June  2014, 7(3): 557-578. doi: 10.3934/dcdss.2014.7.557

Computing travel times from filtered traffic states

1. 

Telenav, Inc, 950 De Guigne Dr, Sunnyvale, CA 94085, United States

2. 

Microsoft, 1065 La Avenida St, Mountain View, CA 94043

3. 

University of Illinois at Urbana-Champaign, 1203 Newmark Civil Engineering Laboratory, 205 N. Mathews Ave, Urbana, IL 61801

Received  July 2013 Revised  August 2013 Published  January 2014

This article experimentally assesses the influence of sensor data rates on travel time estimates computed from filtered traffic speed estimates. Using velocity data obtained from GPS smartphones and inductive loop detector data collected during the Mobile Century experiment near Berkeley, CA, and an evolution equation for average velocity along the roadway, an estimate of the traffic state is obtained via ensemble Kalman filtering. A large--scale batch of computations is run to produce estimates of traffic velocity with varying degrees of input data, and instantaneous and a posteriori dynamic travel times are compared to travel times recorded using license plate re-identification. We illustrate that dynamic travel time estimates can be computed with less than 10% error regardless of the data source, and that existing inductive loop detector data can significantly improve the accuracy of travel time estimates when GPS data is sparse.
Citation: Pierre-Emmanuel Mazaré, Olli-Pekka Tossavainen, Daniel B. Work. Computing travel times from filtered traffic states. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 557-578. doi: 10.3934/dcdss.2014.7.557
References:
[1]

A. Alessandri, R. Bolla and M. Repetto, Estimation of freeway traffic variables using information from mobile phones,, in Proc. of the American Control Conference, (2003), 4089. Google Scholar

[2]

V. Astarita and M. Florianz, The use of mobile phones in traffic management and control,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2001), 10. doi: 10.1109/ITSC.2001.948621. Google Scholar

[3]

H. Bar-Gera, Evaluation of a cellular phone-based system for measurements of traffic speeds and travel times: A case study from Israel,, Transportation Research Part C: Emerging Technologies, 15 (2007), 380. doi: 10.1016/j.trc.2007.06.003. Google Scholar

[4]

S. Blandin, G. Bretti, A. Cutolo and B. Piccoli, Numerical simulations of traffic data via fluid dynamic approach,, Applied Mathematics and Computation, 210 (2009), 441. doi: 10.1016/j.amc.2009.01.057. Google Scholar

[5]

G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks,, SIAM Journal on Applied Dynamical Systems, 7 (2008), 510. doi: 10.1137/070697768. Google Scholar

[6]

Caltrans, Performance Measurement System (PeMS),, , (). Google Scholar

[7]

H. Chen and H. A. Rakha, Prediction of dynamic freeway travel times based on vehicle trajectory construction,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2012), 576. doi: 10.1109/ITSC.2012.6338825. Google Scholar

[8]

P. Cheng, Z. Qiu and B. Ran, Particle filter based traffic state estimation using cell phone network data,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2006), 1047. Google Scholar

[9]

R. Colombo, Hyperbolic phase transitions in traffic flow,, SIAM Journal on Applied Mathematics, 63 (2002), 708. doi: 10.1137/S0036139901393184. Google Scholar

[10]

E. Cristiani, C. de Fabritiis and B. Piccoli, A fluid dynamic approach for traffic forecast from mobile sensor data,, Communications in Applied and Industrial Mathematics, 1 (2010), 54. Google Scholar

[11]

C. F. Daganzo, The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory,, Transportation Research Part B: Methodological, 28 (1994), 269. doi: 10.1016/0191-2615(94)90002-7. Google Scholar

[12]

C. F. Daganzo, The cell transmission model, part II: network traffic,, Transportation Research Part B: Methodological, 29 (1995), 79. doi: 10.1016/0191-2615(94)00022-R. Google Scholar

[13]

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,, Journal of Geophysical Research, 99 (1994), 10143. doi: 10.1029/94JC00572. Google Scholar

[14]

G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation,, Ocean Dynamics, 53 (2003), 343. doi: 10.1007/s10236-003-0036-9. Google Scholar

[15]

M. Garavello and B. Piccoli, Traffic Flow on Networks,, American Institute of Mathematical Sciences, (2006). Google Scholar

[16]

J.-C. Herrera and A. Bayen, Incorporation of Lagrangian measurements in freeway traffic state estimation,, Transportation Research Part B: Methodological, 44 (2010), 460. doi: 10.1016/j.trb.2009.10.005. Google Scholar

[17]

