Computing travel times from filtered traffic states

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

Computing travel times from filtered traffic states

Pierre-Emmanuel Mazaré ^1, , Olli-Pekka Tossavainen ^2, and Daniel B. Work ^3,

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

Abstract
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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.

Keywords: scalar conservation laws, experimental data., vehicular traffic, Traffic estimation, traffic flow.

Mathematics Subject Classification: Primary: 90B20, 35L65; Secondary: 62L1.

Citation: Pierre-Emmanuel Mazaré, Olli-Pekka Tossavainen, Daniel B. Work. Computing travel times from filtered traffic states. Discrete and 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, 4089-4094.
[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, 10-15. doi: 10.1109/ITSC.2001.948621.
[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), 380-391. doi: 10.1016/j.trc.2007.06.003.
[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), 441-454. doi: 10.1016/j.amc.2009.01.057.
[5]	G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks, SIAM Journal on Applied Dynamical Systems, 7 (2008), 510-531. doi: 10.1137/070697768.
[6]	Caltrans, Performance Measurement System (PeMS),, , ().
[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, 576-581. doi: 10.1109/ITSC.2012.6338825.
[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, 1047-1052.
[9]	R. Colombo, Hyperbolic phase transitions in traffic flow, SIAM Journal on Applied Mathematics, 63 (2002), 708-721. doi: 10.1137/S0036139901393184.
[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), 54-71.
[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), 269-287. doi: 10.1016/0191-2615(94)90002-7.
[12]	C. F. Daganzo, The cell transmission model, part II: network traffic, Transportation Research Part B: Methodological, 29 (1995), 79-93. doi: 10.1016/0191-2615(94)00022-R.
[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), 10143-10162. doi: 10.1029/94JC00572.
[14]	G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynamics, 53 (2003), 343-367. doi: 10.1007/s10236-003-0036-9.
[15]	M. Garavello and B. Piccoli, Traffic Flow on Networks, American Institute of Mathematical Sciences, Springfield, MO, 2006.
[16]	J.-C. Herrera and A. Bayen, Incorporation of Lagrangian measurements in freeway traffic state estimation, Transportation Research Part B: Methodological, 44 (2010), 460-481. doi: 10.1016/j.trb.2009.10.005.
[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), 568-583. doi: 10.1016/j.trc.2009.10.006.
[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, Applications, and Services, 2008, 15-28. doi: 10.1145/1378600.1378604.
[19]	R. E. Kalman, A new approach to linear filtering and prediction problems, Transactions of the ASME Journal of Basic Engineering, 82 (1960), 35-45. doi: 10.1115/1.3662552.
[20]	J. Kwon, K. Petty and P. Varaiya, Probe vehicle runs or loop detectors? Transportation Research Record, 2012 (2007), 57-63. doi: 10.3141/2012-07.
[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), 317-345. doi: 10.1098/rspa.1955.0089.
[22]	H. Liu, A. Danczyk, R. Brewer and R. Starr, Evaluation of cell phone traffic data in minnesota, Transportation Research Record, 2086 (2008), 1-7. doi: 10.3141/2086-01.
[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.
[24]	P. I. Richards, Shock waves on the highway, Operations Research, 4 (1956), 42-51. doi: 10.1287/opre.4.1.42.
[25]	B. Smith, H. Zhang, M. Fontaine and M. Green, Cell Phone Probes as an ATMS Tool, Technical Report UVACTS-15-5-79, University of Virginia Center for Transportation Studies, 2003.
[26]	S. Smulders, Control of freeway traffic flow by variable speed signs, Transportation Research Part B: Methodological, 24 (1990), 111-132. doi: 10.1016/0191-2615(90)90023-R.
[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), 1-35.
[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, University of California Berkeley Institute of Transportation Studies, 2000.
[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, University of California Berkeley Institute of Transportation Studies, 2001.
[30]	, Mobile Millennium,, , ().

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, 4089-4094.
[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, 10-15. doi: 10.1109/ITSC.2001.948621.
[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), 380-391. doi: 10.1016/j.trc.2007.06.003.
[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), 441-454. doi: 10.1016/j.amc.2009.01.057.
[5]	G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks, SIAM Journal on Applied Dynamical Systems, 7 (2008), 510-531. doi: 10.1137/070697768.
[6]	Caltrans, Performance Measurement System (PeMS),, , ().
[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, 576-581. doi: 10.1109/ITSC.2012.6338825.
[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, 1047-1052.
[9]	R. Colombo, Hyperbolic phase transitions in traffic flow, SIAM Journal on Applied Mathematics, 63 (2002), 708-721. doi: 10.1137/S0036139901393184.
[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), 54-71.
[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), 269-287. doi: 10.1016/0191-2615(94)90002-7.
[12]	C. F. Daganzo, The cell transmission model, part II: network traffic, Transportation Research Part B: Methodological, 29 (1995), 79-93. doi: 10.1016/0191-2615(94)00022-R.
[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), 10143-10162. doi: 10.1029/94JC00572.
[14]	G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynamics, 53 (2003), 343-367. doi: 10.1007/s10236-003-0036-9.
[15]	M. Garavello and B. Piccoli, Traffic Flow on Networks, American Institute of Mathematical Sciences, Springfield, MO, 2006.
[16]	J.-C. Herrera and A. Bayen, Incorporation of Lagrangian measurements in freeway traffic state estimation, Transportation Research Part B: Methodological, 44 (2010), 460-481. doi: 10.1016/j.trb.2009.10.005.
[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), 568-583. doi: 10.1016/j.trc.2009.10.006.
[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, Applications, and Services, 2008, 15-28. doi: 10.1145/1378600.1378604.
[19]	R. E. Kalman, A new approach to linear filtering and prediction problems, Transactions of the ASME Journal of Basic Engineering, 82 (1960), 35-45. doi: 10.1115/1.3662552.
[20]	J. Kwon, K. Petty and P. Varaiya, Probe vehicle runs or loop detectors? Transportation Research Record, 2012 (2007), 57-63. doi: 10.3141/2012-07.
[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), 317-345. doi: 10.1098/rspa.1955.0089.
[22]	H. Liu, A. Danczyk, R. Brewer and R. Starr, Evaluation of cell phone traffic data in minnesota, Transportation Research Record, 2086 (2008), 1-7. doi: 10.3141/2086-01.
[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.
[24]	P. I. Richards, Shock waves on the highway, Operations Research, 4 (1956), 42-51. doi: 10.1287/opre.4.1.42.
[25]	B. Smith, H. Zhang, M. Fontaine and M. Green, Cell Phone Probes as an ATMS Tool, Technical Report UVACTS-15-5-79, University of Virginia Center for Transportation Studies, 2003.
[26]	S. Smulders, Control of freeway traffic flow by variable speed signs, Transportation Research Part B: Methodological, 24 (1990), 111-132. doi: 10.1016/0191-2615(90)90023-R.
[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), 1-35.
[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, University of California Berkeley Institute of Transportation Studies, 2000.
[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, University of California Berkeley Institute of Transportation Studies, 2001.
[30]	, Mobile Millennium,, , ().

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