Mathematical Problems in Engineering

Volume 2015, Article ID 407512, 10 pages

http://dx.doi.org/10.1155/2015/407512

## Intersection Group Dynamic Subdivision and Coordination at Intraregional Boundaries in Sudden Disaster

^{1}State Key Laboratory of Automobile Dynamic Simulation, Jilin University, Changchun 130022, China^{2}College of Transportation, Jilin University, Changchun 130022, China

Received 6 June 2014; Accepted 17 August 2014

Academic Editor: Huimin Niu

Copyright © 2015 Ciyun Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper aims at the traffic flow agglomeration effect characteristics and rapid evacuation requirement in sudden disaster; operation time of intraregional boundaries traffic signal coordination was presented firstly. Then intraregional boundaries intersection group dynamic subdivision and consolidation method based on relative similarity degree and similarity coefficient of adjacent intersections was put forward. As to make the traffic control strategy adapt to traffic condition of different intraregional boundaries intersection groups, this paper proposes an intraregional boundaries traffic signal coordination and optimization technology based on organic computing theory. Finally, this paper uses Delphi 7.0, MapX, and Oracle developing a software package, combined with Paramics V6 Simulator to validate the methods of this paper. The result shows that it can obviously improve disaster affected regional traffic signal control efficiency which reduces average traffic delay by 30–35%, decreases vehicle queue by more than 20% and reduces evacuation time more than 13.06%.

#### 1. Introduction

In urban traffic signal control system, any kind of traffic signal control strategy is established in given road geometry conditions and traffic flow characteristics. Only when the traffic network road geometry and its traffic flow characteristics meet or are close to application conditions of traffic signal control strategy, traffic signal control system operation efficiency and effect can be in the best status. Therefore, in accordance with different traffic flow characteristics and performing the suitable traffic signal control strategy, experienced traffic engineer uses the method of dynamical subdivision intersection form intersection groups or consolidate intersection to intersection groups based on traffic flow spatial-temporal distribution characteristics and traffic flow platoon dispersion characteristics.

For the past few years, as the urban traffic congestion is increasing seriously, the requirement of enhancing traffic signal control efficiency and effect is becoming the first and foremost. The method to dynamically subdivide and consolidate intersection groups plays an important role in improving traffic signal control efficiency and adapting to the changing traffic flow in urban network. Moreover, it has become a hot topic which is widely researched in the last years around the world. Lin and Tsao [1] studied the intersection group dynamical subdivision and consolidation in regional traffic signal control system based on searching algorithm in order to conform to the different traffic demands of time of day. Moore and Jovanis [2] using traffic signal cycle, traffic flow, and length of adjacent intersection as the division and consolidation principle, with the data provided by traffic flow guidance system, proposed a dynamical subdivision method for regional traffic signal control system. Wong [3] presented an approach using the parameters of cycle ratio, offset ratio, and split ratio to decide whether to divide from intersection group or consolidate to intersection group. Pranevicius and Kraujalis [4], using fuzzy control theory, put forward an intersection group fuzzy and dynamical subdivision and consolidation method based on coordinated coefficients. Based on the traffic network hypergraph division model, Chandler [5] raised a high-speed intersection group subdivision and consolidation method for traffic control network to solve the large-scale traffic signal control system. Wang and Bie [6] put forward an intersection group subdivision model for coordination of traffic signal control system using correlation degree of adjacent intersections. Hsu and Peeta [7], according to the correlation of adjacent intersections on the basis of spectral analysis, proposed three adaptive subdivision and consolidation methods for regional traffic signal control system. Lee et al. [8], using the genetic algorithm and dimension reduction processing to optimize the traffic signal control strategy for intersection group in regional traffic signal control system, presented a set of subdivision and consolidation methods for intersection group to traffic signal control and coordination.

However, the methods of intersection group subdivision and consolidation are mainly focused on the interior of regional traffic signal control system. And according to the traffic flow status in adjacent intersections, these papers deciding whether to subdivide from the intersection group or consolidate to intersection group are under the normal traffic network and traffic flow conditions. Furthermore, current traffic signal control systems with the regional or intersection group as its units operate independently; they are unable to subdivide or consolidate between regional boundaries intersections to form an individual intersection group and lack signal coordination between regional boundaries intersections. Therefore, traffic blocking often occurs in the road sections of intraregional boundaries, which can quickly lead to traffic congestion at interregional boundaries, even more to the all traffic signal control network. In sudden disaster especially, a large number of people and logistics in disaster affected area need imminent evacuation to nearby emergency evacuation point in the adjacent region. But with the current regional traffic signal control mode, the adjacent regional traffic signal control system unable to foresee the large number of traffic flows is coming at the entrance road section in the intraregional boundaries and is unable to adjust the traffic signal control strategy real-time to let the traffic flow pass through the boundaries intersection quickly. So traffic congestion is likely to occur in the intraregional boundaries, which may directly affect the emergency rescue work.

