Travel time estimation for ambulances using Bayesian data augmentation. (English) Zbl 1288.62044

Summary: We introduce a Bayesian model for estimating the distribution of ambulance travel times on each road segment in a city, using Global Positioning System (GPS) data. Due to sparseness and error in the GPS data, the exact ambulance paths and travel times on each road segment are unknown. We simultaneously estimate the paths, travel times, and parameters of each road segment travel time distribution using Bayesian data augmentation. To draw ambulance path samples, we use a novel reversible jump Metropolis-Hastings step. We also introduce two simpler estimation methods based on GPS speed data.
We compare these methods to a recently published travel time estimation method, using simulated data and data from Toronto EMS. In both cases, out-of-sample point and interval estimates of ambulance trip times from the Bayesian method outperform estimates from the alternative methods. We also construct probability-of-coverage maps for ambulances. The Bayesian method gives more realistic maps than the recently published method. Finally, path estimates from the Bayesian method interpolate well between sparsely recorded GPS readings and are robust to GPS location errors.


62F15 Bayesian inference
62P99 Applications of statistics


Full Text: DOI arXiv Euclid


[1] Aladdini, K. (2010). EMS response time models: A case study and analysis for the region of Waterloo. Master’s thesis, Univ. Waterloo.
[2] Alanis, R., Ingolfsson, A. and Kolfal, B. (2012). A Markov Chain model for an EMS system with repositioning. Production and Operations Management 22 216-231.
[3] Breslow, N. E. and Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika 82 81-91. · Zbl 0823.62059
[4] Brotcorne, L., Laporte, G. and Semet, F. (2003). Ambulance location and relocation models. European J. Oper. Res. 147 451-463. · Zbl 1037.90554
[5] Budge, S., Ingolfsson, A. and Zerom, D. (2010). Empirical analysis of ambulance travel times: The case of Calgary emergency medical services. Management Sci. 56 716-723.
[6] Chen, W., Li, Z., Yu, M. and Chen, Y. (2005). Effects of sensor errors on the performance of map matching. The Journal of Navigation 58 273-282.
[7] Dean, S. F. (2008). Why the closest ambulance cannot be dispatched in an urban emergency medical services system. Prehospital and Disaster Medicine 23 161-165.
[8] Erkut, E., Ingolfsson, A. and Erdoğan, G. (2008). Ambulance location for maximum survival. Naval Res. Logist. 55 42-58. · Zbl 1279.90104
[9] Fitch, J. J. (1995). Prehospital Care Administration : Issues , Readings , Cases . Mosby-Year Book, St. Louis.
[10] Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal. 1 515-533 (electronic). · Zbl 1331.62139
[11] Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457-472. · Zbl 1386.65060
[12] Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis , 2nd ed. Chapman & Hall/CRC, Boca Raton, FL. · Zbl 1039.62018
[13] Goldberg, J. B. (2004). Operations research models for the deployment of emergency services vehicles. EMS Management Journal 1 20-39.
[14] Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732. · Zbl 0861.62023
[15] Hastie, T., Tibshirani, R. and Friedman, J. (2005). The Elements of Statistical Learning , 2nd ed. Springer, New York. · Zbl 1273.62005
[16] Henderson, S. G. (2010). Operations research tools for addressing current challenges in emergency medical services. In Wiley Encyclopedia of Operations Research and Management Science . (J. J. Cochran, ed.). Wiley, New York.
[17] Ingolfsson, A., Budge, S. and Erkut, E. (2008). Optimal ambulance location with random delays and travel times. Health Care Manag. Sci. 11 262-274.
[18] Kan, K. H. F., Reesor, R. M., Whitehead, T. and Davison, M. (2009). Correcting the bias in Monte Carlo estimators of American-style option values. In Monte Carlo and Quasi-Monte Carlo Methods 2008 439-454. Springer, Berlin. · Zbl 1182.91199
[19] Krumm, J., Letchner, J. and Horvitz, E. (2007). Map matching with travel time constraints. In Society of Automotive Engineers ( SAE ) 2007 World Congress . SAE Inernational, Detroit, MI.
[20] Lou, Y., Zhang, C., Zheng, Y., Xie, X., Wang, W. and Huang, Y. (2009). Map-matching for low-sampling-rate GPS trajectories. In Proceedings of the 17 th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems 352-361. ACM, New York. · Zbl 0746.00063
[21] Marchal, F., Hackney, J. and Axhausen, K. W. (2005). Efficient map matching of large Global Positioning System data sets: Tests on speed-monitoring experiment in Zurich. Transportation Research Record : Journal of the Transportation Research Board 1935 93-100.
[22] Mason, A. J. (2005). Emergency vehicle trip analysis using GPS AVL data: A dynamic program for map matching. In Proceedings of the 40 th Annual Conference of the Operational Research Society of New Zealand 295-304. Operations Research Society of New Zealand, Wellington, New Zealand.
[23] McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics 105-142. Academic Press, New York.
[24] Nilsson, N. J. (1998). Artificial Intelligence : A New Synthesis . Morgan Kaufmann, San Francisco. · Zbl 1012.68605
[25] Rakha, H. and Zhang, W. (2005). Estimating traffic stream space mean speed and reliability from dual-and single-loop detectors. Transportation Research Record : Journal of the Transportation Research Board 1925 38-47.
[26] Robert, C. P. and Casella, G. (2004). Monte Carlo Statistical Methods , 2nd ed. Springer, New York. · Zbl 1096.62003
[27] Roberts, G. O. and Rosenthal, J. S. (2001). Optimal scaling for various Metropolis-Hastings algorithms. Statist. Sci. 16 351-367. · Zbl 1127.65305
[28] Soriguera, F. and Robuste, F. (2011). Estimation of traffic stream space mean speed from time aggregations of double loop detector data. Transportation Research Part C : Emerging Technologies 19 115-129.
[29] Syed, S. (2005). Development of map aided GPS algorithms for vehicle navigation in urban canyons. Master’s thesis, Univ. Calgary.
[30] Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-550. · Zbl 0619.62029
[31] Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762. · Zbl 0829.62080
[32] Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers 2 325-378.
[33] Westgate, B. S., Woodard, D. B., Matteson, D. S. and Henderson, S. G. (2013). Supplement to “Travel time estimation for ambulances using Bayesian data augmentation.” . · Zbl 1288.62044
[34] Witte, T. H. and Wilson, A. M. (2004). Accuracy of non-differential GPS for the determination of speed over ground. J. Biomech. 37 1891-1898.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.