dis

tanc

e)

5

J2

J3

Station nodeSegment arc Delay arc

High-speed train

Space-Time Network Representation

Two-stage Recourse Model

1st Stage Objective– Minimize total trains’ trip time

,1

( ) = ( )n

i i m ii

Min c x w e r=

−∑

J1

J4

1

2

3

4

Stat

ion,

(dis

tanc

e)

5

J2

J3

High-speed train (i)

Medium-speed train (j)

Time

Segment J1 r1

d1,3

f3,1

b2,1

e2,4

Illustration of model variables

Segment J4

Two-stage Recourse Model…

2nd Stage Objective– Minimize Schedule deviation

( )+, , , , , ,1

( , ) ( ) ( )n

i i m i m i i m i mi

g y x w e e w e eω ω ω+ − −

=

= − + −∑

segment 1

high-speed train

medium-speed train

station 1

station 4

Time

station 2

station 3

segment 3

segment 2

1,3d

1,1,f ω

1r

3,1f 3,1s 3,2b

3,2e

2r1,r ω

realized schedule segment 4

3r

3,3,b ω

3,3,e ω

station 0

1,3h

Solution Strategies

Sequential Decomposition– First plan high-speed trains and then medium-speed

trains Space-time network representation

– To reformulate the problem as shortest-path problem Stochastic shortest path reformulation

– a priori stochastic least expected time path problem – with the cost function as schedule delay late – the recourse decisions taken once random variables

are realized

Solution Algorithm…

J1

J4

1

2

3

4

Stat

ion

(dis

tanc

e)

5

J2

J3

High-speed train

Medium-speed train

Time

Segment J1

Segment J4

J1

J4

1

2

3

4

5

J2

J3

Segment J1

Segment J4

delay!

J1

J4

1

2

3

4

5

J2

J3

Segment J1

Segment J4

On time!

Slack time

?

Solution Algorithm…

J1

J4

1

2

3

4

5

J2

J3

Time

Segment J1

Segment J4

Many alternative paths

Stat

ion

(Dis

tanc

e)

Stochastic Time-depende Shortest Path Problem

Strategies for a Single Train Problem

Constructing random segment running times

– vector with given probability

Stochastic dominance rules

– I: Timetable v'' first-order stochastically dominatestimetable v', if. the CDF of delay distribution fortimetable v'' is above or overlapping with thecounterpart in timetable v'.

– II: Timetable v'' second-order stochastically dominatestimetable v', if , i.e., the expected delay in timetablev'' is less than its counterpart in timetable v'

, ,i jf ωωρ

Stochastic Dominance Rules

(a) No slack time(do-nothing)

(b) Timetable v' (slack time on segment j-1)

0.75 0.25

1/4

1/2

3/4

Delay

Freq

1/4

1/2

3/4

Delay

Freq

planning arc

scheduling arc PDF PDF

1/4

1/2

3/4

Delay

Freq

PDF

0.5

0.25 0.250.5

station j-2

station j-1 0.5

0.50.5

0.50.5

(c) Timetable v'' (slack time on segment j)

1/4

1/2

3/4

Delay

Freq

CDF

1

1/4

1/2

3/4

Delay

Freq

CDF

1

1/4

1/2

3/4

Delay

Freq

CDF

1

1 1 1

segment j

segment j-1

station j

+1

+1,i je′ ,i je′′

0.5×1+0.5×2=1.50.75×1+0.25×2=1.25

0 0 0

000

''( )F δ

'( )F δ

'( )F δ

Other Issues: Estimating Line Capacity

226 train pairs102 train pairs

Estimating/Simulating Terminal Capacity

Train Routing Problem at Terminals

Given– Track configuration ( track lengths, switcher engines )– Signal configuration– Inflow/Outflow (arrival and departure times of trains)

Find– Train paths through a terminal– Choke points – System performance of a rail facility under a

variety of conditions

Train Routing through Terminals

Switch Grouping

Train Paths– Train type I: switch groups a, b, d– Train type II: switch groups c, d, e– Train type III: switch groups f, g, h

Carey and Lockwood (1995); Carey (1994)– Mixed integer programming formulation– Heuristic solution algorithm

Zwaneveld, Kroon, Hoesel (2001); Kroon, Romeijn, Zwaneveld (1997)– Complexity issues – Node packing model

Recommendations

1. The performance impacts of high-speed passenger trains to freight/ medium-speed trains should be systematically evaluated in all stages of capacity estimation, timetabling and dispatching.

2. Efficient optimization algorithms are critically needed to generate executable, recoverable train timetable with quality guarantee and balanced performance.

3. Heuristic algorithms should take into account randomness of train delays, capacity breakdowns to improve the reliability of sub-optimal solutions.

