Vol. 22 No. 3 (2023): Mapana Journal of Sciences
Research Articles

Mathematical Modelling of Traffic Behaviour

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  • Maria Liya,
  • Santhosh Rajan,
  • Arun Kenath
Maria Liya
CHRIST (Deemed to be University), Bengaluru
Santhosh Rajan
CHRIST (Deemed to be University), Bengaluru
Arun Kenath
CHRIST (Deemed to be University), Bengaluru
DOI: https://doi.org/10.12723/mjs.66.9

Published 2023-12-13

Keywords

  • Mathematical model,
  • Traffic congestion,
  • Psychological experiences,
  • Negative affect

Copyright (c) 2023

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

Mathematical modelling is a powerful tool that can be used to describe and understand complex real-world phenomena through the application of mathematical equations, algorithms, and simulations. Mathematical modelling of traffic flow plays a crucial role in understanding and predicting the dynamics of vehicular movement on roads. Usual modelling of traffic flow is restricted to treating traffic as an inorganic system. In this work, we bring in another layer of parameters that can affect traffic – human behaviour. Here, we argue that a mathematical model with behavioural components could provide a more real-world understanding of traffic flow. The primary aim of the research is to create a mathematical model that incorporates human behaviour.

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References

  1. Bonanno, G. A., Westphal, M. and Mancini, A. D. (2011) “Resilience to loss and potential trauma,” Annual review of clinical psychology, 7(1), pp. 511–535. doi: 10.1146/annurev-clinpsy-032210-104526.
  2. Dratva, J. et al. (2010) “Impact of road traffic noise annoyance on health-related quality of life: results from a population-based study,” Quality of life research: an international journal of quality of life aspects of treatment, care and rehabilitation, 19(1), pp. 37–46. doi: 10.1007/s11136-009-9571-2.
  3. Schaefer, A. (2005) “Commuting takes its toll,” Scientific American mind, 16(3), pp. 14–15. doi: 10.1038/scientificamericanmind1005-14.
  4. Weerasinghe, T. D., Karunarathna, D. I. M. and Subashini, B. L. C. (2020) “Effect of road traffic congestion on stress at work: Evidence from the employees working in metropolitan areas of Colombo, Sri Lanka,” SSRN Electronic Journal. doi: 10.2139/ssrn.3853900.
  5. McEwen, B. S. (1998) “Stress, adaptation, and disease. Allostasis and allostatic load,” Annals of the New York Academy of Sciences, 840(1), pp. 33–44. doi: 10.1111/j.1749-6632.1998.tb09546.x.
  6. Shackman, A. J. et al. (2011) “The integration of negative affect, pain and cognitive control in the cingulate cortex,” Nature reviews. Neuroscience, 12(3), pp. 154–167. doi: 10.1038/nrn2994.
  7. Feng, Z. et al. (2017) “Driving anger and its relationships with type A behavior patterns and trait anger: Differences between professional and non-professional drivers,” PloS one, 12(12), p. e0189793. doi: 10.1371/journal.pone.0189793.
  8. Galovski, T. E. and Blanchard, E. B. (2004) “Road rage: a domain for psychological intervention?,” Aggression and violent behavior, 9(2), pp. 105–127. doi: 10.1016/s1359-1789(02)00118-0.
  9. Hennessy, D. A. and Wiesenthal, D. L. (2001) “Further validation of the driving vengeance questionnaire,” Violence and victims, 16(5), pp. 565–573.
  10. Lupton, D. (2002) “Road rage: drivers’ understandings and experiences,” Journal of sociology (Melbourne, Vic.), 38(3), pp. 275–290. doi: 10.1177/144078302128756660.
  11. Holtcamp, W. (2011) “CARDIOVASCULAR HEALTH. Traffic trigger,” Environmental health perspectives, 119(5), pp. A205–A205. Available at: http://www.jstor.org/stable/41203285.
  12. Zanobetti, A. et al. (2010) “Reduction in heart rate variability with traffic and air pollution in patients with coronary artery disease,” Environmental health perspectives, 118(3), pp. 324–330. doi: 10.1289/ehp.0901003.
  13. Fredrickson, B. L. (2004) “The broaden-and-build theory of positive emotions,” Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 359(1449), pp. 1367–1378. doi: 10.1098/rstb.2004.1512.
  14. Chubb, M. C. and Jacobsen, K. H. (2010) “Mathematical modeling and the epidemiological research process,” European journal of epidemiology, 25(1), pp. 13–19. doi: 10.1007/s10654-009-9397-9.
  15. Li, C., Cao, D. and Du, Q. (2020) “Exact solutions to the nonlinear equation in traffic congestion,” Advances in difference equations, 2020(1). doi: 10.1186/s13662-020-2538-x.
  16. Mahmud, K. and Town, G. E. (2016) “A review of computer tools for modeling electric vehicle energy requirements and their impact on power distribution networks,” Applied energy, 172, pp. 337–359. doi: 10.1016/j.apenergy.2016.03.100.
  17. Risso, M. A. et al. (2017) “A nonlinear algorithm for traffic estimation with state constraints,” Transportation research procedia, 27, pp. 600–608. doi: 10.1016/j.trpro.2017.12.128.