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Large-network travel time distribution estimation for ambulances. (English) Zbl 1346.90565

Summary: We propose a regression approach for estimating the distribution of ambulance travel times between any two locations in a road network. Our method uses ambulance location data that can be sparse in both time and network coverage, such as Global Positioning System data. Estimates depend on the path traveled and on explanatory variables such as the time of day and day of week. By modeling at the trip level, we account for dependence between travel times on individual road segments. Our method is parsimonious and computationally tractable for large road networks. We apply our method to estimate ambulance travel time distributions in Toronto, providing improved estimates compared to a recently published method and a commercial software package. We also demonstrate our method’s impact on ambulance fleet management decisions, showing substantial differences between our method and the recently published method in the predicted probability that an ambulance arrives within a time threshold.

MSC:

90B90 Case-oriented studies in operations research
90B06 Transportation, logistics and supply chain management

Software:

GAMLSS; TomTom
Full Text: DOI

References:

[1] Aladdini, K., EMS response time models: A case study and analysis for the region of Waterloo (2010), University of Waterloo, Master’s thesis
[2] Alanis, R.; Ingolfsson, A.; Kolfal, B., A Markov chain model for an EMS system with repositioning, Production and Operations Management, 22, 216-231 (2013)
[3] Bernard, M.; Hackney, J.; Axhausen, K., Correlation of link travel speeds, Proceedings of the 6th swiss transport research conference (2006), Ascona, Switzerland
[4] Brotcorne, L.; Laporte, G.; Semet, F., Ambulance location and relocation models, European Journal of Operational Research, 147, 451-463 (2003) · Zbl 1037.90554
[5] Budge, S.; Ingolfsson, A.; Zerom, D., Electronic companion to “Empirical analysis of ambulance travel times: The case of Calgary emergency medical services”, Management Science, 56, 716-723 (2010)
[6] Budge, S.; Ingolfsson, A.; Zerom, D., Empirical analysis of ambulance travel times: The case of Calgary emergency medical services, Management Science, 56, 716-723 (2010)
[7] Dean, S., Why the closest ambulance cannot be dispatched in an urban emergency medical services system, Prehospital and Disaster Medicine, 23, 161-165 (2008)
[8] Erkut, E.; Fenske, R.; Kabanuk, S.; Gardiner, Q.; Davis, J., Improving the emergency service delivery in St. Albert, Infor, 39, 416-433 (2001) · Zbl 07677745
[9] Erkut, E.; Ingolfsson, A.; Erdoğan, G., Ambulance location for maximum survival, Naval Research Logistics (NRL), 55, 42-58 (2008) · Zbl 1279.90104
[10] Gelman, A., Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, 1, 515-533 (2006) · Zbl 1331.62139
[11] Gneiting, T.; Balabdaoui, F.; Raftery, A., Probabilistic forecasts, calibration and sharpness, Journal of the Royal Statistical Society: Series B, 69, 243-268 (2007) · Zbl 1120.62074
[12] Gneiting, T.; Raftery, A., Strictly proper scoring rules, prediction, and estimation, Journal of the American Statistical Association, 102, 359-378 (2007) · Zbl 1284.62093
[13] Goldberg, J., Operations research models for the deployment of emergency services vehicles, EMS Management Journal, 1, 20-39 (2004)
[14] Hofleitner, A.; Herring, R.; Abbeel, P.; Bayen, A., Learning the dynamics of arterial traffic from probe data using a dynamic Bayesian network, IEEE Transactions on Intelligent Transportation Systems, 13, 1679-1693 (2012)
[15] Hofleitner, A.; Herring, R.; Bayen, A., Arterial travel time forecast with streaming data: A hybrid approach of flow modeling and machine learning, Transportation Research Part B, 46, 1097-1122 (2012)
[16] Ingolfsson, A.; Budge, S.; Erkut, E., Optimal ambulance location with random delays and travel times, Health Care Management Science, 11, 262-274 (2008)
