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

## Abstract

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.

### Keywords

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

- \({\mathcal{A}}\)
Set of all possible paths for a origin–destination pair in traffic equilibrium

- \({\mathcal{A}}^*\)
Set of shortest path in traffic equilibrium

*c*_{ij}Cost of the link from the node

*i*to the node*j*in traffic equilibrium*C*_{j}^{std}Standards of pollutant

*j**C*_{j}Concentration of pollutant

*j*of a receptor in Gaussian dispersion model*C*_{i}^{t}Cost per unit time in objective function

*C*_{ij}^{f}Fuel cost per unit distance at speed

*j*for vehicle type*i**d*Distance to the preceding vehicle

*d*_{o}Distance to the preceding vehicle on the other lane

*d*_{o,back}distance to the backward vehicle on the other lane

*d*_{c,back}distance to the backward car

*D*Distance between traffic signals (signal distance)

*f*_{k}Traffic flow of path k in traffic equilibrium

*H*Effective stack height in Gaussian dispersion model

*l*Distance of driver can look ahead on the same lane

*l*_{o}Distance of driver can look ahead on the other lane

*l*_{o,back}Distance of driver can look back on the other lane

- \({\mathcal{I}}_i\)
Set of all upstream nodes of all links arriving at node

*i*in traffic equilibrium- \({\mathcal{L}}\)
Set of all links in a network in traffic equilibrium

*L*Length of each site in CA model

*m*Number of vehicle types in objective function

*n*_{i}Number of vehicles of type

*i*in objective function*n*_{ij}Number of vehicles of type

*i*with speed*j*in objective function- \({\mathcal{N}}\)
Set of all nodes in a network in traffic equilibrium

- \({\mathcal{O}}_i\)
Set of all downstream nodes of all links leaving at node

*i*in traffic equilibrium- \({\mathbb{OD}}\)
An origin–destination pair in traffic equilibrium

*p*Random breaking probability

*p*_{change}Lane changing probability

*P*_{f}Failure probability levels

- Pr[·]
Probability of ·

*q*′Total traffic flow of an origin–destination pair in traffic equilibrium

*q*Emission rate in Gaussian dispersion model

*r*A random number generated from standard uniform distribution

*s*Distance to the closest preceding signal

- T
Time interval between red and green lights (signal period)

*T*Vehicle traffic density in objective function

*T*_{i}Traveling cost of vehicle type

*i*in objective function*u*Average wind speed in Gaussian dispersion model

*U*_{h}Actual wind speed in Gaussian dispersion model

*U*_{x}Wind speed perpendicular to the prevailing wind direction in Gaussian dispersion model

*U*_{y}Wind speed along the prevailing wind direction in Gaussian dispersion model

*v*Speed of vehicle

*v*_{max}Maximal speed of vehicle

*v*_{max,C}Maximal speed of a car

*v*_{max,M}Maximal speed of a motorcycle

*v*_{M}Speed of the preceding motorcycle in lane M

*v*_{CM}Speed of the preceding vehicle in lane CM

*V*_{i}^{ave}Average speed of vehicle type

*i**x*_{ij}Traffic flow of the link from the node

*i*to the node*j*in traffic equilibrium- ψ
Prevailing wind direction in Gaussian dispersion model

- θ
Actual wind direction

- δ
_{ij,k} Indicator of whether the link

*ij*is on the path*k*in traffic equilibrium- σ
_{y} Horizontal dispersion coefficients

