1. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Timetabling Components Unit 5: Staff & Fleet Scheduling

2. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Service Planning Steps Crew scheduling Vehicle scheduling Timetabling Frequency determination Route design and stop layout Network design

3. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Timetabling … is the process of developing a schedule of when vehicles will pass each stop on a route … also known as “service schedule” … is critical to ensuring consistent service and minimize operating costs

4. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Connecting to Last Lecture Last time: – Determined the required number of vehicles/hour to meet passenger demand along each route Now: – Determine schedule (and number of) vehicles need to support these frequencies (called a Timetable)

5. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Hawthorne LRT Line Example When is the light rail going to be at each stop? When should I leave to catch it? What happens if I miss the train?

6. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Discussion When you take transit, how do you plan your trip? How early do you leave? What information do you rely on? Are you worried transit will be full?

7. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Poor Scheduling= Unreliable Service Under-serving passenger demand – Vehicles slow down, fill up Over-serving passenger demand – Vehicles run too fast, empty

8. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Scheduling Transit is Challenging Changing passenger demand Changing traffic patterns Limited resources

9. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Schedule Components In order to match demand, we can control: – Departure Times – Number of Vehicles – Layover Times

10. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Many Ways to Schedule Same Service We can choose the best by considering: – Number of Departures/ Runs Route Specific Measure – Required fleet size System Wide Measure

11. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Scheduling Process Determine basic schedule structure – Headways (h) – Travel times between stops (t ij ) – Dispatch time (t 0 ) – Layover time (t l ) Adapt structure to deal with variability

12. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Expected Travel Times t ij = t d +t s t ij – Time between adjacent stops t d – Moving time t s – Stopped time On-time: 1 minute early to 2 minutes late

13. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Diagram of Transit Time Acceleration DecelerationCruising Speed Moving Time

14. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Calculating t d S – Total distance between stops A – Acceleration rate B – Deceleration rate V – See next slide

15. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Calculating t d If there is time to get to cruising speed between stops: …use v= cruising speed If there isn’t time to get to cruising speed between stops: …use v=

16. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Calculating t s Assuming boarding and alighting happen simultaneously… Pick the bigger: – N b t b – N a t a

17. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Typical Board Times Free service: 2-3 seconds Token/ Farecard: 4 seconds Pay Onboard: 10+ seconds …per passenger

18. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Dispatch Times Agencies can choose: – Clockface times Start runs on specific/ recurring times Easy to remember – Coordination times Timed to reduce bus driver idling Saves funds

19. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Do We Even Need to Stop? Agencies predict whether passengers will board/alight at each stop during each headway period using the Poisson distribution – Tells us the probability there will be one or more passengers boarding/alighting – Do per stop or by route – Do by time period or day

20. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Poisson Calculation Probability of Activity= 1-e -(x+y)h x – number of boardings per stop y – number of alightings per stop h – headway time

21. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Hawthorne Example Hawthorne LRT has 16 possible stops, on average 50 boarding/ alighting passenger events, and 20 minute headways. How many stops will the bus actually stop at?

22. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Hawthorne Example x + y= (50 passengers/hr)/(60 min/hr*16 stops) = 0.05 passenger events per stop h = 20 minutes Probability of activity at each stop = 1-e -(0.05)20 = 0.63 Number of stops with activity = 16*0.63 = 11 stop

23. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Equations for Scheduling

24. Materials developed by K. Watkins, J. LaMondia and C. Brakewood The Final Schedule An example with 4 stops…

25. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Space-Time Diagrams

26. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Full Route Space-Time Diagram

27. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Applying Space-Time Diagrams Useful to… – Coordinate passenger transfers Look at overlapping times between routes and set dispatch times to coordinate stops – Reduce vehicle requirements Shows number of vehicles operating at any given time Change dispatch and layover times to reduce number of vehicles

28. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Adjustment Option #1 Adjust timetable to keep even headways Easy for passengers to remember Must be very confident about arrival rates – Leads to uneven numbers of passengers Must be conscientious about traffic levels – Slow down/ speed up service

29. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Adjustment Option #2 Adjust timetable to keep even vehicle loads Keeps demand even amongst vehicles Must be very confident about arrival rates – Need to match spikes in demand Must also be confident about traffic patterns – Need to ensure exact arrival times Can be confusing to passengers, since pattern of headways vary

30. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Adjustment Option #3 Adjust timetable to shorten some vehicle paths If demands and traffic are not compatible, you can have vehicles only serve part of a route Referred to as “Short turns”

31. Materials developed by K. Watkins, J. LaMondia and C. Brakewood In Class Exercise Review the handout with the space-time diagram Answer the questions Group discussion

32. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Communicating Timetables

33. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Communicating Timetables

34. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Communicating Timetables

35. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Successful Timetables If we’ve done our job correctly, passengers should… – Arrive on time for transit – Seamlessly transfer vehicles – Not think too hard about their timing – Find the schedule intuitive – Not realize the work that went into it

36. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Conclusion Coming up with a solid timetable is critical to ensuring transit reliability. There are many components to calculating and adjusting timetables to meet agency needs. Timetables can be displayed in different ways. – Practitioners versus Passengers.

37. Materials developed by K. Watkins, J. LaMondia and C. Brakewood Reference Materials in this lecture were taken from: Mark Hickman, Fundamentals of Transportation wikibook, – “Network Design & Frequency”, http://en.wikibooks.org/wiki/Fundamentals_of_ Transportation/Network_Design_and_Frequency http://en.wikibooks.org/wiki/Fundamentals_of_ Transportation/Network_Design_and_Frequency – “Timetabling & Scheduling”, http://en.wikibooks.org/wiki/Fundamentals_of_ Transportation/Timetabling_and_Scheduling. http://en.wikibooks.org/wiki/Fundamentals_of_ Transportation/Timetabling_and_Scheduling