# 1 Reliability-Based Timepoint Schedules for Long Headway Transit Routes Peter G. Furth, Northeastern University with Theo H.J. Muller, Delft University.

## Presentation on theme: "1 Reliability-Based Timepoint Schedules for Long Headway Transit Routes Peter G. Furth, Northeastern University with Theo H.J. Muller, Delft University."— Presentation transcript:

1 Reliability-Based Timepoint Schedules for Long Headway Transit Routes Peter G. Furth, Northeastern University with Theo H.J. Muller, Delft University of Technology

2 Outline 1.Translating Reliability into User Cost 2.Operations model –Segment running time –Timepoint holding –Layover and dispatch holding 3.Example results

3 Reliability Affects Passenger Travel Time Passengers arrive so that P[miss the bus] < 2% Passengers budget for 95-percentile [wait + ride] time Potential Travel Time = Budgeted Travel Time – mean [Wait + Ride Time]

4

5 Passenger Travel Cost Components Waiting Time: \$9/hr Riding Time:\$6/hr Potential Travel Time:\$4.5/hr Reliability has been captured: Cost = f(Tails of departure and arrival time distributions) Note: Estimating tails requires archived AVL data.

6 Operating Cost for a Route with Holding = Cycle Time c Schedule = Design Parameter Can be fixed or optimized c actual = an outcome, the sum of 3 components: –Mean uncontrolled running time –Mean holding time (running time supplement) –Mean layover time (layover slack) Inconsistent unless c actual ≈ c Schedule –Steady state: f(StartDeviation cycle n ) ≈ f(StartDeviation cycle n+1 )

7 Operations Model Segments (includes necessary dwell time) Random, independent running times Ideally, get distribution from AVL data Timepoints Hold early arrivals Add random holding supplement End of Line Add a random needed layover to become “Ready” Hold early “Ready” Add random dispatch supplement

8 Timepoints: Random Holding Supplement Holding Supplement (min)

9 End of Line: Needed Layover and Dispatch Supplement Needed Layover (min) Dispatch Supplement (min) 16

10 Layover Model: Planning View Labor policies on minimum layover constrain c Schedule Finding: Unreliable service: reliability governs optimal c Schedule Highly reliable service: labor policy governs

11 Analysis Track discretized probability distributions using MatLab 2 Warm-up cycles to achieve quasi-steady state Example route –17 stops, 16 segments –mean running time = 40 min,  = 5 min for base case –mean boardings = 74, max load = 36 pax Optimize w.r.t. two overlapping schedule parameters –Cycle supplement = CycleTime – MeanUncontrolledRunningTime –Running Time supplement = ScheduledRunningTime – MeanUncontrolledRunningTime

12 Cost vs. Running Time Supplement Optimized cycle length -\$60 -\$40 -\$20 \$0 \$20 \$40 -15.0-10.0-5.00.05.010.015.0 Running Time Supplement (min) riding time operating cost potential travel time total cost waiting time

13 Slack Distributions vs. Running Time Supplement c Schedule optimized; dashed line = only 1 timepoint 0.10 0.20 0.30 0.40 -15.0-10.0-5.00.05.010.015.0 Running Time Supplement (min) Layover holding Timepoint holding Total holding

14 Cost vs. Number of Timepoints -\$70 -\$60 -\$50 -\$40 -\$30 -\$20 -\$10 \$0 013714 Number of Timepoints 0 0.5 1 1.5 2 2.5 3 3.5 (Lines) Schedule Supplement as multiple of σ route (Bars) Change in Cost (Base = No Timepoints) (\$/trip) RT suppl, σ route =3 RT suppl, σ route =7 RT suppl, σ route =5 Cycle suppl, σ route =3 Cycle suppl, σ route =5 Cycle suppl, σ route =7 σ route = 3 min σ route = 5 σ route = 7

Optimal Schedule Supplements vs  route dashed line for a single timepoint 15

16 Conclusion and Remarks 1.Archived AVL data makes reliability analysis possible 2.Capturing reliability in the cost function facilitates tradeoff against riding time and operating cost; contrast rules of thumb 3.Schedules should probably have more en-route slack 4.To a large degree, en-route slack and recovery slack simply substitute for one another, meaning en-route slack can be added without increasing cycle time 5.Amount of en-route & layover slack are not easily calculated 6.Optimal departure time depends on boardings & other factors 7.On more reliable routes, layover is governed by operator rest needs 8.What about operator behavior? 9.What about short headway service? 10.What about passengers who make transfers?

Download ppt "1 Reliability-Based Timepoint Schedules for Long Headway Transit Routes Peter G. Furth, Northeastern University with Theo H.J. Muller, Delft University."

Similar presentations