Dr. Xuesong Zhou Assistant Professor Department of Civil and - - PowerPoint PPT Presentation

SLIDE 1

• Dr. Xuesong Zhou

High-speed Passenger Trains on Freight Tracks: Modeling I ssues on Capacity Analysis, Train Tim etabling and Real-Tim e Dispatching

Assistant Professor Department of Civil and Environmental Engineering

• Univ. of Utah

zhou@eng.utah.edu

I n collaboration w ith Dr. Muham m ad Babar Khan ( Pakistan) , Dr. Lingyun Meng ( China)

Prepared for NEXTRANS Seminar Series, Purdue University

• n May 11, 2010

SLIDE 2

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

• f 270 mph.

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

SLIDE 3

High-Speed Trains

E5 Series Shinkan sen in Japan World speed record holding (357mph) TGV

German designed third generation ICEon Cologne-Frankfurt high-speed rail line

SLIDE 4

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

SLIDE 5

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

SLIDE 6

North Am erican Railroad Netw ork

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

SLIDE 7

( Planned) High-Speed Rail System in United States

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

SLIDE 8

SLIDE 9

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_Network http: / / www.midwesthsr.org/ docs/ SNCF_Midwest.pdf

SLIDE 10

Operational High-Speed Lines in Europe

SLIDE 11

High-Speed Lines in East Asia

SLIDE 12

Concepts of the tw o m odes Operation Mode I ( Dedicated Line)

SLIDE 13

Operation Mode I I ( High-speed passenger trains running on freight tracks)

+

SLIDE 14

W hat W e Need to Do in United States?

 1 . Building I nfrastructure

– 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 I nfrastructure 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.

SLIDE 15

Railroad Planning and Operations

Service Network Design Traffic OD Demand Estimation Socio-economic data, interview samples Infrastructure Resources (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 Dispatching Empty Car Distribution Yard and Terminal Management

SLIDE 16

Railroad Netw ork 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

SLIDE 17

OD Dem and -> Routes-> Blocks-> Trains

Station Block a b c d

D ab+D ac+D ad

Blocking Plan 1

D ac+D ad +D bc+D bd D ad+D bd +D cd

D ad

D ab+D ac D ac+D bc+D bd D bd+D cd

a b c d a b c d b c d a Blocking Plan 2 Candidate blocks

b c d 100 a b c 100 500 150 200 50

destination

• rigin

Train schedule Time Terminals

a b c d

SLIDE 18

Background on Train Scheduling

 Planning Applications

– Satisfy passenger and freight traffic demand – Minimize the overall

• perational costs

 Real-time Applications

Adjust the daily and hourly train

• peration 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

SLIDE 19

 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 scheduling Crew scheduling Demand estimation Railway Planning Process

SLIDE 20

Train Scheduling on Beijing-Shanghai High-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

• rder to
• Serve the large volume of traffic

passing through this corridor

 Reduce connecting delay for

interline travel

SLIDE 21

I llustration

 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

SLIDE 22

Part I : Balancing Tw o 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.

SLIDE 23

Challenge I

SLIDE 24

Challenge I I : Model Acceleration and Deceleration Tim e Losses

 Acceleration and deceleration time losses

• High-speed trains: 3 minutes
• Medium-speed trains: 2 minutes

section k Tim ime axis is station k-1 station k station k+1 section k-1 pq(i), k-1 pq(i), k-1

1 ), ( − k i q d

τ

pq(i), k

k i q a ), (

τ

pq(i), k bypass station k stop at station k

SLIDE 25

Form ulating Train Tim etabling 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

SLIDE 26

Notations

i: subscript of trains j: subscript of sections u: 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.

k u

p ,

k u a ,

τ

k u d ,

τ

k v u e

h

, ,

k v u l

h

, ,

k i

s ,

i

d ~

SLIDE 27

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

i

d

i

y

e k i

x ,

l k i

x ,

d k i

B ,

a k i

B ,

k j i

B

, , i

C

d k i

t ,

a k i

t ,

SLIDE 28

Model Acceleration and Deceleration Tim e 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

       = + + = + = + = = 11 10 01 00 ) , , (

, , , , , , , ,

m if p m if p m if p m if p k m u pt

k u d k u a k u k u a k u k u d k u k u

τ τ τ τ

section k

xl

j,k

xe

j,k

section k-1 Tim ime axis is station k+1 station k-1 station k hl

q(j),q(i), k

xl

i,k

pt(q(j),m,k) j i he

q(j),q(i), k

xe

i,k

xl

j,k-1

hl

q(i),q(j), k

he

q(i),q(j), k

SLIDE 29

I nteger Program m ing Form ulation



Allow able adjustm ent for departure tim e: (2N constraints)



I nterdeparture tim e: (Nh -1 constraints for high-speed trains)



Departure tim e: (N constraints)



Total travel tim e: (N constraints)



Dw ell tim e: (N* (K-1) constraints)



Travel tim e on sections: (N×K constraints)



Acceleration tim e: (N×K constraints)



Deceleration tim e: (N×K constraints)

