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【Abstract】Toll plaza is the area on the highway to collect the barrier toll. Our goal is to improve the throughput and reduce the costs of the plaza. To achieve this， we divide the process into two parts： determining better shape and size of plaza and analyzing the performance of the solution in different situation.
Multi-objective optimization model is established to work out the shape and size of the toll plaza. First we determine two shapes of plaza， including the trapezoid shape and the fan shape. Next， we choose the Common type， Multi-window type and Satellite type to showcase the location of toll booths， which can as well descript the size of toll plaza. In combination with the cellular automata， we find that in the same traffic flow， the trapezoid shape costs less and enjoys more throughput than the fan shape， and the satellite type takes less time than others. What's more， we take its risk assessment and merging pattern into consideration， both of which are based on the Queueing theory. Therefore， we can provide the best solution which is composed of the trapezoid shape and satellite type.
What’s more， the solution performance under the circumstances where there are regular and heavy traffic， autonomous vehicles， and even the various proportions of EFC， HC， EC tollbooths will be thoroughly analyzed. We harness the Cellular Automata Model and operate it in so as to solve the problem， and hence to reach the most appropriate conclusion.
According to the result of the Cellular Automata Model， the performance of different situation can be analyzed. First we can obtain how throughput of our solution alters in light and heavy traffic respectively and the truth is that the solution in light traffic is less time-consuming. When counting in the autonomous vehicles， the proportion of ETC increases and the randomization probability slumped and raised the throughput. If the proportion of ETC， HC and EC changes， the mean cost time changes correspondingly. There are three situations： HC： EC： ETC=2：2：4， HC： EC： ETC=4：2：2， HC： EC： ETC=2：4：2， the respectively cost time is：79s，102s，87s， so it is clear that more ETCs will increase the traffic volume. In sensitivity analysis， we analyze the impact of traffic flow change in light and heavy traffic and trapezoid shape change. Finally， we conclude that the growth of the traffic flow in heavy traffic has the largest effect on traffic volume， which also proves that choosing trapezoid shape and satellite size is better than current one. 【Key words】Toll Plaza， Multi-objective Optimization Model， Cellular Automata， Queueing Theory
1 Background
A toll plaza is the area of the highway needed to facilitate the barrier toll， consisting of the fan-out area before the barrier toll， the toll barrier itself， and the fan-in area after the toll barrier. Conventional common highway toll stations are generally designed to be substantially perpendicular to the road， in-line subscription channel for multiple vehicles.？Each charge a fee only channel window.
To increase the number of toll lanes and toll window， traditional toll design methodology， covering only increase the width of the toll stations. Another method is to use the window to increase fees or multi-store duplex tollgate layout.[1]
Through simulation experiments， we have a general understanding of multi-lane merging.[2]
2 Model Overview
2.1 Basic Model
* The shape and size of the plaza.
A toll plaza is a physical structure that may be found on toll roads， exit ramps， or at the ends of toll bridges. It allows motorists to pay required toll charges without having to leave their vehicles.[14]According to some information， we design two shapes and three types to descript the toll plaza.
Shapes：
* Fan shape
* Trapezoid shape
Types：
* Common type. Which means that the toll island just has one tollbooth.
* Multi-window type. Which means the toll island has two tollbooths.
* Satellite type. Which means a multi-layer compact highway toll station containing 2 layers of toll areas in a single travel direction.
* The traffic capacity
After determining the shape and size of the plaza， we can determine the traffic capacity of each combination based on the Queuing theory， the formula to calculate the traffic volume in one tollbooth.
2.2 Costs
The costs are composed of land costs， construction costs and staff costs.
means land costs，means construction costs， and means staff costs
2.3 Merging Pattern
As we have determined the shape of the toll station. We can know， and. For each combination， and is equal. And the Fan and the Trapezoid shapes have no influence in the merging pattern. We just analyze the impact of types.
2.4 Accident Prevention
After determining the shape and size of the toll plaza， we can analyze the prevention of accident. For the prevention of accidents must analyze the factors that cause traffic accidents first， in terms of the toll station vehicles， there are two main types of traffic conflicts： rear-end conflict and the conflict when changing the road[13]. And the traffic operation status of the toll plaza is more complicated than that of the basic section. Therefore， the following traffic flow parameters are selected as the independent variables to measure the traffic conflict 3 Model Analysis and Sensitivity Analysis
We perform the sensitivity analysis by Cellular Automata. First， we consider the impact of increased traffic on the model. Increase the traffic flow by 10% in the light and heavy traffic in the model， get mean cost time. Compare the mean cost time， we can come to the conclusion.
Second， we consider the effect of trapezoid length. We change the trapezoid length and analyze the mean cost time by Cellular Automata in ， then effect of different trapezium length on the traffic capacity is also obtained.
Running Cellular Automata in， we find that traffic flow in the light and heavy traffic increases， the model mean cost time increases. When the other factors are not changed， trapezoid length reduces， mean cost time increases. The effect diagram and data is in appendix.
By comparing the increase rate of in time with the change rate of traffic flow and trapezium length， the ratio of them is the elasticity of point.
4 Future Work
* The three types and two shapes are discussed independently and not considered in combination. If combined， they may complement each other， thus the solution will achieve more remarkable results.
* In the actual traffic conditions， there exists the classification of vehicles， including large and small passenger cars， small， medium and large trucks， and other types of special vehicles. Although the article use conversion factor to unified discuss， in reality， their impact on the model is certainly not similar. Therefore， a more realistic model need to introduce different types of vehicles.
