Download - Yanbo Zhao Petros Ioannou
Dynamic Train Headway Selection
and Its Effect on Capacity Yanbo Zhao Petros Ioannou
Email: [email protected], [email protected].
Evaluation & Results
Motivation & Introduction
Proposed Method
Headway Policy Switch
Location
Velocity
Brake Characteristics
Driver Response
Track
Track Grade
Track Curvature
Track Occupy
Status
Comm
Obtain Inputs
Define and
Start
( )fa t( )la t
Set Time Step Interval T
(0) (0) 0l fS S
min lH L
0k
Add safe margin and
output ( ) 0fV kT
minH
( 1)
(( 1) ) ( ) ( ) ( )k T
l l lkT
V k T V kT a d
( 1)
(( 1) ) ( ) ( ) ( )k T
f f fkT
V k T V kT a d
( 1)
(( 1) ) ( ) ( ) ( )k T
l l lkT
S k T S kT V d
( 1)
(( 1) ) ( ) ( ) ( )k T
f f fkT
S k T S kT V d
max (( 1) ) (( 1) ), 0f lS S k T S k T
minlS L H
min lH S L
1k k
No
No
Yes
Yes
0 10 20 30 40 50 60 70 80 900
2000
4000
6000
8000
10000
12000
Time (second)
Positio
n (
feet)
Following Train
Leading Train
0 10 20 30 40 50 60 70 80 900
2000
4000
6000
8000
10000
12000
Time (second)
Positio
n (
feet)
Following Train
Leading Train
0 2 4 6 8 10 12 14 16 18 20 226400
6420
6440
6460
6480
6500
6520
Inner
Dis
tance (
feet)
Time (second)
Input Factors
Signal Signal Signal
Fixed Block System
Moving Block System
Brick-wall Headway PolicyBrick-wall Headway Policy
Communication
Network
Train Dispatch
Center
Communication Based Train
Control System
Leading
Train
Following
Train
Braking distance
Dynamic Headway Policy
•Communication Based
•Continuous Updating
•Reducing Headway
•Improving Capacity
Train
Communication
Interval Time
Communication
Delay
H = max {Hmin, Following Train Emergency Stopping Distance + Leading Train Length}
Numeric Headway Calculation Algorithm
Failure Tolerance Headway Selection
•Decelerate Trains to New
Operation Velocity
•Check The Received Signal
If Green, Switch Successfully
If Not, Continue Deceleration
Dynamic Headway Policy to Brick-wall Policy when Communication Network Fails
Brick-wall Policy to Dynamic Headway Policy when Communication Network Recovers
Passenger Train Freight Train
Length, feet 250 3000
Maximum Service
Brake Rate
(feet/min2)
5280 1950
Maximum
Emergency Brake
Rate (feet/min2)
10560 3900
Brake System
Response Time (sec)0.5 0.5
Brake System
Build-up
Time (sec)
2.0 2.0
Velocity (mph) 60 40
Driver Reaction
Time
(sec)
0.5 0.5
Communication
Delay
(sec)
1
Track Grade 0
Track Curvature
Radius (feet)0
Safe Margin
Distance (feet)200
Time Interval in
Timetable Headway
Policy (min)
5
Timetable
Policy (5 min)
Brick-wall
Policy
Dynamic
Policy
Case 1 P-P 26550 ft 3286 ft 1858 ft
Case 2 P-F 20600 ft 3758 ft 3410 ft
Case 3 F-P 29300 ft 6036 ft 4376 ft
Case 4 F-F 23600 ft 6508 ft 4847 ft
Factor ValueHeadway
(ft)
Line
Capacity
(trains/hour)
Initial
Velocity
(mph)
20 3627 29.1
30 4138 38.3
40 4847 43.6
50 5755 45.0
60 6862 46.2
Service/Eme
rgency
Brake
Capability
(feet/min2)
975/1950 6436 32.8
1560/3120 5244 40.2
1950/3900 4847 43.6
2340/4680 4583 46.1
2925/5850 4318 48.9
Driver
Reaction
Time
Difference
(sec)
-2 4730 44.7
-1 4788 44.1
0 4847 43.6
1 4906 43.1
2 4965 42.5
Track
Grade
-3‰ 5403 39.1
-2‰ 5189 40.7
-1‰ 5005 42.1
0 4847 43.6
+1‰ 4710 44.8
+2‰ 4589 46.0
+3‰ 4482 47.1
Communica
tion Delay
(sec)
0 4789 44.1
0.4 4800 43.9
0.8 4824 43.7
1.0 4847 43.6
1.2 4859 43.4
1.6 4870 43.2
2.0 4905 43.0
Input Parameters Sensitivity Analysis (Case F-F)
Headways of Different Policies
Signal Signal Signal
vf
vf’
vl
vl’P.
Case 1
Signal Signal Signal
vf vl
vl’P.
Case 2
•Accelerate Trains to Reduce Inner Distance
until Reaching Minimum Secure Dynamic Headway
Examples
Switch to Brick-wall Policy Switch to Dynamic Policy
•Find the Minimum Headway
between two trains such that the
Following Train front should not
run across the Leading Train rear
until the Following Train comes to
a fully stop
•Two trains in a straight track line
•If an emergency occurs, the
Leading Train starts to decelerate
and send event report to the
Following Train
•The Following Train will start to
brake when receiving event report
from the Leading Train