- σ
_{z} Vertical dispersion coefficients

*EF*Emission factor in Gaussian dispersion model

- TC
Average traveling cost per unit distance

- FC
Average fuel cost per unit distance

### References

- Amundsen A, Klæboe R, Fyhri A (2008) Annoyance from vehicular air pollution: exposure–response relationships for norway. Atmos Environ 42(33):7679–7688CrossRefGoogle Scholar
- Bates D (1992) Health indices of the adverse effects of air pollution: the question of coherence. Environ Res 59:336–349CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- Davis S (1997) Transportation energy data book, edn 17. Technical report ORNL-6919. Center for Transportation Analysis, Energy Division, Oak Ridge National LaboratoryGoogle Scholar
- Dupuis A, Chopard B (2003) Cellular automata simulations of traffic: a model for the city of Geneva. Netw Spat Econ 3:9–21CrossRefGoogle Scholar
- Energy Information Administration (2009) Monthly energy review. Technical report DOE/EIA-0035. U.S. Department of Energy, November 2009Google Scholar
- 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
- Gilbert M (1996) Introduction to environmental engineering and science, 2nd edn. Prentice Hall, New JerseyGoogle Scholar
- Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Kluwer Academic Publishers, BostonGoogle Scholar
- 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
- 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
- Harrington W, McConnell V, Ando A (2000) Are vehicle emission inspection programs living up to expectations? Transport Res D 5(3):153–172CrossRefGoogle Scholar
- 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
- Kumar U, Jain V (2010) Arima forecasting of ambient air pollutants. Stoch Environ Res Risk Assess 24:751–760CrossRefGoogle Scholar
- Kuo Y-C (2003) Trip costs of urban transportation. Master’s thesis, Department of Civil Engineering, National Taiwan University, TaiwanGoogle Scholar
- 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
- 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
- Martin D (1976) The change of concentration standard deviation with distance. J Air Pollut Control Assoc 24(2):145–147Google Scholar
- McWilliams B, Sprevak D (1980) Estimation of the parameters of the distribution of wind speed and direction. Wind Eng 4(4):227–238Google Scholar
- McWilliams B, Newmann M, Sprevak D (1979) Probability distribution of wind velocity and direction. Wind Eng 3(4):269–273Google Scholar
- 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
- Ministry of Economic Affairs Bureau of Energy (2010) Fuel cost information management and analysis system. April 2010. http://www.moeaboe.gov.tw/oil102/
- Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys I France 2:2221–2229CrossRefGoogle Scholar
- National Weather Bureau Southern Region Weather Center. http://south.cwb.gov.tw/
- Nijkamp P, Blaas E (1994) Impact assessment and evaluation in transportation planning. Springer, BerlinGoogle Scholar
- OECD (2002) Towards sustainable household consumption? Trends and policies in OECD countries. Organization for Economic Co-operation and Development (OECD), ParisGoogle Scholar
- 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
- 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
- Patel I, Kumar A, Manne G (2003) Sensitivity analysis of cal3qhc roadway intersection model. Transport Res Rec 1842:109–117CrossRefGoogle Scholar
- 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
- Rickert M, Nagel K, Schreckenberg M, Latour A (1996) Two lane traffic simulations using cellular automata. Physica A 231(4):534–550CrossRefGoogle Scholar
- 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
- 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
- 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
- Sheffi Y (1984) Urban transportation network: equilibrium analysis with mathematical programming methods. Prentice-Hall Inc, New JerseyGoogle Scholar
- Simon P, Nagel K (1998) Simplified cellular automaton model for city traffic. Phys Rev E 58(2):1286–1295CrossRefGoogle Scholar
- 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
- Stead D, Banister D (2003) Transport policy scenario-building. Transport Plann Technol 26(6):513–536CrossRefGoogle Scholar
- Taiwan Environmental Protection Agency, Executive Yuan (2010) Taiwan emission data system, April 2010. http://www.ctci.com.tw/air-ei/Default.asp
- 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
- 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
- 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
- Venkatram A, Horst T (2006) Approximating dispersion from a finite line source. Atmos Environ 40(13):2401–2408CrossRefGoogle Scholar
- 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
- 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
- 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
- Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644CrossRefGoogle Scholar
- Wolfram S (2002) A new kind of science. Wolfram Media, ChampaignGoogle Scholar
- Wu J, Hamada M (2000) Experiments: planning, analysis, and parameter design optimization. Wiley, New YorkGoogle Scholar
- 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
- 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