Abstract: Based on the traffic flow pattern in single intersection, this paper advances a design method for intelligent traffic lights in the state of stochastic dynamic change of traffic flow by employing the Fuzzy Control Theory. The application of fuzzy control technology to achieve the traffic lights control system not only breaks the traditional mechanical models but also manages to simulate intelligence control system in which the traffic is directed by the police, making possible signal conversion for different situations and optimum delay time of green light. It is proved that the fuzzy control system can effectively reduce the delay time length of waiting vehicles. In consideration of the randomness and robustness of traffic flow, this paper employs the Monte Carlo method in combination with MATLAB to simulate, which proved to be more effective than the traditional control method. It significantly increases the utilization rate of traffic, thereby generating considerable economic benefits. Copyright © 2013 IFSA

Jing Lin

Wu Bizhi

Wu Lurong

Zeng Shengda

Based on the traffic flow pattern in single intersection, this paper advances a design method for intelligent traffic lights in the state of stochastic dynamic change of traffic flow by employing the Fuzzy Control Theory. The application of fuzzy control technology to achieve the traffic lights control system not only breaks the traditional mechanical models but also manages to simulate intelligence control system in which the traffic is directed by the police, making possible signal conversion for different situations and optimum delay time of green light. It is proved that the fuzzy control system can effectively reduce the delay time length of waiting vehicles. In consideration of the randomness and robustness of traffic flow, this paper employs the Monte Carlo method in combination with MATLAB to simulate, which proved to be more effective than the traditional control method. It significantly increases the utilization rate of traffic, thereby generating considerable economic benefits

