Optimal design and impact analysis of urban traffic regulations under ambient uncertainty

  • Yu-Ta Wu
  • Kuei-Yuan ChanEmail author
Original Paper


Decision-making in traffic regulations is challenging with uncertainty in the environment. In this research we extend probabilistic engineering design concepts to policy decision-making for urban traffic with variability from field data. City traffic is simulated using user equilibrium and cellular automata. A cellular automata (CA) model is developed by combing existing CA models with tailored rules for local traffic behaviors in Tainan, Taiwan. Both passenger sedans and motorcycles are considered with the possibility of passing between different types of vehicles. The tailpipe emissions from all mobile sources are modeled as Gaussian dispersion with finite line sources. Speed limits of all roads are selected as independent policy design variables, resulting in a problem with 50 dimensions. We first study the impacts of a particular policy-setting on traffic behaviors and on the environment under various sources of uncertainties. The genetic algorithm, combined with probabilistic analysis, is then used to obtain the optimal regulations with the minimal cost to the environment in compliance to the current ambient air quality standards.


Optimal policy setting under uncertainty Environmental impact Cellular automata Reliability-based design optimization Uncertainty modeling 

List of symbols


Set of all possible paths for a origin–destination pair in traffic equilibrium


Set of shortest path in traffic equilibrium


Cost of the link from the node i to the node j in traffic equilibrium


Standards of pollutant j


Concentration of pollutant j of a receptor in Gaussian dispersion model


Cost per unit time in objective function


Fuel cost per unit distance at speed j for vehicle type i


Distance to the preceding vehicle


Distance to the preceding vehicle on the other lane


distance to the backward vehicle on the other lane


distance to the backward car


Distance between traffic signals (signal distance)


Traffic flow of path k in traffic equilibrium


Effective stack height in Gaussian dispersion model


Distance of driver can look ahead on the same lane


Distance of driver can look ahead on the other lane


Distance of driver can look back on the other lane


Set of all upstream nodes of all links arriving at node i in traffic equilibrium


Set of all links in a network in traffic equilibrium


Length of each site in CA model


Number of vehicle types in objective function


Number of vehicles of type i in objective function


Number of vehicles of type i with speed j in objective function


Set of all nodes in a network in traffic equilibrium


Set of all downstream nodes of all links leaving at node i in traffic equilibrium


An origin–destination pair in traffic equilibrium


Random breaking probability


Lane changing probability


Failure probability levels


Probability of ·


Total traffic flow of an origin–destination pair in traffic equilibrium


Emission rate in Gaussian dispersion model


A random number generated from standard uniform distribution


Distance to the closest preceding signal


Time interval between red and green lights (signal period)


Vehicle traffic density in objective function


Traveling cost of vehicle type i in objective function


Average wind speed in Gaussian dispersion model


Actual wind speed in Gaussian dispersion model


Wind speed perpendicular to the prevailing wind direction in Gaussian dispersion model


Wind speed along the prevailing wind direction in Gaussian dispersion model


Speed of vehicle


Maximal speed of vehicle


Maximal speed of a car


Maximal speed of a motorcycle


Speed of the preceding motorcycle in lane M


Speed of the preceding vehicle in lane CM


Average speed of vehicle type i


Traffic flow of the link from the node i to the node j in traffic equilibrium


Prevailing wind direction in Gaussian dispersion model


Actual wind direction


Indicator of whether the link ij is on the path k in traffic equilibrium


Horizontal dispersion coefficients


Vertical dispersion coefficients


Emission factor in Gaussian dispersion model


Average traveling cost per unit distance


Average fuel cost per unit distance



The authors would like to thank Prof. T. Y. Hu and his research group in the Department of Transportation and Communication Management Science in NCKU for illuminating certain aspects of DYNA Taiwan. This work is partly supported by the National Science Council in Taiwan under #NSC-98-2221-E-006-048. This support is gratefully acknowledged.