* Because Multi-window type and Satellite type are very rare in the real world and we can’t get enough data to validate our model， so it can only be verified by software. If we can combine the real data and then modify our model， the future may usher in a different era of toll stations.
Multi-objective optimization model is established to work out the shape and size of the toll plaza. First we determine two shapes of plaza， including the trapezoid shape and the fan shape. Next， we choose the Common type， Multi-window type and Satellite type to showcase the location of toll booths， which can as well descript the size of toll plaza. In combination with the cellular automata， we find that in the same traffic flow， the trapezoid shape costs less and enjoys more throughput than the fan shape， and the satellite type takes less time than others. What's more， we take its risk assessment and merging pattern into consideration， both of which are based on the Queueing theory. Therefore， we can provide the best solution which is composed of the trapezoid shape and satellite type.
What’s more， the solution performance under the circumstances where there are regular and heavy traffic， autonomous vehicles， and even the various proportions of EFC， HC， EC tollbooths will be thoroughly analyzed. We harness the Cellular Automata Model and operate it in so as to solve the problem， and hence to reach the most appropriate conclusion.
According to the result of the Cellular Automata Model， the performance of different situation can be analyzed. First we can obtain how throughput of our solution alters in light and heavy traffic respectively and the truth is that the solution in light traffic is less time-consuming. When counting in the autonomous vehicles， the proportion of ETC increases and the randomization probability slumped and raised the throughput. If the proportion of ETC， HC and EC changes， the mean cost time changes correspondingly. There are three situations： HC： EC： ETC=2：2：4， HC： EC： ETC=4：2：2， HC： EC： ETC=2：4：2， the respectively cost time is：79s，102s，87s， so it is clear that more ETCs will increase the traffic volume. In sensitivity analysis， we analyze the impact of traffic flow change in light and heavy traffic and trapezoid shape change. Finally， we conclude that the growth of the traffic flow in heavy traffic has the largest effect on traffic volume， which also proves that choosing trapezoid shape and satellite size is better than current one. 【Key words】Toll Plaza， Multi-objective Optimization Model， Cellular Automata， Queueing Theory
1 Background
A toll plaza is the area of the highway needed to facilitate the barrier toll， consisting of the fan-out area before the barrier toll， the toll barrier itself， and the fan-in area after the toll barrier. Conventional common highway toll stations are generally designed to be substantially perpendicular to the road， in-line subscription channel for multiple vehicles.？Each charge a fee only channel window.
To increase the number of toll lanes and toll window， traditional toll design methodology， covering only increase the width of the toll stations. Another method is to use the window to increase fees or multi-store duplex tollgate layout.[1]
Through simulation experiments， we have a general understanding of multi-lane merging.[2]
2 Model Overview
2.1 Basic Model
* The shape and size of the plaza.
A toll plaza is a physical structure that may be found on toll roads， exit ramps， or at the ends of toll bridges. It allows motorists to pay required toll charges without having to leave their vehicles.[14]According to some information， we design two shapes and three types to descript the toll plaza.
Shapes：
* Fan shape
* Trapezoid shape
Types：
* Common type. Which means that the toll island just has one tollbooth.
* Multi-window type. Which means the toll island has two tollbooths.
* Satellite type. Which means a multi-layer compact highway toll station containing 2 layers of toll areas in a single travel direction.
* The traffic capacity
After determining the shape and size of the plaza， we can determine the traffic capacity of each combination based on the Queuing theory， the formula to calculate the traffic volume in one tollbooth.
2.2 Costs
The costs are composed of land costs， construction costs and staff costs.
means land costs，means construction costs， and means staff costs
2.3 Merging Pattern
As we have determined the shape of the toll station. We can know， and. For each combination， and is equal. And the Fan and the Trapezoid shapes have no influence in the merging pattern. We just analyze the impact of types.
2.4 Accident Prevention
After determining the shape and size of the toll plaza， we can analyze the prevention of accident. For the prevention of accidents must analyze the factors that cause traffic accidents first， in terms of the toll station vehicles， there are two main types of traffic conflicts： rear-end conflict and the conflict when changing the road[13]. And the traffic operation status of the toll plaza is more complicated than that of the basic section. Therefore， the following traffic flow parameters are selected as the independent variables to measure the traffic conflict 3 Model Analysis and Sensitivity Analysis
We perform the sensitivity analysis by Cellular Automata. First， we consider the impact of increased traffic on the model. Increase the traffic flow by 10% in the light and heavy traffic in the model， get mean cost time. Compare the mean cost time， we can come to the conclusion.
Second， we consider the effect of trapezoid length. We change the trapezoid length and analyze the mean cost time by Cellular Automata in ， then effect of different trapezium length on the traffic capacity is also obtained.
Running Cellular Automata in， we find that traffic flow in the light and heavy traffic increases， the model mean cost time increases. When the other factors are not changed， trapezoid length reduces， mean cost time increases. The effect diagram and data is in appendix.
By comparing the increase rate of in time with the change rate of traffic flow and trapezium length， the ratio of them is the elasticity of point.
4 Future Work
* The three types and two shapes are discussed independently and not considered in combination. If combined， they may complement each other， thus the solution will achieve more remarkable results.
* In the actual traffic conditions， there exists the classification of vehicles， including large and small passenger cars， small， medium and large trucks， and other types of special vehicles. Although the article use conversion factor to unified discuss， in reality， their impact on the model is certainly not similar. Therefore， a more realistic model need to introduce different types of vehicles.
* Because Multi-window type and Satellite type are very rare in the real world and we can’t get enough data to validate our model， so it can only be verified by software. If we can combine the real data and then modify our model， the future may usher in a different era of toll stations.