City intersection traffic signal control is an important method to improve the efficiency of road network and alleviate traffic congestion. This paper researches traffic signal fuzzy control method on a single intersection. A twostage traffic signal control method based on traffic urgency degree is proposed according to twostage fuzzy inference on single intersection. At the first stage, calculate traffic urgency degree for all red phases using traffic urgency evaluation module and select the red light phase with large traffic urgency as the next phase to switch. At the second stage, green delay of the current green phase is determined by fuzzy inference based on the amount of vehicles of current green phase and next green phase. The average vehicle delays are used to evaluate the performance of the fuzzy signal controller. Finally, comparisons have been made with pretimed controller and fuzzy logic controller without considering the urgency of red phase. Simulation results show the performance of our proposed method.
The monitoring and control of city traffic are becoming a major problem in many countries. With the ever increasing number of vehicles on the road, the traffic monitoring authority has to find new ways or measures for overcoming such a problem.
Traffic control in most signalized traffic intersections is done with either pretimed signal control or trafficactuated control. Pretimed control is based on preset signal timings and therefore nonresponsive to realtime fluctuations in the traffic demand. Trafficactuated control presents an improvement over pretimed control, but it has limited ability to respond to realtime traffic demand. For an intersection with actuated control, performance generally deteriorates with heavy traffic conditions and the proportion of stopped vehicles is generally high. Adaptive controllers are designed to address these deficiencies, as they have the ability to make realtime adjustments to signal settings in response to both observed and predicted realtime traffic demands.
Several approaches have been proposed for the design and implementation of adaptive signal control systems. The major research focus has been on application of fuzzy logic on intersection control. Fuzzy logic was initiated in 1968 by Zadeh [
There are many earlier applications of fuzzy logic to traffic signal control. Pappis and Mamdani have used fuzzy logic to control isolated twoway intersection, with no turning vehicle movements [
All the researches reviewed above have reported better performance of the fuzzy logic controllers compared to pretimed and actuated controllers. However, the reviewed research switched traffic phase in sequence without considering the urgency of red phase. The main objective of this research is to design a fuzzy logicbased signal controller considering the urgency of red phase for a fourway isolated intersection with through and leftturning vehicle movements. The fuzzy logicbased signal controller will not only decide whether to extend or terminate a current green phase but also decide which red phase will be set as green phase. The average vehicle delays will be used to evaluate the performance of the fuzzy signal controller. The comparisons will be made with pretimed controller and fuzzy logic controller without considering the urgency of red phase.
This paper researches an isolated fourway intersection with through and leftturning vehicle movements (Figure
The typical intersection with four phases.
The fourphase order of an intersection.
The distribution of vehicles arrival is a discrete random distribution, also known as the count distribution. It reflected a random vehicles number within a fixed period of time at a given spot. The common distributions of vehicle arrival are Poisson distribution and binomial distribution. In this paper, we assume that the arrival vehicles from all directions to an intersection are random and obey the Poisson distribution. The vehicle arrival rate is 0~0.4 per second.
The function of Poisson distribution is as follows [
Set
In this paper, the average delay of vehicles is the performance evaluation for traffic signal control of intersection. If the average vehicle delay is smaller, the traffic signal control effect is better. The calculation of vehicle delay model is shown below. The amount of queuing vehicles at time
The total vehicle delay in red light phase can be calculated as follows:
The amount of queuing vehicles at the
The total vehicle delay of green light phase can be calculated as follows:
The total vehicle delay in the
The average vehicle delay can be calculated as follows:
In this paper, the fuzzy logicbased signal controller will not only decide whether to extend or terminate a current green phase but also decide which red phase will be set as green phase. That is, the phase sequence is uncertain. But each phase must be guaranteed one and only one time in a signal cycle. The fuzzy controller based on traffic urgency degree is shown in Figure
The chart of fuzzy control principle based on the urgency degree of red traffic phase.
The core control algorithms for fuzzy logicbased traffic signal include the following steps.
Set a minimum green time for each phase according to the actual traffic condition.
Set the minimum green time for the current green phase.
Calculate traffic urgency degree for all red phases using traffic urgency evaluation module.
Select the red light phase with large traffic urgency as the next phase to switch.
Get the current green phase green light time delay through fuzzy reasoning based on the vehicles number of the current green phase and the next green phase.
Switch to the next green phase; skip to Step
Fuzzy logicbased signal controller based on traffic urgency includes the following two modules.
The traffic urgency degree evaluation module for red light phase: calculate traffic urgency degree for all of the red phase using the traffic urgency evaluation module. Select the red light phase with large traffic urgency as the next phase to switch.
Decision module: get the current green phase green light time delay through fuzzy reasoning according to the vehicles number of the current green phase and the next green phase.
There are two steps in the traffic urgency degree evaluation module for red light phase. Calculate traffic urgency degree for all of the red phase using the traffic urgency evaluation module. Select the red light phase with large traffic urgency as the next phase to switch.
There are two input variables and one output variable for traffic urgency degree evaluation module. The input variables include vehicles number of current red light phase
The domain of
The membership function of input variable
The membership function of input variable
The membership function of output variable
The fuzzy rules of red light phase urgency degree evaluation module are shown in Table
if
The fuzzy rules of evaluation module for red light phase urgency degree.