J.-C. Herrera, D. Work, R. Herring, J. Ban, Q. Jacobson and A. Bayen, Evaluation of traffic data obtained via GPS-enabled mobile phones: the Mobile Century experiment,, Transportation Research Part C: Emerging Technologies, 18 (2010), 568. doi: 10.1016/j.trc.2009.10.006. Google Scholar

[18]

B. Hoh, M. Gruteser, R. Herring, J. Ban, D. Work, J.-C. Herrera, A. Bayen, M. Annavaram and Q. Jacobson., Virtual trip lines for distributed privacy-preserving traffic monitoring,, in 6th International Conference on Mobile Systems, (2008), 15. doi: 10.1145/1378600.1378604. Google Scholar

[19]

R. E. Kalman, A new approach to linear filtering and prediction problems,, Transactions of the ASME Journal of Basic Engineering, 82 (1960), 35. doi: 10.1115/1.3662552. Google Scholar

[20]

J. Kwon, K. Petty and P. Varaiya, Probe vehicle runs or loop detectors?, Transportation Research Record, 2012 (2007), 57. doi: 10.3141/2012-07. Google Scholar

[21]

M. Lighthill and G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A, 229 (1955), 317. doi: 10.1098/rspa.1955.0089. Google Scholar

[22]

H. Liu, A. Danczyk, R. Brewer and R. Starr, Evaluation of cell phone traffic data in minnesota,, Transportation Research Record, 2086 (2008), 1. doi: 10.3141/2086-01. Google Scholar

[23]

P.-E. Mazaré, O.-P. Tossavainen, A. Bayen and D. Work, Trade-offs between inductive loops and GPS probe vehicles for travel time estimation: A Mobile Century case study,, in Proc. of the Transportation Research Board 91st Annual Meeting, (2012). Google Scholar

[24]

P. I. Richards, Shock waves on the highway,, Operations Research, 4 (1956), 42. doi: 10.1287/opre.4.1.42. Google Scholar

[25]

B. Smith, H. Zhang, M. Fontaine and M. Green, Cell Phone Probes as an ATMS Tool,, Technical Report UVACTS-15-5-79, (2003), 15. Google Scholar

[26]

S. Smulders, Control of freeway traffic flow by variable speed signs,, Transportation Research Part B: Methodological, 24 (1990), 111. doi: 10.1016/0191-2615(90)90023-R. Google Scholar

[27]

D. Work, S. Blandin, O.-P. Tossavainen, B. Piccoli and A. Bayen, A traffic model for velocity data assimilation,, Applied Mathematics Research Express, 2010 (2010), 1. Google Scholar

[28]

J. L. Ygnace, C. Drane, Y. B. Yim and R. de Lacvivier, Travel Time Estimation on the San Francisco Bay Area Network Using Cellular Phones as Probes,, Technical Report UCB-ITS-PWP-2000-18, (2000), 2000. Google Scholar

[29]

Y. Yim and R. Cayford, Investigation of Vehicles as Probes Using Global Positioning System and Cellular Phone Tracking: Field Operational Test,, Technical Report UCB-ITS-PWP-2001-9, (2001), 2001. Google Scholar

[30]

, Mobile Millennium,, , (). Google Scholar

show all references

References:
[1]

A. Alessandri, R. Bolla and M. Repetto, Estimation of freeway traffic variables using information from mobile phones,, in Proc. of the American Control Conference, (2003), 4089. Google Scholar

[2]

V. Astarita and M. Florianz, The use of mobile phones in traffic management and control,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2001), 10. doi: 10.1109/ITSC.2001.948621. Google Scholar

[3]

H. Bar-Gera, Evaluation of a cellular phone-based system for measurements of traffic speeds and travel times: A case study from Israel,, Transportation Research Part C: Emerging Technologies, 15 (2007), 380. doi: 10.1016/j.trc.2007.06.003. Google Scholar

[4]

S. Blandin, G. Bretti, A. Cutolo and B. Piccoli, Numerical simulations of traffic data via fluid dynamic approach,, Applied Mathematics and Computation, 210 (2009), 441. doi: 10.1016/j.amc.2009.01.057. Google Scholar

[5]

G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks,, SIAM Journal on Applied Dynamical Systems, 7 (2008), 510. doi: 10.1137/070697768. Google Scholar

[6]

Caltrans, Performance Measurement System (PeMS),, , (). Google Scholar

[7]

H. Chen and H. A. Rakha, Prediction of dynamic freeway travel times based on vehicle trajectory construction,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2012), 576. doi: 10.1109/ITSC.2012.6338825. Google Scholar

[8]

P. Cheng, Z. Qiu and B. Ran, Particle filter based traffic state estimation using cell phone network data,, in Proc. of the IEEE Intelligent Transportation Systems Conference, (2006), 1047. Google Scholar

[9]