ZENG Shengda

WU Lurong

JING Lin

WU Bizhi

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Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  211  Sensors & Transducers © 2013 by IFSAhttp://www.sensorsportal.com       Study on Monte Carlo Simulation of Intelligent Traffic Lights Based on Fuzzy Control Theory  ZENG Shengda, * WU Lurong, JING Lin, WU Bizhi Computer and Information College, Fujian Agriculture and Forestry University,  Fuzhou 350002, China * Tel.: +86 15005098168 E-mail: wulurong1@sina.com   Received: 5 June 2013   /Accepted: 25 August 2013   /Published: 30 September 2013   Abstract: Based on the traffic flow pattern in single intersection, this paper advances a design method for intelligent traffic lights in the state of stochastic dynamic change of traffic flow by employing the Fuzzy Control Theory. The application of fuzzy control technology to achieve the traffic lights control system not only breaks the traditional mechanical models but also manages to simulate intelligence control system in which the traffic is directed by the police, making possible signal conversion for different situations and optimum delay time of green light. It is proved that the fuzzy control system can effectively reduce the delay time length of waiting vehicles. In consideration of the randomness and robustness of traffic flow, this paper employs the Monte Carlo method in combination with MATLAB to simulate, which proved to be more effective than the traditional control method. It significantly increases the utilization rate of traffic, thereby generating considerable economic benefits. Copyright © 2013 IFSA.  Keywords: Single intersection, Fuzzy control, Intelligent traffic lights, Monte Carlo, Simulation.    1. Introduction  With the rapid development of automobile industry, more and more automobile enterprises began to set foot in the field of automobile intellectualization and apply cutting-edge Information Technology to the automobile and its control. According to relevant statistics, over 90 % of innovation in automotive industry is related to automobile intelligent system. Intellectualization is the trend of automobile’s future development and is considered as a revolution in the process of automotive technology development. It is an important and effective means to gain a niche in the future automobile market. Although the automobile intelligent technology has reached a relatively mature stage, the road management cannot be reformed once and for all. The congestion problem has become increasingly prominent and the intersection is the most congested section, where traffic jam is quite often seen. Phenomenon of 2~3 hours congestion is quite common in metropolis like Beijing, Shanghai and Shenzhen. Reform of traffic rules since this year particularly poses a grave challenge to the traffic control. As a result, ideas of using high-tech systems such as intelligent, fuzzy, automation to solve the problems of road traffic are emerging. Referring to the realistic data of China’s traffic situation, considering time difference of traffic flow in different regions with periodic regularity, taking into account of length of the waiting vehicles in stop way of intersection, based on the theory of intelligent fuzzy control and with the help of computer simulation, this paper sets up an automated multi-Article number P_1349 Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  212 phase intelligent traffic control system and establishes a more effective control system compared with the induction time control. The control system is designed to make the vehicle at the intersections wait for the shortest time, thereby reducing their passing time. The control system has the following characteristics: 1) Adopting statistical view, combining the past traffic volume and statistical analysis of computer data to predict real-time traffic; 2) Adopting fuzzy control method, taking prediction of real-time traffic flow as input condition to control the traffic lights; 3) The control methods used have feedback self-directed learning function, and have strong sensitivity to disturbance of special time quantum.   2. Analysis of Intelligent Traffic Signal Control  Time delay distribution of traffic light in single intersection is determined by traffic flow in different intersections. Fig. 1 is the single intersection traffic flow chart.  All of the 4 directions in the three-lane road single intersection have three kinds of traffic flow direction, namely, left, right, straight on [1]. In the control of time delay distribution of traffic light in single intersection, this paper takes into account the effect of queue length of detained traffic flow at intersection during red light and the passing number of vehicles during green light on time delay distribution and draws up corresponding fuzzy control rules, constructs the traffic light intersection fuzzy controller, and achieved the delay timing control of intersections.     Fig. 1. Single intersection traffic flow chart.   According to the analysis of the above traffic flow structure chart of single intersection, considering the effect of queue length of detained traffic flow during red light and the passing number of vehicles during green light on time delay distribution, in realistic control, traffic flow in rush hours and in slack periods are in random change.  Fig. 2 is flow chart of overall control feedback of traffic light, which enables the fuzzy controller of traffic light to accomplish intelligent artificial feedback timing regulation at different stages, so as to shorten the time of traffic congestion.     Fig. 2. Flow chart of overall control feedback of traffic light.   Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  2133. Model Design of Intelligent Traffic Light Control  3.1. Analysis of Traffic Flow Phase  and the Length of Queue  Since the signal control systems of traffic light in the past generally didn’t consider the phase change, we take a periodic change control of “four phase” into consideration in order to cater to the random timing distribution of intelligent automation in different states. Fig. 3 is the traffic patterns of  4 phases. This paper adopts the improved control method of 4 phases in random sequence, based on the statistical analysis of sensor traffic flow, uses phase fuzzy optimization control to calculate and analyze  to determine the execution phase of the next  moment [3].     