session 42 ida kristoffersson

Estimating Preferred Departure Times Ida Kristoffersson & Leonid Engelson

Estimating Preferred Departure Times of Road Users in a Real-

Life Network

Ida Kristoffersson and Leonid EngelsonCentre for Traffic Research

The Royal Institute of Technology Stockholm


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


Outline

• Introduction• The Reverse Engineering (RE) method• The SILVESTER model for Stockholm• Calibration by RE• Results• Conclusion


Current cordon location and charging schedule in Stockholm


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)

( ) ( ) εδγβα +++−+− ++ DTDTDT

ctDTPDTPDTDTmin

Need to know PDT


Where to get PDTs?• Travel survey: expensive, difficult to explain• Assume a distribution of PDT• Assume the current DT• PATSI (Polak & Hun, 1999)• 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

Inconsistent with the DTC model


Reverse engineering approach

tq

0 5 10 3 2

1 6 7 4 2

Preferred demand

Realized demand

τv

∑=τ

ττvPq tt

( )ττ === PDTtDTPt |Prob

vPq = qPv 1−=


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


The model of departure time choice (1)

• Variables: average travel time, standard deviation of travel time and charge per DT interval and OD pair

• Mixed logit • Estimation based on SP and RP data trips in Stockholm County• Same respondents in SP and RP surveys• See Börjesson, 2008 TRE

( ) ( ) εδγβα +++−+− ++ DTDTDT

ctDTPDTPDTDTmin


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

( )ττ === PDTtDTPkwt |Prob


Application of the model

Traffic flows

CONTRAMMesoscopic modelQueuing dynamics

Iterations until steady state

Travel costs

Road network, Charges

kwtqRealised travel demand

kwvτPreferred travel demand

Departure time choice model kwtPτ

kwkwkw vPq =


Calibration of the model (1)

Traffic flows

CONTRAMMesoscopic modelQueuing dynamics

Iterations until steady state

Travel costs

Road network, Charges

Realised travel demand q

Preferred travel demand v

Departure time choice model P

Baseline situation


Calibration of the model(2)

Stage 1: Time-dependent OD matrix estimationCOMEST, 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

kwkwkw vPq = ( ) kwkwkw qPv1−

=(Reverse Engineering)


Reverse engineering

• Good: P is usually nice (diagonal dominant)• Bad: P-1 is never positive

– Feasibility of the solution depends on q– Some although all

• Two methods proposed:– Aggregation of OD pairs– Bounded variation

0<kwvτ 0>kwtq


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


Fixed time work trips and school trips• 3 OD groups by origin zone


Business trips• 3 OD groups by origin zone


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


Flexible trips to work and other trips

• Solution for 4% wide strip around the common


Aggregated PDT and DT for the three trip purposes

total

flexible

fixed

business


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


Thank you !