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)
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