Sparse Travel Time Estimation from Streaming Data

Published Online:https://doi.org/10.1287/trsc.2019.0920

References

  • Abbi R, El-Darzi E, Vasilakis C, Millard P (2008) Analysis of stopping criteria for the EM algorithm in the context of patient grouping according to length of stay. 4th Internat. IEEE Conf. Intelligent Systems (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 3‐9–3‐14.Google Scholar
  • Afonso M, Bioucas-Dias J, Figueiredo M (2010) Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9):2345–2356.CrossrefGoogle Scholar
  • Al-Deek H, Emam E (2006) New methodology for estimating reliability in transportation networks with degraded link capacities. J. Intelligent Transportation Systems 10(3):117–129.CrossrefGoogle Scholar
  • Archambeau C, Lee J, Verleysen M (2003) On convergence problems of the EM algorithm for finite Gaussian mixtures. Proc. 11th Eur. Sympos. Artificial Neural Networks (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 99–106.Google Scholar
  • Arezoumandi M (2011) Estimation of travel time reliability for freeways using mean and standard deviation of travel time. J. Transportation Systems Engrg. Inform. Tech. 11(6):74–84.CrossrefGoogle Scholar
  • Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1):183–202.CrossrefGoogle Scholar
  • Biernacki C, Celeux G, Govaert G (2003) Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Comput. Statist. Data Anal. 41(3):561–575.CrossrefGoogle Scholar
  • Bishop C (2006) Pattern Recognition and Machine Learning (Springer, New York).Google Scholar
  • Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Cacoullos T (1966) Estimation of a multivariate density. Ann. Inst. Statist. Math. 18(1):179–189.CrossrefGoogle Scholar
  • Carey M, Ge Y (2005a) Alternative conditions for a well-behaved travel time model. Transportation Sci. 39(3):417–428.LinkGoogle Scholar
  • Carey M, Ge Y (2005b) Convergence of a discretised travel-time model. Transportation Sci. 39(1):25–38.LinkGoogle Scholar
  • Chakraborty S, Ong S (2017) Mittag-Leffler function distribution—A new generalization of hyper-Poisson distribution. J. Statist. Distributions Appl. 4(8):1–17.Google Scholar
  • Chen P, Yin K, Sun J (2014) Application of finite mixture of regression model with varying mixing probabilities to estimation of urban arterial travel times. Transportation Res. Record 2442(1):96–105.CrossrefGoogle Scholar
  • Chen S (2000) Probability density function estimation using Gamma kernels. Ann. Inst. Statist. Math. 52(3):471–480.CrossrefGoogle Scholar
  • Chen S, Hong X, Harris C (2004) Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization. IEEE Trans. Systems Man Cybernetics B 34(4):1708–1717.CrossrefGoogle Scholar
  • Chen S, Hong X, Harris C (2008) An orthogonal forward regression technique for sparse kernel density estimation. Neurocomputing 71(4):931–943.CrossrefGoogle Scholar
  • Del Castillo J, Benitez F (1995) On the functional form of the speed-density relationship. i: General theory, ii: Empirical investigation. Transportation Res. Part B: Methodological 29(5):373–406.CrossrefGoogle Scholar
  • Dilip D, Freris N, Jabari S (2017) Sparse estimation of travel time distributions using Gamma kernels. Transportation Research Board 96th Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Du L, Peeta S, Kim Y (2012) An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks. Transportation Res. Part B: Methodological 46(1):235–252.CrossrefGoogle Scholar
  • Emam E, Al-Deek H (2006) Using real-life dual-loop detector data to develop new methodology for estimating freeway travel time reliability. Transportation Res. Record 1959(1):140–150.CrossrefGoogle Scholar
  • Feng Y, Hourdos J, Davis G (2014) Probe vehicle based real-time traffic monitoring on urban roadways. Transportation Res. Part C: Emerging Tech. 40(March):160–178.CrossrefGoogle Scholar
  • Fosgerau M, Fukuda D (2012) Valuing travel time variability: Characteristics of the travel time distribution on an urban road. Transportation Res. Part C: Emerging Tech. 24(October):83–101.CrossrefGoogle Scholar
  • Franklin R (1961) The structure of a traffic shock wave. Civil Engrg. Public Works Rev. 56(1):1186–1188.Google Scholar
  • Freris N, Öçal O, Vetterli M (2013a) Recursive compressed sensing. Working paper, NYU Tandon School of Engineering, New York.Google Scholar
  • Freris N, Öçal O, Vetterli M (2013b) Compressed sensing of streaming data. Proc. 51st Allerton Conf. Comm. Control Comp. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 1242–1249.Google Scholar
  • Ghiani G, Guerriero E (2014) A note on the Ichoua, Gendreau, and Potvin (2003) travel time model. Transportation Sci. 48(3):458–462.LinkGoogle Scholar