As to solve the problem mentioned above, this paper aims at the traffic flow agglomeration effect characteristics and rapid evacuation requirement in sudden disaster and attempts to use intraregional boundaries intersection group subdivision and consolidation, intraregional boundaries intersection group traffic signal control strategy optimization, and intraregional boundaries intersection groups coordination to divert and rapidly dissipate the traffic flow in intraregional boundaries, preventing traffic congestion occurring at the intraregional boundaries, in order to let emergency rescue work be implemented faster and smoother in sudden disaster.

#### 2. Deciding the Operation Time of Coordination

The objective of deciding the operation time of traffic signal coordination between intraregional boundaries intersection groups is to make the intraregional boundaries intersection group running with suitable traffic signal control strategy under different traffic flow conditions so that it can improve the traffic capacity of intraregional boundaries intersection group. In this paper, we use the interconnected index of adjacent intersections in intraregional boundaries as the decision and evaluation index of operation time of traffic signal coordination for intraregional boundaries [9]:where is interconnected index; is average travel time between adjacent intersections in intraregional boundaries; is the lane numbers that traffic flow can enter into downstream intersection; is the traffic volume of straight lanes in upstream intersection; is the total traffic volume from upstream intersection. Consider where is length of adjacent intersection in intraregional boundaries; is average travel speed; and is the sum of left turn ratio and right turn ratio.

Put (2) into (1):When or , it is the time to subdivide intersection from intersection group or consolidate intersection to intersection group and formulate different traffic signal control intersection group in intraregional boundaries, where is the threshold limit value of subdivision and is the threshold limit value of consolidation.

#### 3. Intersection Group Dynamical Subdivision or Consolidation

##### 3.1. Impact Factor Analysis

Traffic signal control system is made up of signalized intersections in traffic network. Each signalized intersection has its status variables and control variables. Status variables describe intersection’s geometric design and traffic flow at each inbound link. Control variables describe traffic control parameters, consisting of cycle, offset, and split and the capacity at specified performance levels. These variables are interrelated and interacting. At the same time, traffic flow in adjacent intersections has the potential incidence relation of similarity and coupling. With the passage of time and the transition of space, relationships between adjacent intersections are changing continuously. In sudden disaster, besides the changing relationships between adjacent intersections, the layout and the function of the traffic network are also changing by road damage, road closure, separation by traffic management, and so on. Therefore, in sudden disaster, it needs more functions to make the traffic signal control strategy to suit for the changing traffic flow and traffic network and let each intersection group in regional traffic signal control system have its own control objectives based on its traffic flow characteristics. The intersection group subdivision and consolidation are considered to be the best way to achieve the goal as mentioned above. It can improve the practicability, reliability, and instantaneity of traffic signal control models and algorithms in regional traffic signal control system.

According to the traffic flow characteristics and traffic network geometric topology information, the data attributes of signalized intersection can be described in different forms. From the perspective of time factors, status variables and control variables can be classified as dynamic variables and static variables. From the perspective of space factors, status variables and control variables can be classified as link variables and node variables. In this paper, stands for the state of the signalized intersection. Considerwhere is the state of th intersection in th intersection group. is the node matrix of th intersection in th intersection group. is the link matrix of th intersection in th subzone intersection group. Node and link matrices both include static and dynamic vectors that describe node or link’s status variable and control variable. , , , mean intersection geometric type, critical intersection or not, and signal phase number, respectively. , Ct, Sat, Ca mean signal cycle, saturation, and capacity of the intersection, respectively. , Lk, Id, Lg, Ld mean the vector of each inbound link has a connected intersection or not, the connected intersection id, the length of the link and lane numbers in the link, respectively. , , , , mean the vector of each inbound link’s volume, average speed, average occupancy, and split of signal, respectively.

##### 3.2. Standardization State Matrix

Both signalized intersection’s status variables and control variables make up the intraregional boundaries traffic signal control network’s status. The status of intraregional boundaries traffic signal control network can be described as the status matrix [10]:

In order to eliminate difference among status variables and control variables, it is needed to transform the matrix to standardization matrix. In intraregional boundaries traffic signal control network status matrix , towards the status variables, letwhere status variables and .

For control variables, letwhere control variables and .

So the standardization matrix is

Traffic network layout and its functional design, traffic flow distribution, and characteristics decide the intersection in the network that will undertake different objectives and make different influence on traffic flow operating. The significant degree of intersection in the network not only is related to the geographic position and geometric topology in the network, but also has a close relationship with the dynamic traffic flow that passes through or comes to the intersection. However, the role of influence factors that impact intersection is different. And the value of influence is difficult to define as the diversity, complexity of traffic environment, and limited awareness of human acknowledge. So, in this paper, we use the theory of multiple attribute decision making (MADM) to measure the intersection status matrix of intraregional boundaries traffic signal control network [11]. Considerwhere is the weight of variables. is the standardization matrix of intraregional boundaries traffic signal control network.