  1. Amundsen A, Klæboe R, Fyhri A (2008) Annoyance from vehicular air pollution: exposure–response relationships for norway. Atmos Environ 42(33):7679–7688CrossRefGoogle Scholar
  2. Bates D (1992) Health indices of the adverse effects of air pollution: the question of coherence. Environ Res 59:336–349CrossRefGoogle Scholar
  3. Berkowicz R, Palmgren F, Hertel O, Vignati E (1996) Using measurements of air pollution in streets for evaluation of urban air quality—meteorological analysis and model calculations. Sci Total Environ 189–190:259–265Google Scholar
  4. Biham O, Middleton A, Levine D (1992) Self-organization and a dynamical transition in traffic-flow models. Phys Rev A 46(10):R6124–R6127CrossRefGoogle Scholar
  5. Brando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995) Dynamical model of traffic congestion and numerical simulation. Phys Rev E 51(2):1035–1042CrossRefGoogle Scholar
  6. Chan K-Y, Papalambros P, Skerlos S (2010) A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study. Stoch Environ Res Risk Assess 24:101–116Google Scholar
  7. Chen W-C (2006) The verification of vehicle emission models with the Gaussian dispersion model and CFD model. Master’s thesis, Department of Mechanical Engineering, National Chung Hsing University, TaiwanGoogle Scholar
  8. Cremer M, Ludwig J (1986) A fast simulation model for traffic flow on the basis of Boolean operations. Math Comput Simul 28(4):297–303CrossRefGoogle Scholar
  9. Davis S (1997) Transportation energy data book, edn 17. Technical report ORNL-6919. Center for Transportation Analysis, Energy Division, Oak Ridge National LaboratoryGoogle Scholar
  10. Dupuis A, Chopard B (2003) Cellular automata simulations of traffic: a model for the city of Geneva. Netw Spat Econ 3:9–21CrossRefGoogle Scholar
  11. Energy Information Administration (2009) Monthly energy review. Technical report DOE/EIA-0035. U.S. Department of Energy, November 2009Google Scholar
  12. Eriksson L, Garvill J, Nordlund A (2008) Acceptability of single and combined transport policy measures: the importance of environmental and policy specific beliefs. Transport Res A 42:1117–1128Google Scholar
  13. Gilbert M (1996) Introduction to environmental engineering and science, 2nd edn. Prentice Hall, New JerseyGoogle Scholar
  14. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Kluwer Academic Publishers, BostonGoogle Scholar
  15. Haldenbilen S, Ceylan H (2005) The development of a policy for road tax in turkey, using a genetic algorithm approach for demand estimation. Transport Res A 39:861–877Google Scholar
  16. Hanks J, Lomax T (1991) Roadway congestion in major urban areas, 1982 to 1988. In: 70th annual meeting of the Transportation Research Board, Washington, DC, USAGoogle Scholar
  17. Harrington W, McConnell V, Ando A (2000) Are vehicle emission inspection programs living up to expectations? Transport Res D 5(3):153–172CrossRefGoogle Scholar
  18. Hu T-Y, Chen L-W, Chen I-I, Huang Y-K, Chiang M-L (2005) A new simulation-assignment model DynaTAIWAN for mixed traffic flows. In: Proceedings of the 12th world congress on ITS, San Francisco, CA, USA, p 3678Google Scholar
  19. Kumar U, Jain V (2010) Arima forecasting of ambient air pollutants. Stoch Environ Res Risk Assess 24:751–760CrossRefGoogle Scholar
  20. Kuo Y-C (2003) Trip costs of urban transportation. Master’s thesis, Department of Civil Engineering, National Taiwan University, TaiwanGoogle Scholar
  21. Lau J, Hung W, Cheung C, Yuen D (2008) Contributions of roadside vehicle emissions to general air quality in Hong Kong. Transport Res D 13(1):19–26CrossRefGoogle Scholar
  22. Lin C, Chen Y, Lu S, Cho S, Lin K, Chiu Y, Tang X (2008) Relationships between characteristics of motorcycles and hydrocarbon emissions in Taiwan: a note. Transport Res D 13(5):351–354CrossRefGoogle Scholar
  23. Martin D (1976) The change of concentration standard deviation with distance. J Air Pollut Control Assoc 24(2):145–147Google Scholar
  24. McWilliams B, Sprevak D (1980) Estimation of the parameters of the distribution of wind speed and direction. Wind Eng 4(4):227–238Google Scholar
  25. McWilliams B, Newmann M, Sprevak D (1979) Probability distribution of wind velocity and direction. Wind Eng 3(4):269–273Google Scholar
  26. Meng J, Dai S, Dong L, Zhang J (2007) Cellular automaton model for mixed traffic flow with motorcycles. Physica A 380(1):470–480CrossRefGoogle Scholar
  27. Ministry of Economic Affairs Bureau of Energy (2010) Fuel cost information management and analysis system. April 2010.
  28. Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys I France 2:2221–2229CrossRefGoogle Scholar
  29. National Weather Bureau Southern Region Weather Center.