  • Gómez A, Mariño R, Akhavan-Tabatabaei R, Medaglia AL, Mendoza JE (2016) On modeling stochastic travel and service times in vehicle routing. Transportation Sci. 50(2):627–641.LinkGoogle Scholar
  • Grant M, Boyd S (2014) CVX: Matlab software for disciplined convex programming, version 2.1. Accessed December 20, 2018, http://cvxr.com/cvx.Google Scholar
  • Guo F, Rakha H, Park S (2010) Multistate model for travel time reliability. Transportation Res. Record 2188(1):46–54.CrossrefGoogle Scholar
  • Haight F (1963) Mathematical Theories of Traffic Flow (Academic Press, New York).Google Scholar
  • Haubold H, Mathai A, Saxena R (2011) Mittag-Leffler functions and their applications. J. Appl. Math. 2011:298628.CrossrefGoogle Scholar
  • Hofleitner A, Herring R, Bayen A (2012a) Arterial travel time forecast with streaming data: A hybrid approach of flow modeling and machine learning. Transportation Res. Part B: Methodological 46(9):1097–1122.CrossrefGoogle Scholar
  • Hofleitner A, Herring R, Bayen A (2012b) Probability distributions of travel times on arterial networks: A traffic flow and horizontal queuing theory approach. Transportation Research Board 91st Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Hofleitner A, Rabbani T, El Ghaoui L, Bayen A (2013) Online homotopy algorithm for a generalization of the LASSO. IEEE Trans. Automatic Control 58(12):3175–3179.CrossrefGoogle Scholar
  • Hofleitner A, Rabbani T, Rafiee M, El Ghaoui L, Bayen A (2014) Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO. Discrete Continuous Dynamical Systems 7(3):503–523.CrossrefGoogle Scholar
  • Hunter T, Das T, Zaharia M, Abbeel P, Bayen A (2013) Large-scale estimation in cyberphysical systems using streaming data: A case study with arterial traffic estimation. IEEE Trans. Automation Sci. Engrg. 10(4):884–898.CrossrefGoogle Scholar
  • Ichoua S, Gendreau M, Potvin JY (2003) Vehicle dispatching with time-dependent travel times. Eur. J. Oper. Res. 144(2):379–396.CrossrefGoogle Scholar
  • Jabari S, Zheng J, Liu H (2014) A probabilistic stationary speed–density relation based on Newell’s simplified car-following model. Transportation Res. Part B: Methodological 68(October):205–223.CrossrefGoogle Scholar
  • Jabari S, Zheng F, Liu H, Filipovska M (2018) Stochastic Lagrangian modeling of traffic dynamics. Transportation Res. Board 97th Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Jenelius E, Koutsopoulos H (2013) Travel time estimation for urban road networks using low frequency probe vehicle data. Transportation Res. Part B: Methodological 53(July):64–81.CrossrefGoogle Scholar
  • Jenelius E, Koutsopoulos H (2015) Probe vehicle data sampled by time or space: Consistent travel time allocation and estimation. Transportation Res. Part B: Methodological 71(January):120–137.CrossrefGoogle Scholar
  • Ji Y, Zhang H (2013) Travel time distributions on urban streets: Estimation with hierarchical Bayesian mixture model and application to traffic analysis with high-resolution bus probe data. Transportation Res. Board 92nd Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Karlis D, Xekalaki E (2003) Choosing initial values for the EM algorithm for finite mixtures. Comput. Statist. Data Anal. 41(3):577–590.CrossrefGoogle Scholar
  • Kazagli E, Koutsopoulos H (2013) Estimation of arterial travel time from automatic number plate recognition data. Transportation Res. Record 2391(1):22–31.CrossrefGoogle Scholar
  • Kharoufeh JP, Gautam N (2004) Deriving link travel-time distributions via stochastic speed processes. Transportation Sci. 38(1):97–106.LinkGoogle Scholar
  • Kim J, Mahmassani H (2014) A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times. Transportation Res. Part C: Emerging Tech. 46(September):83–97.CrossrefGoogle Scholar
  • Kim J, Mahmassani H (2015) Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Res. Part B: Methodological 80(October):40–63.CrossrefGoogle Scholar
  • Kim S, Koh K, Lustig M, Boyd S, Gorinevsky D (2007) An interior-point method for large-scale-regularized least squares. IEEE J. Selected Topics Signal Processing 1(4):606–617.CrossrefGoogle Scholar
  • Lacour C, Massart P, Rivoirard V (2017) Estimator selection: A new method with applications to kernel density estimation Sankhya A 79(2):298–335.Google Scholar
  • Lighthill M, Whitham G (1955) On kinematic waves. I: Flood movement in long rivers, ii: A theory of traffic flow on long crowded roads. Proc. Royal Soc. Lond. A. 229:281–345.CrossrefGoogle Scholar
  • Lin W, Wang Y, Zhuang Y, Zhang S (2013) Evaluate the number of clusters in finite mixture models with the penalized histogram difference criterion. J. Process Control 23(8):1052–1062.CrossrefGoogle Scholar
  • Mukherjee S, Vapnik V (2000) Support vector method for multivariate density estimation. Solla S, Leen T, Müller K-R, eds. Proc. 12th Conf. Adv. Neural Inform. Processing Systems (NIPS) (MIT Press, Cambridge, MA), 659–665.Google Scholar
