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Session 42 Ida Kristoffersson
1. Estimating Preferred Departure
Times of Road Users in a Real-
Life Network
Ida Kristoffersson and Leonid Engelson
Centre for Traffic Research
The Royal Institute of Technology
Stockholm
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
2. Problem setting
• Purpose: develop a tool for evaluation of congestion
charging schemes for Stockholm
• Proper modelling of congestion needs representation of
queue accumulation and discharge -> Time Dependent
Assignment (TDA)
• Time dependent assignment requires demand matrices by
time slice
• Choice of time interval is an important part of the travel
demand model
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
3. Outline
• Introduction
• The Reverse Engineering (RE) method
• The SILVESTER model for Stockholm
• Calibration by RE
• Results
• Conclusion
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
4. Current cordon location and
charging schedule in Stockholm
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
5. Basic idea for choice
of departure time
• The traveller weights deviation from their Preferred
Departure Time (PDT) against travel cost (time,
uncertainty, charge)
• Utility maximisation, discrete choice model (Small 1982)
min α (DT − PDT )+ + β (PDT − DT )+ + γt DT + δcDT + ε
DT
Need to know PDT
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
6. Where to get PDTs?
• Travel survey: expensive, difficult to explain
• Assume a distribution of PDT Inconsistent
• Assume the current DT with the
• PATSI (Polak & Hun, 1999) DTC model
• Reversal Engineering (Teekamp et al, 2002):
Reconstruct PDT from the observed DT and the
DT model. Illustrated for one OD pair
• Berkum & Amelsfort, 2003: Demonstrated for a
small network with 4 OD pairs.
• This paper: apply Reverse Engineering to a real-
life network
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
8. SILVESTER
• Model for Stockholm with suburbs (ca 1.5 mln)
• 315 zones, 35 120 OD pairs
• Extended peak (06:30-09:30)
• Drivers choose DT between 15 minutes
intervals based on deviation from their PDT,
travel time, travel time uncertainty and charge for
that DT
• Even possible to depart before 06:30, after
09:30 or switch to public transport
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
9. The model of departure
time choice (1)
• Variables: average travel time, standard deviation of travel time and charge
per DT interval and OD pair
min α (DT − PDT )+ + β (PDT − DT )+ + γt DT + δcDT + ε
DT
• Mixed logit
• Estimation based on SP and RP data trips in Stockholm County
• Same respondents in SP and RP surveys
• See Börjesson, 2008 TRE
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
10. The model of departure
time choice (2)
• Trip purpose segments:
• Trips to work with fixed office hours and trips to school
• Business trips
• Trips to work with flexible office hours and other trips
• Result: For each trip purpose k and OD-pair w, the probability
to choose a departure time period given a preferred departure
time period
Ptτ = Prob(DT = t | PDT = τ )
kw
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
11. Application of the model
kw
Preferred travel demand vτ
kw
Departure time choice model Ptτ
kw Travel
q kw
=P v
kw kw
Realised travel demand qt
costs
CONTRAM
Traffic Mesoscopic model
Queuing dynamics
Road
flows network,
Iterations until steady state
Charges
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
12. Calibration of the model (1)
Preferred travel demand v Baseline
situation
Departure time choice model P
Travel
Realised travel demand q
costs
CONTRAM
Traffic Mesoscopic model
Queuing dynamics
Road
flows network,
Iterations until steady state
Charges
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
13. Calibration of the model(2)
Stage 1: Time-dependent OD matrix estimation
COMEST, performed before the model estimation
Stage 2: OD matrix subdivision by trip purposes k
Stage 3: Revealing the preferred departure times for
each trip purpose k and OD-pair w
q kw
=P v kw kw
v kw
= P ( ) kw −1 kw
q
(Reverse Engineering)
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
14. Reverse engineering
• Good: P is usually nice (diagonal dominant)
• Bad: P-1 is never positive
– Feasibility of the solution depends on q
– Some vτkw < 0 although all qtkw > 0
• Two methods proposed:
– Aggregation of OD pairs
– Bounded variation
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
15. Aggregation of OD pairs
• OD’s are grouped by geographical or socio-
economical properties (origin zone, destination
zone, distance, income,…)
• An optimal PDT profile is sought for each
group by the least squares method
• If the profiles are similar or infeasible, the
groups are united
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
16. Fixed time work trips and school trips
• 3 OD groups by origin zone
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
17. Business trips
• 3 OD groups by origin zone
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
18. Bounded variation
• Find a best common PDT profile for all OD
pairs (the least square method)
• For each OD pair, find a best PDT profile
within a certain strip around the common profile
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
19. Flexible trips to
work and other trips
• Solution for 4% wide strip around the common
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
20. Aggregated PDT and DT
for the three trip purposes
total
flexible
fixed
business
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
21. Conclusion
• The Reverse engineering approach for
estimation of preferred departure times is
applicable for a large urban network
• The result is consistent with skimmed travel
times and the departure time choice model
• The least square method for groups of OD pairs
relieves the problem of negative solutions and
delivers reasonable PDT profiles
Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson
