Dr. Xuesong Zhou

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Oct 29, 2013 (3 years and 11 months ago)

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Dr. Xuesong Zhou

High
-
speed
Passenger Trains
on
Freight Tracks
:
Modeling Issues
on
Capacity Analysis
,
Train Timetabling
and
Real
-
Time Dispatching


Assistant Professor

Department of Civil and Environmental
Engineering

Univ. of Utah

zhou@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

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

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

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_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 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?


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.

Railroad Planning and Operations

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

Background on Train Scheduling


Planning Applications


Satisfy passenger and
freight traffic demand


Minimize the overall
operational costs


Real
-
time Applications


Adjust 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

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 (1
50

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



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 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.



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

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

Integer Programming Formulation


Allowable

adjustment

for

departure

time
:


(
2
N

constraints)



Interdeparture

time
:


(N
h

-
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)



Integer Programming Formulation (Cont’)


Minimum

headway
:

(N
×

(N
-
1
)

×
K
×

4

constraints)


To model the above “either
-
or” type constraints


Illustration of a Double
-
Track Train Schedule

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 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







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
.


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 Z
1

by calculating
variance of departure times for
existing
high
-
speed trains.


Step 4:
(
Evaluation 2
)

Obtain
objective function Z
2

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.

Subproblem 1
: Determine departure
time of high
-
speed trains

Subproblem 2
: Schedule all medium
-
speed trains

Non
-
Dominated Schedules

Z
1
(b)

Z
1
(a)

2nd objective

1st objective

Dominated Schedule

Non
-

Dominated
Schedule


Z
2
(a)

Z
2
(b)

First objective: Expected waiting time for high
-
speed trains at
origin

Second objective: Average travel time for medium
-
speed trains

b

a

Construction of Non
-
Dominated 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




out of the set.



Objective 2



Objective 2



Objective 2



Illustration of Dominance Rules

Decision
point


Main Idea
:

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

Heuristic Algorithm


Beam search algorithm uses a certain evaluation rule to select
the
k
-
best

nodes to be computed at next level


Limitation of Branch
-
and
-
Bound Algorithm


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


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)

Trade
-
Off Curves for

Two Conflicting Objectives


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

Space
-
Time

Network

Representation

Two
-
stage Recourse Model



1st Stage Objective


Minimize total trains


trip time



Two
-
stage Recourse Model



2nd Stage Objective


Minimize Schedule deviation



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


?

Solution Algorithm


Stochastic Time
-
dependent
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

dominates

timetable

v',

if
.

the

CDF

of

delay

distribution

for

timetable

v''

is

above

or

overlapping

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'


Stochastic Dominance Rules

Other Issues: Estimating Line Capacity


226 train pairs

102 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 from

The Slotted Railway
-

Living With Passenger Trains


Sebastian Schilling

Railion Deutschland AG

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


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 from

The Slotted Railway
-

Living With Passenger Trains


Sebastian Schilling

Railion 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)