##### 3.3. Hamming Osculating

Define the ideal state as a signalized intersection in the best status that can be subdivided from an intersection group in intraregional boundaries and improve the traffic signal control efficiency. And the negative state is a signalized intersection in the best status that can be consolidated to an intersection group in intraregional boundaries or else can reduce traffic signal control performance. The ideal state is expressed as :

The negative state is expressed as :

Then, the distance of current status of signalized intersection to the ideal state that should be subdivided from an intersection group in intraregional boundaries can be expressed as

The distance of current status of signalized intersection to the negative state that would be consolidated to an intersection group in intraregional boundaries can be expressed as

Signalized intersection is suitable to be subdivided from an intersection group or to be consolidated into an intersection group in intraregional boundaries which is decided by hamming osculating. Considerwhere . As is close to 0, approaches 0; traffic signal control performance reduces when the signalized intersection consolidates to an intersection group or subdivides from an intersection group in intraregional boundaries. And as approaches 1 and approaches 0, traffic signal control system will get better performance when consolidating a signalized intersection to an intersection group or subdividing it from an intersection group in intraregional boundaries. And the hamming osculating of the whole intraregional boundaries traffic network is

##### 3.4. Coefficient of Adjacent Intersection

In algebra, a cosine is usually used between two angles to represent the similarity between vectors; in this paper, we show the similarity of two signalized intersections by calculating the cosine between two state vectors of adjacent signalized intersections:

So the similarity matrix of intraregional boundaries signalized intersections is

##### 3.5. Dynamic Cluster Analysis

Dynamic cluster analysis is used to analyze hamming osculating and coefficient of adjacent intersections in intraregional boundaries. The processing is described as below.

*Step 1. *Make cluster and set initial cluster center in a rough set for hamming osculating and coefficient of adjacent intersections, respectively.(1)Calculate the distance between intersections to its adjacent intersection.(2)Order the distance from small to large.(3)The similar distance elements are classified as a class, initializing the m clusters, and calculate the average value of all objects corresponding coordinates in each cluster, as the initial cluster centers.

*Step 2. *Based on the cluster radius and interval, sort out the hamming osculating and coefficient , respectively.

*Step 3. *When the signalized intersection’s hamming osculating and coefficient are classified into the same cluster, consolidate the signalized intersection to an intersection group and classify it to the intersection group cluster.

*Step 4. *When all the signalized intersections have been classified, calculate the distance between the clusters and output and sort the distance of adjacent intersections.

(1) Calculate link segment saturation aswhere is the saturation of the link segment. is the flow rate of the link at time . is the saturation in the link segment .

(2) Assume that there are link segments in the intersection group, boundaries intersections contain link segments (); the threshold saturation of the intersection group that decides to start cluster analysis for subdividing and consolidating is

The saturation of remaining link segments is

(3) The saturation of intersection group can be calculated by weighting coefficient that considers the importance of the link:

*Step 5. *Confirm the threshold value based on cluster distance.

*Step 6. *Merge the cluster when the cluster distance is less than the threshold value and then export the cluster result of the intraregional boundaries.

*Step 7. *Determine whether clustering results are rational or not and finish the cluster analysis and output the cluster results if the answer is yes; then wait for the next cycle. If it returns NO, go back to Step 2.

#### 4. Traffic Signal Optimization and Coordination for Intraregional Boundaries

Organic computing is a form of distributed and biologically inspired computing with organic properties. It develops from the idea that central nervous system of human neural network maintains and automatically adjust the balance of body system based on the exogenous and endogenous environment information perceived by human organics. Organic computing has emerged recently as a challenging vision for future information processing system. It has outstanding performance in the distributed, dynamic and heterogeneous network environment. Organic computing system is a technical system which is equipped with sensors and actuators as to be aware of the environment accurately, communicate freely, and organize the response plan automatic like organisms. Organic computing system adapts dynamically to exogenous and endogenous changes, solves the conflict of different systems, and responds to the unpredictable emergency problems by its functional characteristics of self-properties, such as self-monitoring, self-organization, and self-optimization [12]. This paper uses organic computing system techniques to automatically detect and monitor the traffic flow in disaster affected region and optimize the traffic signal to resolve the conflict problems in intraregional boundaries when emergency evacuation occurs in sudden disaster. Organic computing for intraregional boundaries traffic signal control system is composed by four modules. There are traffic flow self-monitoring, traffic signal self-optimization, traffic signal coordination knowledge self-organization, and traffic signal control plan self-classification.

##### 4.1. Traffic Flow Self-Monitoring

Traffic flow self-monitoring module is the sensors and actuators of the organic computing system, which was used to percept the environment condition and implement the control commands. In intraregional traffic signal control system, traffic flow self-monitoring uses traffic detectors (including loop coil vehicle detector, microwave vehicle detector, and video detector) which distribute in traffic network to detect and monitor the traffic flow condition in intraregional boundaries and provide reliable, real-time, and comprehensive traffic information for traffic signal control system.

##### 4.2. Traffic Signal Self-Optimization

###### 4.2.1. Traffic Signal Cycle Online Adjustment

Define the as the expected traffic signal cycle of signalized intersection in intraregional boundaries. is the optimal traffic signal cycle calculated by Webster cycle formula based on real-time traffic flow data. or , . Define the as the coordination traffic signal cycle of signalized intersection in intraregional boundaries. It is the signal cycle that local traffic signal controllers agree to coordinate and optimize. The common signal cycle of intersection group in intraregional boundaries is calculated as in Algorithm 1 [13].