I i g d d g d

i i i i i

∈ ∀ + ≤ ≤ − ~ ~

1

\{ }

i i i h h

y d d i I N

+

= − ∀ ∈

I i d x

i e i

∈ ∀ =

1 ,

I i x x C

e i l K i i

∈ ∀ − =

1 , ,

} 1 { \ ,

, 1 , ,

= ∈ ∀ ∈ ∀ ≥ −

−

k V k I i s x x

k i l k i e k i

V k I i t t p x x

d k i a k i k i q e k i l k i

∈ ∀ ∈ ∀ + + = − ,

, , ), ( , ,

1 }, 1 { \ ,

1 , 1 , , ,

= = ∈ ∀ ∈ ∀ − ≥ ×

− a i l k i e k i a k i

B k V k I i x x M B

V k I i B t

k i q a a k i a k i

∈ ∀ ∈ ∀ × = ,

), ( , ,

τ 1 }, { \ , *

, , 1 , ,

= = ∈ ∀ ∈ ∀ − ≥

+ d K i l k i e k i d k i

B K k V k I i x x M B

V k I i B t

k i q d d k i d k i

∈ ∀ ∈ ∀ × = ,

), ( , ,

τ

SLIDE 30

I nteger Program m ing Form ulation ( Cont’)

 Minim um headw ay: (N× (N-1) ×K× 4 constraints)

V k I j i j i h x x

• r

h x x either

k j q i q e e k i e k j k i q j q e e k j e k i

∈ ∀ ∈ ≠ ∀ ≥ − ≥ − , , ,

), ( ), ( , , ), ( ), ( , ,

V k I j i j i h x x

• r

h x x either

k j q i q l l k i l k j k i q j q l l k j l k i

∈ ∀ ∈ ≠ ∀ ≥ − ≥ − , , ,

), ( ), ( , , ), ( ), ( , ,

V k I j I i j i M B h x x

k j i i q j q e e k j e k i

∈ ∀ ∈ ∈ ≠ ∀ × − − ≥ − , , , ) 1 (

, , ) ( ), ( , ,

V k I j I i j i M B h x x

k j i j q i q e e k i e k j

∈ ∀ ∈ ∈ ≠ ∀ × − ≥ − , , ,

, , ) ( ), ( , ,

V k I j I i j i M B h x x

k j i i q j q l l k j l k i

∈ ∀ ∈ ∈ ≠ ∀ × − − ≥ − , , , ) 1 (

, , ) ( ), ( , ,

V k I j I i j i M B h x x

k j i j q i q l l k i l k j

∈ ∀ ∈ ∈ ≠ ∀ × − ≥ − , , ,

, , ) ( ), ( , ,

To model the above “either-or” type constraints

SLIDE 31

I llustration of a Double-Track Train Schedule

section k section k-2

xl

j,k

xe

j,k

section k-1 di section 1 hl

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

Tim ime axis is

i i

g d − ~

i i

g d + ~

i

d ~

station k+1 station 1 station k-2 station k-1 station k

xl

j,k-1

dj

... ... ... ...

he

q(i),q(j),k

SLIDE 32

Utility Function for High-speed Trains Passengers

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

– U= – 0 .0 0 9 9 ( I n- vehicle travel tim e) – 0 .0 4 2 6 ( Out- of- vehicle w aiting tim e)

– Calibrated by the study for high-speed rail in the Toronto- Montreal corridor (KPMG Peat Marwick, Koppelman, 1990) – I n-vehicle travel tim e:

• Out-of-vehicle w aiting tim e

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

SLIDE 33

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 train

If 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 2 1

) ( ) (

h

N i i i

y y Y Var Z Min

∑

+ =

=

N N i i

h

C Z Min

1 2

SLIDE 34

Branch-and-Bound Solution Algorithm

 Step 1 : ( I nitialization)

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)

I f all of active nodes in L have been visited, then terminate.

 Step 4 : ( Conflict set construction)

Update the schedulable set in the selected node . I nsert these tasks and task t(i,j) into the current conflict set.

i j i j h i j h

Conflict Additional delay i first j first

SLIDE 35

Branch-and-Bound Algorithm for Generating Non-dom inated Solutions



Step 1: (I nitialization) 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. I nsert new nodes into the active node list.



Step 3: (Evaluation 1) Obtain

• bjective function Z1 by calculating

variance of departure times for existing high-speed trains.



Step 4: (Evaluation 2) Obtain

• bjective 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

SLIDE 36

Non-Dom inated Schedules

Z1(b) Z1(a)

2nd objective

1st objective

Dominated Schedule

Non- Dominated Schedule

Z2(a) Z2(b) First objective: Expected waiting time for high-speed trains at

• rigin

Second objective: Average travel time for medium-speed trains

b a

SLIDE 37

Construction of Non-Dom inated Set

Objective 2 Objective 1

Case 1:The new schedule replaces all the schedules in the set

Objective 1 Objective 1 Objective 1

Case 2:The new schedule replaces some of the schedules in the set Case 3:The new schedule is added to the set. Case 4:The new schedule is

• ut of the set.

