228
Views
1
CrossRef citations to date
0
Altmetric
Articles

A stochastic risk model for incident occurrences and duration in road networks

, &
Article: 2077469 | Received 26 Aug 2021, Accepted 21 Apr 2022, Published online: 31 May 2022

References

  • Abramowitz, M., and I. A. Stegun 1964. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Vol. 55.
  • Avanzi, B., H. Gerber, and E. S. W. Shiu. 2007. “Optimal Dividends in the Dual Model.” Insurance: Mathematics and Economics 41 (1): 111–123.
  • Azaïs, R., J.-B. Bardet, A. Genadot, N. Krell, and P.-A. Zitt. 2014. “Piecewise Deterministic {Markov} Process — Recent Results.” ESAIM: Proceedings 44: 276–290.
  • Baykal-Gürsoy, M., W. Xiao, and K. Ozbay. 2009. “Modeling Traffic Flow Interrupted by Incidents.” European Journal of Operational Research 195 (1): 127–138.
  • Benaïm, M., S. Le Borgne, F. Malrieu, and P.-A. Zitt. 2015. “Qualitative Properties of Certain Piecewise Deterministic Markov Processes.” Annales de L'Institut Henri Poincaré, Probabilités et Statistiques 51 (3): 1040–1075.
  • Benouaret, Z., and D. Aissani. 2010. “Strong Stability in a Two-Dimensional Classical Risk Model with Independent Claims.” Scandinavian Actuarial Journal 2: 83–92.
  • Borovkov, K. A., and D. C. Dickson. 2008. “On the Ruin Time Distribution for a Sparre Andersen Process with Exponential Claim Sizes.” Insurance: Mathematics and Economics 42 (3): 1104–1108.
  • Bouziane, H. 2011. Calcul et estimation d'une probabilité de ruine. ummto.
  • Chung, Y. 2010. “Development of an Accident Duration Prediction Model on the Korean Freeway Systems.” Accident Analysis & Prevention 42 (1): 282–289.
  • Cramér, H. 1930. On the Mathematical Theory of Risk. Centraltryckeriet.
  • Davis, M. H. 1984. “Piecewise-deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models.” Journal of the Royal Statistical Society: Series B Methodological 46 (3): 353–376.
  • Dunn, W. M. 2003. Safe and Quick Clearance of Traffic Incidents: A Synthesis of Highway Practice (Vol. 318). Transportation Research Board.
  • Enikeeva, F., V. Kalashnikov, and D. Rusaityte. 2001. “Continuity Estimates for Ruin Probabilities.” Scandinavian Actuarial Journal 1: 18–39.
  • Ghosh, B., and J. Dauwels. 2021. “Comparison of Different Bayesian Methods for Estimating Error Bars with Incident Duration Prediction.” Journal of Intelligent Transportation Systems: 1–17.
  • Golob, T. F., W. W. Recker, and J. D. Leonard. 1987. “An Analysis of the Severity and Incident Duration of Truck-Involved Freeway Accidents.” Accident Analysis & Prevention 19 (5): 375–395.
  • Hamad, K. A.-R., W. Zeiada, S. Abu Dabous, and M. A. Khalil. 2020. “Predicting Incident Duration Using Random Forests.” Transportmetrica A: Transport Science 16 (3): 1269–1293.
  • He, J.-M., R. Wu, and H.-Y. Zhang. 2008. “Ruin Probabilities of a Surplus Process Described by PDMPs.” Acta Mathematicae Applicatae Sinica, English Series 24 (1): 117–128.
  • Javid, R. J., and R. J. Javid. 2018. “A Framework for Travel Time Variability Analysis Using Urban Traffic Incident Data.” IATSS Research 42 (1): 30–38.
  • Jeihani, M., P. James, A. A. Saka, and A. Ardeshiri. 2015. “Traffic Recovery Time Estimation Under Different Flow Regimes in Traffic Simulation.” Journal of Traffic and Transportation Engineering (English Edition) 2 (5): 291–300.
  • Jin, L., and S. Amin. 2016. “Analysis of a Stochastic Switching Model of Freeway Traffic Incidents.” IEEE Transactions on Automatic Control 64: 1093–1108.
  • Jones, B., L. Janssen, and F. Mannering. 1991. “Analysis of the Frequency and Duration of Freeway Accidents in Seattle.” Accident Analysis & Prevention 23 (4): 239–255.
  • Junhua, W., C. Haozhe, and Q. Shi. 2013. “Estimating Freeway Incident Duration Using Accelerated Failure Time Modeling.” Safety Science 54: 43–50.
  • Knuth, D. E. 1996. “On the Lambert W Function.” Advances in Computational Mathematics 5 (1): 329–359.
  • Laman, H., S. Yasmin, and N. Eluru. 2018. “Joint Modeling of Traffic Incident Duration Components (Reporting, Response, and Clearance Time): A Copula-Based Approach.” Transportation Research Record 2672 (30): 76–89.
  • Li, R., and M. Guo. 2015. “Competing Risks Analysis on Traffic Accident Duration Time.” Journal of Advanced Transportation 49 (3): 402–415.
  • Lundberg, F. 1926. Försäkringsteknisk riskutjämning. F. Englunds boktryckeri.
  • Nam, D., and F. Mannering. 2000. “An Exploratory Hazard-Based Analysis of Highway Incident Duration.” Transportation Research Part A: Policy and Practice 34 (2): 85–102.
  • Rusaityte, D. 2002. Stability Bounds for Ruin Probabilities in a Markov Modulated Risk Model with Investments. Laboratory of Actuarial Mathematics. University of Copenhagen.
  • Schmidt, T. 2017. “Shot-noise Processes in Finance.” In From Statistics to Mathematical Finance, 367–385. Springer.
  • Skabardonis, A., K. F. Petty, R. L. Bertini, P. P. Varaiya, H. Noeimi, and D. Rydzewski. 1997. “I-880 Field Experiment: Analysis of Incident Data.” Transportation Research Record 1603 (1): 72–79.
  • Tavassoli Hojati, A., L. Ferreira, S. Washington, and P. Charles. 2013. “Hazard Based Models for Freeway Traffic Incident Duration.” Accident Analysis & Prevention 52: 171–181.
  • Touazi, A., Z. Benouaret, D. Aissani, and S. Adjabi. 2017. “Nonparametric Estimation of the Claim Amount in the Strong Stability Analysis of the Classical Risk Model.” Insurance: Mathematics and Economics 74: 78–83.
  • Tressou, J., S. Clémençon, and P. Bertail. 2008. “A Storage Model with Random Release Rate for Modeling Exposure to Food Contaminants.” Mathematical Biosciences and Engineering 5 (1): 35–60.
  • Wang, H., K. Rudy, J. Li, and D. Ni. 2010. “Calculation of Traffic Flow Breakdown Probability to Optimize Link Throughput.” Applied Mathematical Modelling 34 (11): 3376–3389.
  • Weng, J., W. Qiao, X. Qu, and X. Yan. 2015. “Cluster-based Lognormal Distribution Model for Accident Duration.” Transportmetrica A: Transport Science 11 (4): 345–363.
  • Zhang, Z., J. Liu, X. Li, and A. J. Khattak. 2021. “Do Larger Sample Sizes Increase the Reliability of Traffic Incident Duration Models? A Case Study of East Tennessee Incidents.” Transportation Research Record 2675 (6): 265–280.
  • Zou, Y., K. Henrickson, D. Lord, Y. Wang, and K. Xu. 2016. “Application of Finite Mixture Models for Analysing Freeway Incident Clearance Time.” Transportmetrica A: Transport Science 12 (2): 99–115.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.