Fig. 3. Phase traffic patterns.   In Fig. 1, )12,1(,i iL  represents the current length of fleet in different lanes. The maximal length that passes the intersection in current moment is called length of passage and the maximal length of two fleets that pass in the phase next moment is called waiting degree. Therefore, the length of passage and value of waiting length of 4 phases can be obtained according to the traffic patterns of 4 phases [2].   3.2. The Fuzzy Delay Control Rule of Traffic Light and its Quantification  Use the theoretical achievements of fuzzy controller to turn the control strategy described by nature language into fuzzy control rules in order to realize fuzzy control. In this regard, the variable that is used for fuzzy control has the following 3 parts: fuzzification, fuzzy control rules and defuzzification. Use the theoretical achievements of fuzzy controller to turn the control strategy described by nature language into fuzzy control rules in order to realize fuzzy control. In this regard, the variable that is used for fuzzy control has the following 3 parts: fuzzification, fuzzy control rules and defuzzification [4, 5]. In fuzzy control, input is decided through considering the queue length of the current phase and the next phase. The queue length consists of passing queue length and waiting queue length L; Output is the delay time T of green light. Set the distance of sensor as 100 m, load length of every queue phase as 4m and the traffic flow of each phase as 50 vehicles. It follows that the domain of discourse of the passing queue length and waiting queue length in question is [0, 54]; since the shortest delay time of green light is 8 seconds and the longest 90 seconds, the domain of discourse of delay time during green light is [8, 90].   Table 1. Passing queue length and waiting queue length of four phases.  Phase Traffic queue length Wait length 1 Max（L5+L11） Max（L1+L3+L7+L9, L4+L6+L10+ L12, L2+ L8） 2 Max（L4+L6+L10+L12） Max（L1+L3+L7+L9,L5+L11, L2+L8） 3 Max（L2+L8） Max（L1+L3+L7+L9,L5+L11,L4+L6+L10+L12） 4 Max（L1+L3+L7+L9） Max（L5+L11,L4+L6+L10+L12,L2+L8）   Fuzzifying the input and output, we can get: The basic domain of discourse of passing queue length is{3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54}, the basic domain of discourse of waiting queue length is{3, 6, 9, 12, 1518, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54}, the basic domain of discourse of delay time during green light is {8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 90}. When it comes to red light, compare the traffic flow of the east and west straight-on lanes and choose the larger one. Then, if the traffic flow at last 8 seconds is less than  5 vehicles, reduce the next-round green light time quantum by 4 seconds [6-7]; if more than  10 vehicles, increase by 4 seconds; if within  5-10 vehicles, the next-round green time quantum remains unchanged. (As shown in Fig. 2) On the amount of input and output, we set up the model of fuzzy subset: {NB (very few), NS(few), ZE(Medium), PS(many), PB(plenty)}[8] and get Table 3.  Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  214 Table 2. Time control of traffic flow before the end of green light.  Order number Traffic flow Green time of next round 1 Less than 5 vehicles Reduced by 4seconds 2 5-10 vehicles Unchanged 3 More than 10 vehicles Increased by 4 seconds   Table 3. The rule table of fuzzy delay control.  T NB NS ZE PS PB NB NB NB NB NB NB NS NS NB NB NB NB ZE ZE NS NS NB NB PS PS ZE ZE NS NB PB PB PS ZE ZE ZE   3.3. The Rules of Fuzzy Delay Control  and Analysis of Matlab Program  Based on the above principles, we can set the appropriate parameters and consider the probability distribution of traffic flow that accord with Queuing Theory. (Poisson distribution). Supposing that the traffic flow accords with the random quantity of Poisson distribution, then calculate the number of waiting vehicles and stopping length of time during red light in the west and the number of waiting vehicles and total stopping length of time in both the east and the west, generating the red light waiting time and number of waiting vehicles in each intersection. It’s therefore defined that the next red light time quantum is the sum of green light time quantum of the rest three intersections. This paper adopts the fuzzy inference method of Mamdani [6], the arithmetic of conjunctions "and", "or" and "also" of MATLAB fuzzy logic toolbox and fuzzy implication and comprehensive defuzzification are as follow [9]: 1) The calculation of “and”  ))(),(min(),( WNWN BABA     2) The calculation of “or”  ))(),(max(),( WNWN BABA     3) The calculation of Implication  ))(),(min(),( WNWN BABA     4) The calculation of Aggregation  ))(),(max(),( WNWN BABA     5) The calculation of Defuzzification Employing Center of Area, that is, determine the fuzzy set membership function curve and center of abscissa surrounding area and choose the center’s corresponding abscissa value as the representative value of the fuzzy set [10]. The following are some Matlab procedure codes: while t1_WEST<x_1a  while v1_WEST<=x_1a  v1_WEST=v1_WEST+CAR1_WEST(i1_WEST) i1_WEST=i1_WEST+1 while v1_WEST>=x_1a-m if v1_WEST>x_1a break  end j1_WEST=j1_WEST+1 v1_WEST=v1_WEST+CAR1_WEST(i1_WEST) i1_WEST=i1_WEST+1  t1_WEST=t1_WEST+1 end end t1_WEST=t1_WEST+1 end … d=d1+d2+d3+d4 s=s1+s2+s3+s4 p=(y_1a+y_2a+y_3a+y_4a)/(d+s) l=(d+s)*60/7 y=y_1a+y_2a+y_3a+y_4a Firstly, through the theoretical analysis and construction of traffic light fuzzy neural network of traffic flow, we establish the expert fuzzy control rule library; and by constant adjustment and learning in the MATLAB fuzzy system (FIS) [11]-[12], we achieve the queue length membership function and green light delay membership function value and map out the corresponding membership function diagram [4], as shown in Fig. 4:  L Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  215  Fig. 4. The membership function diagram of queue length in traffic flow and the delay time during green light.   