R. Colombo, Hyperbolic phase transitions in traffic flow,, SIAM Journal on Applied Mathematics, 63 (2002), 708. doi: 10.1137/S0036139901393184. Google Scholar

[10]

E. Cristiani, C. de Fabritiis and B. Piccoli, A fluid dynamic approach for traffic forecast from mobile sensor data,, Communications in Applied and Industrial Mathematics, 1 (2010), 54. Google Scholar

[11]

C. F. Daganzo, The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory,, Transportation Research Part B: Methodological, 28 (1994), 269. doi: 10.1016/0191-2615(94)90002-7. Google Scholar

[12]

C. F. Daganzo, The cell transmission model, part II: network traffic,, Transportation Research Part B: Methodological, 29 (1995), 79. doi: 10.1016/0191-2615(94)00022-R. Google Scholar

[13]

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,, Journal of Geophysical Research, 99 (1994), 10143. doi: 10.1029/94JC00572. Google Scholar

[14]

G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation,, Ocean Dynamics, 53 (2003), 343. doi: 10.1007/s10236-003-0036-9. Google Scholar

[15]

M. Garavello and B. Piccoli, Traffic Flow on Networks,, American Institute of Mathematical Sciences, (2006). Google Scholar

[16]

J.-C. Herrera and A. Bayen, Incorporation of Lagrangian measurements in freeway traffic state estimation,, Transportation Research Part B: Methodological, 44 (2010), 460. doi: 10.1016/j.trb.2009.10.005. Google Scholar

[17]

J.-C. Herrera, D. Work, R. Herring, J. Ban, Q. Jacobson and A. Bayen, Evaluation of traffic data obtained via GPS-enabled mobile phones: the Mobile Century experiment,, Transportation Research Part C: Emerging Technologies, 18 (2010), 568. doi: 10.1016/j.trc.2009.10.006. Google Scholar

[18]

B. Hoh, M. Gruteser, R. Herring, J. Ban, D. Work, J.-C. Herrera, A. Bayen, M. Annavaram and Q. Jacobson., Virtual trip lines for distributed privacy-preserving traffic monitoring,, in 6th International Conference on Mobile Systems, (2008), 15. doi: 10.1145/1378600.1378604. Google Scholar

[19]

R. E. Kalman, A new approach to linear filtering and prediction problems,, Transactions of the ASME Journal of Basic Engineering, 82 (1960), 35. doi: 10.1115/1.3662552. Google Scholar

[20]

J. Kwon, K. Petty and P. Varaiya, Probe vehicle runs or loop detectors?, Transportation Research Record, 2012 (2007), 57. doi: 10.3141/2012-07. Google Scholar

[21]

M. Lighthill and G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A, 229 (1955), 317. doi: 10.1098/rspa.1955.0089. Google Scholar

[22]

H. Liu, A. Danczyk, R. Brewer and R. Starr, Evaluation of cell phone traffic data in minnesota,, Transportation Research Record, 2086 (2008), 1. doi: 10.3141/2086-01. Google Scholar

[23]

P.-E. Mazaré, O.-P. Tossavainen, A. Bayen and D. Work, Trade-offs between inductive loops and GPS probe vehicles for travel time estimation: A Mobile Century case study,, in Proc. of the Transportation Research Board 91st Annual Meeting, (2012). Google Scholar

[24]

P. I. Richards, Shock waves on the highway,, Operations Research, 4 (1956), 42. doi: 10.1287/opre.4.1.42. Google Scholar

[25]

B. Smith, H. Zhang, M. Fontaine and M. Green, Cell Phone Probes as an ATMS Tool,, Technical Report UVACTS-15-5-79, (2003), 15. Google Scholar

[26]

S. Smulders, Control of freeway traffic flow by variable speed signs,, Transportation Research Part B: Methodological, 24 (1990), 111. doi: 10.1016/0191-2615(90)90023-R. Google Scholar

[27]

D. Work, S. Blandin, O.-P. Tossavainen, B. Piccoli and A. Bayen, A traffic model for velocity data assimilation,, Applied Mathematics Research Express, 2010 (2010), 1. Google Scholar

[28]

J. L. Ygnace, C. Drane, Y. B. Yim and R. de Lacvivier, Travel Time Estimation on the San Francisco Bay Area Network Using Cellular Phones as Probes,, Technical Report UCB-ITS-PWP-2000-18, (2000), 2000. Google Scholar

[29]

Y. Yim and R. Cayford, Investigation of Vehicles as Probes Using Global Positioning System and Cellular Phone Tracking: Field Operational Test,, Technical Report UCB-ITS-PWP-2001-9, (2001), 2001. Google Scholar

[30]

, Mobile Millennium,, , (). Google Scholar

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