Objective 2 Objective 2 Objective 2

SLIDE 38

I llustration of Dom inance Rules

Decision point

Partial 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 1 8 1 2 3 8 1 2 3 9 9

 Main I dea:

Cut dominated partial schedule at early as possible

 Conditions for node a dominating 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

SLIDE 39

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

SLIDE 40

Lim itation of Branch-and-Bound Algorithm

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

rapidly

10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000 3 4 5 6 # of high-speed trains to be considered # of solutions Possible Solutions Non-dominated partial schedules

SLIDE 41

I llustration of One Non-Dom inated Schedule

SLIDE 42

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

SLIDE 43

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

Beam width = 50 346 348 350 352 354 356 358 360 362 20 40 60 80 100 120

Variance of interdeparture times Average travel time for medium-speed trains (mins) Exact solutions Utility evaluation rule Random selection rule

SLIDE 44

Trade-Off Curves for Tw o Conflicting Objectives

335 340 345 350 355 360 365 14.5 15 15.5 16 16.5 17 17.5

Expected waiting time for high-speed trains (mins) Average travel time for medium-speed trains (mins) Exact solutions for 6 high- speed trains Utility evaluation rule for 24 high-speed trains w ith beam w idth = 50 Utility evaluation rule for 24 high-speed trains w ith beam w idth = 100

2 0 m in 2 m in 1 hour optimization horizon 6 hour optimization horizon

SLIDE 45

Part I I : Optim izing Slack Tim e 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

SLIDE 46

Model Form ulation

J1 J4 1 2 3 4

Time Station (distance)

5 J2 J3

Station node Segment arc Delay arc High-speed train

Space-Time Network Representation

SLIDE 47

Tw o-stage Recourse Model

 1st Stage Objective

– Minimize total trains’ trip time

, 1

( ) = ( )

n i i m i i

Min c x w e r

=

−

∑

J1 J4 1 2 3 4 Station, (distance) 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

SLIDE 48

Tw o-stage Recourse Model…

 2nd Stage Objective

– Minimize Schedule deviation

( )

+ , , , , , , 1

( , ) ( ) ( )

n i i m i m i i m i m i

g y x w e e w e e

ω ω ω + − − =

= − + −

∑

segment 1 high-speed train medium-speed train station 1 station 4 Time station 2 station 3 segment 3 segment 2

1,3

d

1,1,

f

ω 1

r

3,1

f

3,1

s

3,2

b

3,2

e

2

r

1,

r ω realized schedule segment 4

3

r

3,3,

b

ω 3,3,

e

ω

station 0

1,3

h

SLIDE 49

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

SLIDE 50

Solution Algorithm …

J1 J4 1 2 3 4

Station (distance)

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

?

SLIDE 51

Solution Algorithm …

J1 J4 1 2 3 4 5 J2 J3

Time

Segment J1 Segment J4

Many alternative paths

Station (Distance)

Stochastic Tim e-depende Shortest Path Problem

SLIDE 52

Strategies for a Single Train Problem



Constructing random segment running times – vector with given probability



Stochastic dominance rules – I: Timetable v'' first-order stochastically dominates timetable v', if. the CDF of delay distribution for timetable v'' is above

• r
• verlapping

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

, , i j

f

ω

ω

ρ

SLIDE 53

Stochastic Dom inance 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 0.25 0.5

station j-2 station j-1

0.5 0.5 0.5 0.5 0.5

(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 j

e′

, i j

e′′

0.5×1+0.5×2=1.5 0.75×1+0.25×2=1.25

''( ) F δ '( ) F δ '( ) F δ

SLIDE 54

Other I ssues: Estim ating Line Capacity

226 train pairs 102 train pairs

SLIDE 55

Estim ating/ Sim ulating Term inal Capacity

SLIDE 56

Train Routing Problem at Term inals

 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

SLIDE 57

Train Routing through Term inals

 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

SLIDE 58

Recom m endations

 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.

SLIDE 59

 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 2 0 0 1 in Germ any

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

Extracted from The Slotted Railway - Living With Passenger Trains Sebastian Schilling Railion Deutschland AG

SLIDE 60

Scheduling Freight And Passenger Trains

High-Speed passenger train Regional passenger train A* B C

location

1.

Mixed traffic - reduced capacity

Basic

Line Capacity Layout Connecting passenger services

2.

Mixed traffic - capacity enlargement

A B C

3.

Network 21 `Harmonizing`

A B C A B C

Additional freight train slots Extracted from The Slotted Railway - Living With Passenger Trains Sebastian Schilling Railion Deutschland AG Freight train

SLIDE 61

 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

• n demand
• n demand

100% + XX min >24 h

Extracted from The Slotted Railway - Living With Passenger Trains Sebastian Schilling Railion Deutschland AG

SLIDE 62

Research Directions



Robust schedule design – Executable vs. recoverable, from planning to real-time decision – I mprove 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

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

• Separation of track from traction in Europe

– I mpact on traffic demand and operating plans (train schedule, fleet sizing and repositioning) – Shipper logistics modeling – Demand estimation and prediction model

SLIDE 63

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)