  • Nesterov Y (2013) Gradient methods for minimizing composite functions. Math. Programming 140(1):125–161.CrossrefGoogle Scholar
  • Newell G (1961) Nonlinear effects in the dynamics of car following. Oper. Res. 9(2):209–229.LinkGoogle Scholar
  • Parikh N, Boyd S (2014) Proximal Algorithms. Foundations Trends Optim. 1(3):127–239.CrossrefGoogle Scholar
  • Parzen E (1962) On estimation of a probability density function and mode. Ann. Math. Statist. 33(3):1065–1076.CrossrefGoogle Scholar
  • Polus A (1979) A study of travel time and reliability on arterial routes. Transportation 8(2):141–151.CrossrefGoogle Scholar
  • Pu W (2011) Analytic relationships between travel time reliability measures. Transportation Res. Record 2254(1):122–130.CrossrefGoogle Scholar
  • Punzo V, Borzacchiello M, Ciuffo B (2011) On the assessment of vehicle trajectory data accuracy and application to the Next Generation SIMulation (NGSIM) program data. Transportation Res. Part C: Emerging Tech. 19(6):1243–1262.CrossrefGoogle Scholar
  • Rahmani M, Jenelius E, Koutsopoulos HN (2015) Non-parametric estimation of route travel time distributions from low-frequency floating car data. Transportation Res. Part C: Emerging Tech. 58(September):343–362.CrossrefGoogle Scholar
  • Rakha H, El-Shawarby IMA, Dion F (2006) Estimating path travel-time reliability. Proc. 2006 IEEE Conf. Intelligent Transportation Systems (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 236–241.Google Scholar
  • Rakha HA, Du J, Park S, Guo F, Doerzaph Z, Viita D, Golembiewski G, Katz B, Kehoe N, Rigdon H (2011) Feasibility of using in-vehicle video data to explore how to modify driver behavior that causes nonrecurring congestion. Report S2-L10-RR-01, Second Strategic Highway Research Program, Transportation Research Board, Washington, DC.Google Scholar
  • Ramezani M, Geroliminis N (2012) On the estimation of arterial route travel time distribution with Markov chains. Transportation Res. Part B: Methodological 46(10):1576–1590.CrossrefGoogle Scholar
  • Ramezani M, Geroliminis N (2015) Queue profile estimation in congested urban networks with probe data. Comput.-Aided Civil Infrastructure Engrg. 30(6):414–432.CrossrefGoogle Scholar
  • Raudys Š (1991) On the effectiveness of Parzen window classifier. Informatica 2(2):434–454.Google Scholar
  • Redner R, Walker H (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26(2):195–239.CrossrefGoogle Scholar
  • Richards P (1956) Shock waves on the highway. Oper. Res. 4(1):42–51.LinkGoogle Scholar
  • Richardson A, Taylor M (1978) Travel time variability on commuter journeys. High Speed Ground Transportation J. 12(1):77–99.Google Scholar
  • Silverman B (1986) Density Estimation for Statistics and Data Analysis, vol. 26 (CRC Press, Boca Raton, FL).CrossrefGoogle Scholar
  • Sopasakis P, Freris N, Patrinos P (2016) Accelerated reconstruction of a compressively sampled data stream. 24th IEEE Eur. Signal Processing Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 1078–1082.Google Scholar
  • Taylor M (2017) Fosgerau’s travel time reliability ratio and the Burr distribution. Transportation Res. Part B: Methodological 97(March):50–63.CrossrefGoogle Scholar
  • Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J. Royal Statist. Soc. B. 58(1):267–288.CrossrefGoogle Scholar
  • Wan N, Gomes G, Vahidi A, Horowitz R (2014) Prediction on travel-time distribution for freeways using online expectation maximization algorithm. Transportation Res. Board 93rd Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Wright S, Nowak R, Figueiredo M (2009) Sparse reconstruction by separable approximation. IEEE Trans. Signal Processing 57(7):2479–2493.CrossrefGoogle Scholar
  • Wu C (1983) On the convergence properties of the EM algorithm. Ann. Statist. 11(1):95–103.CrossrefGoogle Scholar
  • Xu X, Chen A, Cheng L, Lo H (2014) Modeling distribution tail in network performance assessment: A mean-excess total travel time risk measure and analytical estimation method. Transportation Res. Part B: Methodological 66(August):32–49.CrossrefGoogle Scholar
  • Yang F, Yun M, Yang X (2014) Travel time distribution under interrupted flow and application to travel time reliability. Transportation Res. Record 2466(1):114–124.CrossrefGoogle Scholar
  • Zheng F, Van Zuylen H, Liu X (2017) A methodological framework of travel time distribution estimation for urban signalized arterial roads. Transportation Sci. 51(3):893–917.LinkGoogle Scholar
  • Zheng F, Jabari S, Liu H, Lin D (2018) Traffic state estimation using stochastic Lagrangian dynamics. Transportation Res. Part B: Methodological 115(September):143–165.CrossrefGoogle Scholar
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