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

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## 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

## Notes

### Acknowledgments

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.

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