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 () f a t () l at Set Time Step Interval T (0) (0) 0 l f S S min l H L 0 k Add safe margin and output ( ) 0 f V kT min H ( 1) (( 1) ) ( ) ()() k T l l l kT V k T V kT a d ( 1) (( 1) ) ( ) ()() k T f f f kT V k T V kT a d ( 1) (( 1) ) ( ) ()() k T l l l kT S k T S kT V d ( 1) (( 1) ) ( ) ()() k T f f f kT S k T S kT V d max (( 1) ) (( 1) ), 0 f l S S k T S k T min l S L H min l H S L 1 k k No No Yes Yes 0 10 20 30 40 50 60 70 80 90 0 2000 4000 6000 8000 10000 12000 Time (second) Position (feet) Following Train Leading Train 0 10 20 30 40 50 60 70 80 90 0 2000 4000 6000 8000 10000 12000 Time (second) Position (feet) Following Train Leading Train 0 2 4 6 8 10 12 14 16 18 20 22 6400 6420 6440 6460 6480 6500 6520 Inner Distance (feet) Time (second) Input Factors Signal Signal Signal Fixed Block System Moving Block System Brick-wall Headway Policy Brick-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/min 2 ) 5280 1950 Maximum Emergency Brake Rate (feet/min 2 ) 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 Value Headway (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