 

VS  S  M  L  VL  
VS  VS  VS  S  S  M 
S  VS  S  S  M  M 
M  M  S  M  M  B 
L  B  M  M  B  VB 
VL  B  M  B  VB  VB 
This fuzzy rule can be described by natural languages as follows: “If the queue number of current red light phase is very short and the light duration of current red light phase is very short, so the urgency degree of current red light phase is very small.”
In decision module, the current green phase green light time delay can be acquired according to the vehicles number of the current green phase and the next green phase. There are two input variables and one output variable for the decision module. The input variables include
The domain of
if
The fuzzy rules of decision module for the delay time of current green light phase.

 

VS  S  M  L  VL  
VS  VS  VS  VS  VS  VS 
S  S  S  S  VS  VS 
M  M  M  M  M  S 
L  L  L  L  M  M 
VL  VL  VL  L  L  L 
This fuzzy rule can be described by natural languages as follows: “If the queue number of current green light phase is very short and the queue number of next green light phase is short, so the delay time of current green light phase is very small.”
The average vehicle delays were used to evaluate the performance of the fuzzy signal controller. The comparisons have been made with pretimed controller and fuzzy logic controller without considering the urgency of red phase.
In order to make comparisons, identical conditions have to be set during the simulations. The minimum green time and the delay time were set as follows.
The minimum green time of eastwest straight phase and northsouth straight phase was set as 20 seconds.
The minimum green time of eastwest left turn phase was set as 15 seconds.
The maximum delay of green light for green light phase was set as 30 seconds.
If the vehicle arriving in the intersection is stochastic and the traffic flow is not large, the vehicle arrival obeys the Poisson distribution. So, the vehicle arrival rate in the intersection was set as 0~0.4 per second.
Assume that the vehicle leaving rate is one car leaving waiting team per second, when a phase from red to green light.
Set the simulation time as 1 hour.
In this paper, the vehicle arrival rate is divided into three types, including low traffic flow, middle traffic flow, and high traffic flow. The ranges of each stage vehicle rate are as follows: 0~0.15 car per second, 0.15~0.3 car per second, and 0.3~0.4 car per second. The average delay of pretimed control, fuzzy control, and fuzzy control with traffic urgency degree is shown in Table
Average vehicle delays of low traffic flow.
Number of simulation  Pretimed control  Fuzzy control  Fuzzy control with traffic urgency degree 

1  73.5387  45.6423  40.7576 
2  85.3338  42.7256  37.5516 
3  82.7172  42.1008  42.0751 
4  79.6795  44.7148  43.9731 
5  91.9941  41.3830  40.4205 
Average delay 



Average vehicle delays of middle traffic flow.
Number of simulation  Pretimed control  Fuzzy control  Fuzzy control with traffic urgency degree 

1  146.6501  82.4300  76.7970 
2  108.8296  63.1138  59.2166 
3  187.9133  82.8549  78.5025 
4  150.2061  78.3128  71.8656 
5  175.1695  86.8280  74.6925 
Average delay 



Average vehicle delays of high traffic flow.
Number of simulation  Pretimed control  Fuzzy control  Fuzzy control with traffic urgency degree 

1  304.7168  211.6806  208.7081 
2  314.6766  213.7743  209.5257 
3  308.4338  219.8659  206.8460 
4  310.3295  210.5916  209.1864 
5  311.6645  219.8842  216.4840 
Average delay 



From Tables
In the low traffic flow, the average vehicle delay of fuzzy control with traffic urgency degree is reduced by 45.6% compared to pretimed control and is deduced by 5.4% compared to fuzzy control.
In the middle traffic flow, the average vehicle delay of fuzzy control with traffic urgency degree is reduced by 48.8% compared to pretimed control and is deduced by 8.2% compared to fuzzy control.
In the high traffic flow, the average vehicle delay of fuzzy control with traffic urgency degree is reduced by 30.6% compared to pretimed control and is deduced by 2.36% compared to fuzzy control.
From the contrast of simulation results, the control effect of fuzzy control for traffic urgency degree is better than the pretimed control and common fuzzy control. The order of green light phase can be adjusted for some special traffic flow in fuzzy traffic control with traffic urgency degree.
This paper has analyzed the deficiency of existing fuzzy controller and put forward the strategies of improving fuzzy control based on traffic urgency degree. First, in order to determine the max urgency degree of red phase, the traffic urgency degrees of red phases were evaluated during the current green phase. The green light delay of current green phase was determined by fuzzy reasoning according to the number of vehicles of the current green phase and the next green phase. This algorithm has considered traffic factors and has more objectively reflected the intersection of each phase traffic demand urgent degree. Finally, the comparisons have been made with pretimed controller and fuzzy logic controller and fuzzy traffic control considering the urgency of red phase. From the contrast of the simulation results, the performance of fuzzy control for traffic urgency degree is better than the pretimed control and common fuzzy control method.
The author declares that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (Grant no. 61273180), the Natural Science Foundation of Shandong Province, China (Grant nos. ZR2009GQ013, ZR2011FQ005, and ZR2011FL010), the Project of Shandong Province Higher Educational Science and Technology Program, China (J14LN74), and the International Cooperation Program for Excellent Lecturers of 2012 by Shandong Provincial Education Department, China.