  30. Nijkamp P, Blaas E (1994) Impact assessment and evaluation in transportation planning. Springer, BerlinGoogle Scholar
  31. OECD (2002) Towards sustainable household consumption? Trends and policies in OECD countries. Organization for Economic Co-operation and Development (OECD), ParisGoogle Scholar
  32. Oettl D, Almbauer R, Sturm P, Pretterhofer G (2003) Dispersion modelling of air pollution caused by road traffic using a Markov chain-Monte Carlo model. Stoch Environ Res Risk Assess 17:58–75CrossRefGoogle Scholar
  33. Palmgren F, Berkowicz R, Ziv A, Hertel O (1999) Actual car fleet missions estimated from urban air quality measurements and street pollution models. Sci Total Environ 235:101–109CrossRefGoogle Scholar
  34. Patel I, Kumar A, Manne G (2003) Sensitivity analysis of cal3qhc roadway intersection model. Transport Res Rec 1842:109–117CrossRefGoogle Scholar
  35. Rehman T, Romero C (2006) Formulating generalized ‘goal games’ against nature: an illustration from decision-making under uncertainty in agriculture. Appl Math Comput 175:486–496CrossRefGoogle Scholar
  36. Rickert M, Nagel K, Schreckenberg M, Latour A (1996) Two lane traffic simulations using cellular automata. Physica A 231(4):534–550CrossRefGoogle Scholar
  37. Ruedi M (2004) A method to include in LCA road traffic noise and its health effects. Int J Life Cycle Assess 9(2):76–85CrossRefGoogle Scholar
  38. Sattler M (2006) Transportation and air quality/environment: a suggested course addition to the environmental engineering/science curriculum. J Environ Eng Sci 23(3):479–492CrossRefGoogle Scholar
  39. Schadschneider A, Chowdhury D, Brockfeld E, Klauck K, Santen L, Zittartz J (1999) A new cellular automata model for city traffic. In: Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) Traffic and granular flow 1999: social, traffic, and granular dynamics. Springer, HeidelbergGoogle Scholar
  40. Sheffi Y (1984) Urban transportation network: equilibrium analysis with mathematical programming methods. Prentice-Hall Inc, New JerseyGoogle Scholar
  41. Simon P, Nagel K (1998) Simplified cellular automaton model for city traffic. Phys Rev E 58(2):1286–1295CrossRefGoogle Scholar
  42. Solomon D (1964) Accidents on main rural highways related to speed, driver, and vehicle. Technical report, U.S. Department of Commerce/Bureau of Public RoadsGoogle Scholar
  43. Stead D, Banister D (2003) Transport policy scenario-building. Transport Plann Technol 26(6):513–536CrossRefGoogle Scholar
  44. Taiwan Environmental Protection Agency, Executive Yuan (2010) Taiwan emission data system, April 2010.
  45. Tamaki T, Kita E (2004) City traffic simulation using cellular automata with stochastic velocity model. Technical report 2004-MPS-50, IPSJ SIG technical reportGoogle Scholar
  46. Ülengin F, Onsel S, Topcu Y, Aktas E, Kabak O (2007) An integrated transportation decision support system for transportation policy decisions: the case of turkey. Transport Res A 41:80–97Google Scholar
  47. Vardoulakis S, Gonzalez-Flesca N, Fisher B (2002) Assessment of traffic-related air pollution in two street canyons in Paris: implications for exposure studies. Atmos Environ 36:1025–1039CrossRefGoogle Scholar
  48. Venkatram A, Horst T (2006) Approximating dispersion from a finite line source. Atmos Environ 40(13):2401–2408CrossRefGoogle Scholar
  49. Vignati E, Berkowicz R, Hertel O (1996) Comparison of air quality in streets of Copenhagen and Milan, in view of the climatological conditions. Sci Total Environ 189-190:467–473Google Scholar
  50. Wang I, Rote D (1975) A finite line source dispersion model for mobile source air pollution. J Air Pollut Control Assoc 25(7):2401–2408Google Scholar
  51. Wee V (2007) Treats from car traffic to the quality of urban life: problems, causes and solutions. In Gärling T, Steg L (eds) Environmental effects of urban traffic. Elsevier, Amsterdam, pp 11–32Google Scholar
  52. Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644CrossRefGoogle Scholar
  53. Wolfram S (2002) A new kind of science. Wolfram Media, ChampaignGoogle Scholar
  54. Wu J, Hamada M (2000) Experiments: planning, analysis, and parameter design optimization. Wiley, New YorkGoogle Scholar
  55. Yan Y (2001) Tainan urban area origin-destination transport survey. Technical report MOTC-IOT-I-C-89-001, Transportation Institute, Ministry of Transportation, TaiwanGoogle Scholar
  56. Zhao T, Sundararajan S, Tseng C (2004) Highway development decision-making under uncertainty: a real options approach. J Infrastruct Syst 10(1):23–32CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan

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