[17] Jenelius, E.; Koutsopoulos, H., Travel time estimation for urban road networks using low frequency probe vehicle data, Transportation Research Part B, 53, 64-81 (2013)
[18] Kaparias, I.; Bell, M.; Belzner, H., A new measure of travel time reliability for in-vehicle navigation systems, Journal of Intelligent Transportation Systems, 12, 202-211 (2008) · Zbl 1209.90126
[19] Kelton, W.; Law, A., Simulation modeling and analysis (2000), McGraw Hill, Boston
[20] Kolesar, P.; Walker, W.; Hausner, J., Determining the relation between fire engine travel times and travel distances in New York City, Operations Research, 23, 614-627 (1975)
[21] Lou, Y.; Zhang, C.; Zheng, Y.; Xie, X.; Wang, W.; Huang, Y., Map-matching for low-sampling-rate GPS trajectories, Proceedings of the 17th ACM SIGSPATIAL international conference on advances in geographic information systems, 352-361 (2009), ACM, New York
[22] Mason, A., Emergency vehicle trip analysis using GPS AVL data: A dynamic program for map matching, Proceedings of the 40th annual conference of the operational research society of New Zealand, 295-304 (2005), Wellington, NZ
[23] Maxwell, M.; Restrepo, M.; Henderson, S.; Topaloglu, H., Approximate dynamic programming for ambulance redeployment, INFORMS Journal on Computing, 22, 266-281 (2010) · Zbl 1243.90109
[24] Mazloumi, E.; Currie, G.; Rose, G., Using GPS data to gain insight into public transport travel time variability, Journal of Transportation Engineering, 136, 623-631 (2009)
[25] McLay, L., Emergency medical service systems that improve patient survivability, Wiley encyclopedia of operations research and management science (2010), Wiley, New York
[26] Potvin, J.; Xu, Y.; Benyahia, I., Vehicle routing and scheduling with dynamic travel times, Computers & Operations Research, 33, 1129-1137 (2006) · Zbl 1079.90021
[27] Quddus, M.; Ochieng, W.; Noland, R., Current map-matching algorithms for transport applications: State-of-the art and future research directions, Transportation Research Part C, 15, 312-328 (2007)
[28] Rahmani, M.; Koutsopoulos, H., Path inference from sparse floating car data for urban networks, Transportation Research Part C, 30, 41-54 (2013)
[29] Ramezani, M.; Geroliminis, N., On the estimation of arterial route travel time distribution with Markov chains, Transportation Research Part B, 46, 1576-1590 (2012)
[30] Rigby, R.; Stasinopoulos, D., Generalized additive models for location, scale and shape, Journal of the Royal Statistical Society: Series C, 54, 507-554 (2005) · Zbl 1490.62201
[31] Roberts, G.; Rosenthal, J., Optimal scaling for various Metropolis-Hastings algorithms, Statistical Science, 16, 351-367 (2001) · Zbl 1127.65305
[32] Schmid, V., Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming, European Journal of Operational Research, 219, 611-621 (2012) · Zbl 1253.90155
[33] Stasinopoulos, D.; Rigby, R., Generalized additive models for location scale and shape (GAMLSS) in R, Journal of Statistical Software, 23, 1-46 (2007)
[34] Tierney, L., Markov chains for exploring posterior distributions, The Annals of Statistics, 22, 1701-1728 (1994) · Zbl 0829.62080
[35] Topaloglu, H., A parallelizable dynamic fleet management model with random travel times, European Journal of Operational Research, 175, 782-805 (2006) · Zbl 1142.90329
[36] Westgate, B., Vehicle travel time distribution estimation and map-matching via markov chain Monte Carlo methods (2013), Cornell University, (Ph.D. thesis)
[37] Westgate, B.; Woodard, D.; Matteson, D.; Henderson, S., Travel time estimation for ambulances using Bayesian data augmentation, Annals of Applied Statistics, 7, 1139-1161 (2013) · Zbl 1288.62044
[38] Yuan, J.; Zheng, Y.; Zhang, C.; Xie, W.; Xie, X.; Sun, G.; Huang, Y., T-drive: driving directions based on taxi trajectories, Proceedings of the 18th SIGSPATIAL international conference on advances in geographic information systems, 99-108 (2010), ACM
[39] Zhen, L.; Wang, K.; Hu, H.; Chang, D., A simulation optimization framework for ambulance deployment and relocation problems, Computers & Industrial Engineering, 72, 12-23 (2014)
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