Maximum speed design and capacity of the line

Expected speed of the train

Slot flexibility (special factors for interdependent trains in linked systems)

Gross weight of freight train

Deviation from the standard,(e.g.: dimensional, overweight etc.)

Factors in DB Netz´s slot price system

Slot Price System 2001 in Germany

Slot price = base price x product factors x special multipliers + special additions x regional factor

Extracted fromThe Slotted Railway -Living With Passenger Trains

Sebastian SchillingRailion Deutschland AG

Scheduling Freight And Passenger Trains

High-Speed passenger trainRegional passenger train

A*B

Clo

catio

n

1.Mixed traffic -

reduced capacity

BasicLine Capacity Layout

Connecting passenger services

2.Mixed traffic -

capacity enlargement

AB

C

3.Network 21

`Harmonizing`

AB

C

AB

CAdditional freight train slots

Extracted fromThe Slotted Railway -Living With Passenger Trains

Sebastian SchillingRailion Deutschland AG

Freight train

Number of trains*2

Railion´s Product Design

Products for unit trains (CT & IT*1)

Plantrain Variotrain Flextrain

*1: CT & IT: conventional & intermodal transport*2: per year*3: regular services; cancellations (< 10% of services) until week before service possible

Slot

Days of service

Price

Ordering date

> 50

fixed

regular

100%

service fixed*3

> 30

fixed (reserved)

flexible

100% + X

week before departure

flexible

on demand

on demand

100% + XX

min >24 h

Extracted fromThe Slotted Railway -Living With Passenger Trains

Sebastian SchillingRailion Deutschland AG

Research Directions

Robust schedule design– Executable vs. recoverable, from planning to real-time decision– Improve freight railroad service reliability

Disruption management under real time information– Service networks (blocking and line planning)– Train dispatching– Rail network and terminal capacity recovery plan– Locomotive and crew recovery plan

Integrated pricing and demand management model– Long term and short term pricing schemes and cost structures

Separation of track from traction in Europe

– Impact on traffic demand and operating plans (train schedule, fleet sizing and repositioning)

– Shipper logistics modeling– Demand estimation and prediction model

New Vision for High-speed and Intercity Passenger Rail Service in America

“Imagine whisking through towns at speeds over 100 miles an hour, walking only a few steps to public transportation, and ending up just blocks from your destination. Imagine what a great project that would be to rebuild America.”– President Obama announcing a new vision for high-speed and intercity passenger rail service in America (April 16, 2009)

Slide Number 1DefinitionsHigh-Speed TrainsFirst High-speed Service TrainSlide Number 5North American Railroad Network(Planned) High-Speed Rail System in United StatesSlide Number 8Chicago Hub Network�Operational High-Speed Lines in EuropeHigh-Speed Lines in East AsiaConcepts of the two modes�Operation Mode I (Dedicated Line)Operation Mode II �(High-speed passenger trains running on freight tracks)What We Need to Do in United States?Railroad Planning and OperationsRailroad Network CapacityOD Demand -> Routes-> Blocks-> TrainsBackground on Train SchedulingSlide Number 19Train Scheduling on Beijing-Shanghai� High-Speed Passenger Railroad in ChinaIllustrationPart I: Balancing Two Conflicting Objectives Challenge I�Challenge II:�Model Acceleration and Deceleration Time LossesFormulating Train Timetabling and Dispatching ProblemNotationsDecision VariablesModel Acceleration and Deceleration Time LossesInteger Programming FormulationInteger Programming Formulation (Cont’)Illustration of a Double-Track Train ScheduleUtility Function for High-speed Trains PassengersObjectivesBranch-and-Bound Solution AlgorithmBranch-and-Bound Algorithm for Generating Non-dominated SolutionsNon-Dominated SchedulesConstruction of Non-Dominated SetIllustration of Dominance RulesHeuristic AlgorithmLimitation of Branch-and-Bound AlgorithmIllustration of One Non-Dominated ScheduleEvaluation RulesExact Algorithm (B&B) vs. Heuristic Algorithm (Beam Search)Trade-Off Curves for�Two Conflicting Objectives Part II: Optimizing Slack Time AllocationModel FormulationTwo-stage Recourse Model�Two-stage Recourse Model…Solution StrategiesSolution Algorithm…Solution Algorithm…Strategies for a Single Train ProblemStochastic Dominance RulesOther Issues: Estimating Line CapacityEstimating/Simulating Terminal CapacityTrain Routing Problem at Terminals Train Routing through Terminals RecommendationsSlide Number 59Scheduling Freight And Passenger TrainsSlide Number 61Research DirectionsNew Vision for High-speed and Intercity Passenger Rail Service in America