Trip-timing decisions with traffic incidents in the bottleneck model

Trip-timing decisions with traffic incidents in the bottleneck model Mogens Fosgerau (Technical University of Denmark; CTS Sweden; ENS Cachan) Robin Lindsey (University of British Columbia) Tokyo, March 2013

Outline • Literature review • The model • No-toll user equilibrium • System optimum Quasi-system optimum Full optimum • Numerical examples • Conclusions/further research

Literature on traffic incidents Simulation studies: many Analytical static models Emmerink (1998), Emmerink and Verhoef (1998) … Analytical dynamic models (a) Flow congestion. Travel time has constant and exogenous variance. Gaver (1968), Knight (1974), Hall (1983), Noland and Small (1995), Noland (1997). (b) Bottleneck model. Travel time has constant, exogenous and independent variance over time. No incidents per se. Xin and Levinson (2007). (c) Bottleneck model with incidents Arnott et al. (1991, 1999), Lindsey (1994, 1999), Stefanie Peer and Paul Koster (2009).

Bottleneck model studies Scheduling utility approach Vickrey (1973), Ettema and Timmermans (2003), Fosgerau and Engelson (2010), Tseng and Verhoef (2008), Jenelius, Mattsson and Levinson (2010).

The model

Scheduling utility: Zero travel time As in Engelson and Fosgerau (2010) Move from H to W at t* u

Scheduling utility: Positive travel time u

The model (cont.)

No-toll user equilibrium in deterministic model cumulative departures cumulative arrivals Queuing time u

No-toll user equilibrium with major incidents cumulative departures Driver m causes incident cumulative arrivals u

No-toll user equilibrium properties Similar to pre-trip incidents model.

No-toll user equilibrium (cont.) Similar to pre-trip incidents model.

System optimum Deterministic SO Maximize aggregate utility. Optimal departure rate = s (design capacity) Stochastic SO Maximize aggregate expected utility. What is optimal departure rate?

General properties of system optimum (w)

System optimal approaches Quasi-system optimum (x) Departure rate Choose optimal Full optimum (w) Choose optimal and

Outline • Literature review • The model • No-toll user equilibrium • System optimum Quasi-system optimum (QSO) Full optimum • Numerical examples • Conclusions/further research

Quasi-system optimum (QSO)

Full system optimum (SO)

System optimum with queue persistence cumulative departures Driver m causes incident cumulative potential arrivals n

Departure rate n Interval 1 Interval 2

System optimum (major incidents, queue persistence)

Calibration of schedule utility functions Source: Tseng et al. (2008, Figure 3)

Calibration of schedule utility functions (cont.) Source: Authors’ calculation using Tseng et al. mixed logit estimates for slopes.

Calibration of incident duration Mean incident duration estimates Golob et al. (1987): 60 mins. (one lane closed) Jones et al. (1991): 55 mins. Nam and Mannering (2000): 162.5 mins. Select:

Other parameter values N = 8,000; s = 4,000 f(n)=f, fN = 0.2

Results: Major incidents

Results: Major incidents Total cost of incident in NTE

Results: Major incidents Total cost of incident in QSO

Results: Major incidents Total cost of incident in NTE Total cost of incident in QSO

Results: Major incidents, individual costs NTE, no incident occurred NTE, incident occurred

Results: Major incidents, individual costs NTE, no incident occurred NTE, incident occurred QSO, incident occurred QSO, no incident occurred

Minor incidents Complication: NTE departure rate depends on lagged values of itself  • No closed-form analytical solution. • Requires fixed-point iteration to solve. • Results reported here use an approximation.

Results: Minor incidents Initial departure time

Results: Minor incidents Increase in expected travel cost due to incidents

Modified example with SO different from QSO s = 4,000 N = 3,000 fN = 0.4 Explanation for parameter changes: • Shorter peak: Lower cost from moderating departure rate • Higher incident probability and duration: Greater incentive to avoid queuing by reducing departure rate

Results: Modified example Departure rates for QSO and SO

Results: Modified example

6. Conclusions (partial) • Properties of SO differ for endogenous-timing and pre-trip incidentsmodels • Plausible that QSO is a full SO: optimal departure rate = design capacity (same as without incidents), but with departures beginning earlier

Future research Theoretical • Further properties of NTE and QSO for minor incidents. • SO for minor incidents. • Stochastic incident duration Caveat: Analytical approach becomes difficult! Empirical • Probability distribution of capacity during incidents • Dependence of incident frequency on level of traffic flow, time of day, etc.

Thank you mf@transport.dtu.dk

Trip-timing decisions with traffic incidents in the bottleneck model

Trip-timing decisions with traffic incidents in the bottleneck model

Presentation Transcript

Network Traffic Model

 Bottleneck effect 

Population Bottleneck

Timing Margin Recovery With Flexible Flip-Flop Timing Model

Traffic Bottleneck

Dynamic Traffic Light Timing

Traffic Model

Seeing Through The Bottleneck

Seeing Through The Bottleneck

Information Bottleneck

MTO TRAFFIC MODEL

Timing Model

PFS setup timing model

SIGNAL TIMING WITHOUT TRAFFIC COUNTS

The Random Trip Mobility Model

Bottleneck identification

Traffic Control at Emergency Incidents

Timing Model Reduction for Hierarchical Timing Analysis

Traffic Model

Solving cities traffic problem through Ai driven traffic light timing.

Timing with loran

Traffic Model Simulation