4. Monte Carlo Simulation  In order to reflect the advantages of intelligent traffic light control system, this paper proposes empirical method of control algorithm and combines real-time data to carry out Monte Carlo system simulation. According to the required intelligent control system features, this paper works out a Matlab simulated program and makes a simulation study on the traffic flow and control system, crystallizing the entire system to make a more direct and obvious comparison with the traditional traffic light. At first, we use the date obtained from an intersection in Cangshan district of Fuzhou to carry out fuzzy control and compare the statistical data with the traditional control method, as shown in the following Table 4:   Table 4. Comparison of the number of waiting vehicles at the intersection for 20 minutes.  Intersection Traditional traffic light Intelligent traffic lights East 50 38 South 15 12 West 128 112 North 39 30   Obviously, we find that the intelligent traffic light control is superior to traditional traffic light control. In order to reflect the uncertainty and mathematical regularity of traffic flow, we use Monte Carlo method in combination with MATLAB to carry out simulation data. Simulation of traffic flow is based on on-the-spot and long-time statistical traffic flow volume, MATLAB simulation and Poisson distribution rule, generating a large amount of simulation data. In MATLAB, we can use the function of POISSFIT (X) to obtain the sample X, and calculate the point estimate of parameter   in Poisson distribution, thereby calculating the Poisson parameter estimation function. We can use [LAMBDAHAT, LAMBDACI] = POISSFIT(X, AL-PHA) to get the value of sample X. Calculate the parameter point estimate of Poisson distribution LAMDA and its confidence coefficient and we get interval estimation 100(1-ALPHA). Use the sample data to replace X in matrix form and we get the sample value of ALPHA and then use the formula R = POISSRND(LAMBDA,M,N) to get Poisson distribution lamda=LAMDA and random number matrix of line M and row N. Generally, the M in random number matrix is set as 1, then in the process of determine N, a certain amount of random number can be simulated. Here we set N as 10000, that is, there will be a random number of 10000 vehicles passing through the intersection. According to the above simulation analysis, it is evident that no matter the input flow and output flow are known/certain or unknown/random, the traditional control is inferior to the intelligent fuzzy control.   5. Conclusion  The signal time delay controller of intelligent fuzzy traffic light, which is based on Monte Carlo theory and fuzzy mathematics control method, is practical in traffic control at single intersections. This paper puts forward a preferable intelligent control project of traffic light. Since this project is not subject to time, region or weather, strictly conforms to traffic rules, and has memory and learning function, it has universal practical applicability. No matter in rush hours or slack hours of traffic, imbalance of traffic flow in different direction of the same phase will not increase the vehicle’s waiting time in other phases or the average vehicle’s delay time. This is a big advantage of this project. This paper just analyzes the traffic light situation at single intersections, and the design of traffic light at multiple intersections will be extended and taken as the future research. Sensors & Transducers, Vol. 156, Issue 9, September 2013, pp. 211-216  216 Table 5. Monte Carlo simulation results.  Traditional traffic light Intelligent traffic light The last N second of green light The number of stopping vehicles The average vehicle stopping time Number of stopping vehicles Average stopping time 1 1086 189.3 924 147.4 2 919 148.4 813 129.5 3 853 125.4 787 108.7 4 732 109.6 642 106.3 5 658 94.7 532 84.4 6 692 95.2 586 93.5 7 774 112.1 667 90 8 832 123.2 795 109.8 9 982 152.8 960 134.6 10 1053 186.3 1024 162.4   Acknowledgements  The research work was jointly supported by National Innovation Practice of Undergraduate (Grant No. 201210389017), and Fujian province Innovation Practice of Undergraduate in China (Grant No.111ZC1258).   References  [1]. Xiaoguang Yang, Bailei Chan, Guoxiong Peng, Study on pedestrian traffic control signal settings, Journal of China Highway and Transport, 14, 1, 2001, pp. 73-80. [2]. Zhiyong Liiu, Intelligent traffic control theory and its application, Science Press, Beijing, 2000. [3]. Weikang Qiu, Weizhi Wang, Traffic signal control based on fuzzy neural network, Jiangsu Electric, 04, 2008, pp. 22-26. [4]. Xiaoli Wu, Zhehui Lin, MATLAB aided fuzzy system design, Xi’an University of Electronic Science and Technology Press, Xi’an, 2002. [5]. Jing Li, Fuzzy control and Simulation of traffic signal intersection, Micro Computer Information, 22, 7, 2006, pp. 33-35. [6]. Yassine Hadjadj Aoul, Ahmed Mehaoua, Charalabos Skianis, A fuzzy logic-based AQM for real-time traffic over internet, Science Direct, 6, 2007,  pp. 4617-4633. [7]. Chou Chil-H Sun, Teng Jen-Chao, A fuzzy logic controller for traffic junction signals, Information Sciences, 143, 1, 2002, pp. 73-86. [8] Hallapuro A., Lappalainen V., Hamalainen D., Performance Analysis of Low bit Rate H. 26L Video Encoder, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’01), 2, May 2001,  pp. 1129-1132. [9] Tarte S. M., Talib H., Ballester M. Evaluating Partial Surface Matching for Fracture Reduction Assessment, in Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, USA, 4, 2006, pp. 514-517. [10] Jee-Hyong Lee, Hyung Lee-Kwang, Distributed and Coorperative Fuzzy, Controllers for Traffic Intersection Group, IEEE Transactions on System, Man and Cybernetics, 29, 1999, pp. 263-271. [11]. Richardon B., Rodriquez D., ITS in developing countries: strategic opportunities, ITS Quartely, 5, 3, 1997, pp. 7-15. [12]. Carlsson C., Fuller R., Optimization under fuzzy if then rules, Fuzzy Sets and Systems, 11, 4, 2001,  pp. 111-118.  ___________________                 2013 Copyright ©, International Frequency Sensor Association (IFSA). All rights reserved. (http://www.sensorsportal.com)  

Study on Monte Carlo Simulation of Intelligent Traffic Lights Based on Fuzzy Control Theory

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Study on Monte Carlo Simulation of Intelligent Traffic Lights Based on Fuzzy Control Theory

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