Managing Headways in Single-Track Emergencies

Internet Version of a Technical Briefing
Prepared by Paul Niquette
September 5, 2008

ABSTRACT:

Emergency management in fixed-guideway transit systems often must confront the reality that, in single-track territories, headway is determined by trip-time.  This technical briefing (a) reviews the impact of prolonged emergencies on passenger services, (b) analyzes trade-offs between trip-time and volume in single-track operations, and (c) proposes operational alternatives that may offset the requirement for capital-intensive crossovers.

BACKGROUND:

Passengers on light-rail, full-metro or commuter trains are familiar with occasional service delays, especially during rush-hour.  Most occur at stations. A medical emergency may hold up departure for a few minutes.  Responding to a security alert may take an hour or more.  If the delay exceeds the headway, other trains, each possibly carrying hundreds of passengers, will be adversely affected.  One door-leaf stuck open can require taking a whole train out of service.  All of its passengers must then offload and wait on the platform for the next train.  Meanwhile, the empty, otherwise healthy consist rejoins the normal traffic flow and continues to the nearest available pocket-track or siding and eventually to the maintenance shop. 

Brake lock-ups are rare.  However, in the worst-case, the faulty train cannot be moved.  Same for an onboard fire.  The occupied platform effectively blocks normal running on the corresponding track.  Dispatchers and train controllers must then invoke single-track procedures, aligning routes that permit train movements in alternating directions, sharing common trackage.  Extreme cases may require setting up bus-bridges to shuttle passengers on surface streets around blocked trackage.

EXECUTIVE SUMMARY:

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HEADWAY
 
 
 

DOUBLE-TRACK HEADWAYS:
 
 

With both trackways and all stations fully operational over a given route, headway, measured as time between succesive  are prescribed by time-table.  Headway is the mathematical reciprocal of flow-rate.  On any branch line, which supports neither divergent nor convergent services, flow-rate must be the same at every point along the branch line, like current in an electrical circuit.  The time allowed for turn-backs at end-points determines the stagger in the schedule for trains traveling in each direction at any given station.  
 
 

Following-move train protection, of course, will impose limits on both trip-time and headway, influenced more by the parameters of station stops than by train speed and limitations in trail-braking

For Case 0, with all interlockings aligned for Normal Running, the model estimates a through-train trip-time either NB or SB of about 9.5 min between BAS and SCS.  A time-table headway of, say, 10 min means that no more than two trains (one in each direction) will be concurrently operating within the indicated territory.  In Normal Running, the trackways operate independently of each other in opposite directions.  We will see that single-track emergencies demand strict coordination of train movements over the common track-way.

PARTIAL REVERSE RUNNING:

Four operational cases are diagrammed below, depicting bad-order trains at each of the underground stations.  Single-track routes are emphasized.  Headways are limited by loop-times.  For example, in Case 1, Normal Running NB train departing DSJ must the S55 interlocking before ///

MODEL FOR ILLUSTRATION:

Schematics herein depict a simplified model of a commuter rail segment for which at this writing preliminary engineering phase has been completed.  The segment comprises 6.7 miles of double-track guideway, five stations (three underground), and three double crossovers.  

Conservative train parameters have been chosen as follows:
 

Parameter
Symbol
Value
Unit
 
Parameter
Symbol
Value
Unit
Train Length
xL
700
ft
Dwell Time 
tD
20
sec
Cruise Speed
vC
70
mph
Crossover Speed
vI
27
mph
Acceleration
aS
1.9
mphps  
Deceleraton
dS
2.1
mphps
The civil locations tabulated below apply to all cases processed by the model and presented here.
.
Civil Locations on Track S1 and S2
BASn
524+60
 
S85n
692+86
 
S83n
833+84
BASs
531+60
 
S85s
696+00
 
S83s
839+60
S55n
535+20
 
DSJn
696+50
 
S85n
871+66
S55s
550+90
 
DSJs
703+50
 
S89s
875+95
ARSn
600+78
 
DASn
734+30
 
SCSn
876+95
ARSs
607+78
 
DASs
741+30
 
SCSs
883+95

Each individual transit time has been modeled to include (a) accelerating out of a station at aS to vC, (b) operating between stations at vC, (c) decelerating at dS to a stop in the succeeding station, and (d) waiting out tD.   It should be noted that the distance between DAS and DSJ is only 3,780 ft, which precludes operating at vC.  For calculating t2nb and t2sb, a limited speed vL = 50 mph was found to be appropriate.


Case 1 and Case 2
Case 3 and Case 4
Disabled train is postulated at each of the underground stations on their respective platforms, partially blocking Track S1.  Disabled train is postulated at each of the underground stations on their respective platforms, partially blocking Track S2. 
Normal Running NB trains can complete the trip from SCS to BAS on Track S2 with a trip-time of 9.5 min.  Normal Running SB trains can complete the trip from BAS to SCS on Track S1 with a trip-time of 9.5 min.
Case 1 and Case 3
Case 2 and Case 4
Normal Running NB or SB between DSJ and BAS requires 4.7 min.  Normal Running NB or SB between SCS and DSJ requires 4.8 min.
Reverse Running NB or SB between BAS and DSJ requires 7.0 min. Reverse Running NB or SB between SCS and DSJ requires 6.2 min.
Synchronized Headway = Loop-time between BAS and DSJ = 11.7 min  Synchronized Headway = Loop-time between SCS and DSJ = 11.0 min

 
 
 
 
 
 
 
 
 
 

HEADING 4

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HEADING 5

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CONCLUSIONS:

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RECOMMENDATIONS:

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OPPORTUNITIES:

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REFERENCES:

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TECHNICAL BRIEFINGS by Paul Niquette:

Smart Sensor Networks in Railway Vehicles: Paper for IEEE/NIST Smart Sensor Conference, 1994
Transaction-Based Monitoring Systems: Third Generation in diagnostic hardware and software
Electronically Controlled Pneumatic Brakes: Breakthrough in the technology of the world's railroads
Current Hogging as a Factor in Loss-of-Shunt: A study of the most subtle problem in automatic train control
Confusion-Free Codes: Not to be confused with "Comma-Free Codes."
Streetcar Mystery: Headway vs leeway
Headway vs Leeway: Convenience trumps annoyance -- for now.
Train Speed: Keeping time in the numerator
Trail Braking: Safe following distance
Station Stop: Dispelling a myth about headway
Trip Time: Figuring out how fast trains really travel.
Express vs Local: Who really benefits from express service?
Single Tracking: Practical approach to a common commuting complant.
 
 
 
 
 
 
 

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