基于混杂Petri网的交通流建模
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摘要
摘 要
随着经济的发展、车辆的普及，城市交通需求迅速发展，交通问题日
趋严重。交通流的准确预报和高效的交通控制不但可以减少出行者的施行
成本，而且还能减轻环境污染，减少因交通而带来的经济损失。交通流预
报和交通控制要以准确而有效的交通流模型为基础，传统的交通流模型已
经不能适应越来越复杂、越来越庞大的交通系统，也不能充分表现交通系
统的混杂特性。本文主要是尝试把混杂 Petri 网这一新兴理论应用到交通
系统的建模中去。
本文在分析交通系统混杂特性的基础上，用混杂 Petri 网建立了交通
流模型，主要研究内容如下：
(1) 针对单路段交通流的情况，把单路段分为无出入口匝道和有出入
口匝道两种情况。把每一路段分为 N 段，段内交通属性是相同的，而且对
于有出入口匝道的情况每一段内最多只有一个出口匝道和入口匝道。分别
建立了有出入口匝道和无出入口匝道的路段交通流混杂 Petri 网模型，并
给出了模型参数修改算法。
（2） 针对十字交叉口的红绿灯常见的两相位和四相位的情况，分别
给出了它们的赋时 Petri 网模型。详细分析了十字交叉口的交通流情况，
并对红绿灯控制为四相位时的情况建立了四相位信号灯控制的交叉口交
通流的混杂 Petri 网模型，最后分析了模型的变化运行过程。
路段交通流和交叉口交通流的混杂 Petri 网模型的建立为交通流预报、
交通控制奠定了良好基础，具有一定的参考价值。
Abstract
With the development of the economics, the rapid growth of household
vehicles amount and growth of urban transportation systems demands, traffic
problem becomes more and more serious. Accurate traffic flow forecasting and
highly effective traffic control can solve this question effectively. They can
reduce not only the cost of a journey execution, but also the environmental
pollution, economic loss brought by traffic problem. Traffic flow forecasting
and traffic control need accurate and effective traffic model as foundation.
Traditional traffic flow models are not to be able to adapt the situation that
transportation system is getting more and more complex, and they cannot fully
represent the hybrid characteristic of transportation system. In this thesis,
hybrid Petri net was applied in transportation system modelling.
In this thesis hybrid characteristics of transportation system was analyzed,
and traffic flow modelling using Hybrid Petri Net was proposed, main studies
content and research results are as follows:
1. Traffic flows of single road was studied. There are two kinds of roads:
road with ramps and road without ramps. Every single road is divided into N
sections, and traffic attribute in every section are the same. And for the road
with ramps there are only one on-ramp and one off-ramp. Then in this thesis
two models was introduced: hybrid Petri net model of traffic flow of single
road without ramps and hybrid Petri net model of traffic flow of single road
with ramps, finally a model parameter modify algorithm is presented for the
two models.
2. Two-phase and four-phase traffic light of intersection was studied, and
their Timed Petri net models were presented. Traffic flow of intersection was
analyzed, and a Hybrid Petri Net model for traffic flow under four-phase
traffic signal control was accessed, finally the model running process was
analyzed.
Hybrid Petri Net models of single road traffic flow and intersection
traffic flow make a contribution to traffic flow forecasting and traffic flow
control in theory and application.
随着经济的发展、车辆的普及，城市交通需求迅速发展，交通问题日
趋严重。交通流的准确预报和高效的交通控制不但可以减少出行者的施行
成本，而且还能减轻环境污染，减少因交通而带来的经济损失。交通流预
报和交通控制要以准确而有效的交通流模型为基础，传统的交通流模型已
经不能适应越来越复杂、越来越庞大的交通系统，也不能充分表现交通系
统的混杂特性。本文主要是尝试把混杂 Petri 网这一新兴理论应用到交通
系统的建模中去。
本文在分析交通系统混杂特性的基础上，用混杂 Petri 网建立了交通
流模型，主要研究内容如下：
(1) 针对单路段交通流的情况，把单路段分为无出入口匝道和有出入
口匝道两种情况。把每一路段分为 N 段，段内交通属性是相同的，而且对
于有出入口匝道的情况每一段内最多只有一个出口匝道和入口匝道。分别
建立了有出入口匝道和无出入口匝道的路段交通流混杂 Petri 网模型，并
给出了模型参数修改算法。
（2） 针对十字交叉口的红绿灯常见的两相位和四相位的情况，分别
给出了它们的赋时 Petri 网模型。详细分析了十字交叉口的交通流情况，
并对红绿灯控制为四相位时的情况建立了四相位信号灯控制的交叉口交
通流的混杂 Petri 网模型，最后分析了模型的变化运行过程。
路段交通流和交叉口交通流的混杂 Petri 网模型的建立为交通流预报、
交通控制奠定了良好基础，具有一定的参考价值。
Abstract
With the development of the economics, the rapid growth of household
vehicles amount and growth of urban transportation systems demands, traffic
problem becomes more and more serious. Accurate traffic flow forecasting and
highly effective traffic control can solve this question effectively. They can
reduce not only the cost of a journey execution, but also the environmental
pollution, economic loss brought by traffic problem. Traffic flow forecasting
and traffic control need accurate and effective traffic model as foundation.
Traditional traffic flow models are not to be able to adapt the situation that
transportation system is getting more and more complex, and they cannot fully
represent the hybrid characteristic of transportation system. In this thesis,
hybrid Petri net was applied in transportation system modelling.
In this thesis hybrid characteristics of transportation system was analyzed,
and traffic flow modelling using Hybrid Petri Net was proposed, main studies
content and research results are as follows:
1. Traffic flows of single road was studied. There are two kinds of roads:
road with ramps and road without ramps. Every single road is divided into N
sections, and traffic attribute in every section are the same. And for the road
with ramps there are only one on-ramp and one off-ramp. Then in this thesis
two models was introduced: hybrid Petri net model of traffic flow of single
road without ramps and hybrid Petri net model of traffic flow of single road
with ramps, finally a model parameter modify algorithm is presented for the
two models.
2. Two-phase and four-phase traffic light of intersection was studied, and
their Timed Petri net models were presented. Traffic flow of intersection was
analyzed, and a Hybrid Petri Net model for traffic flow under four-phase
traffic signal control was accessed, finally the model running process was
analyzed.
Hybrid Petri Net models of single road traffic flow and intersection
traffic flow make a contribution to traffic flow forecasting and traffic flow
control in theory and application.
引文
[1]. 宫晓燕，汤淑明，王知学，陈德望。高速公路交通流建模综述。交
通运输工程学报，2002，2（1）：74-79
[2]. 荆便顺. 道路交通控制工程. 人民交通出版社，1995：1-130
[3]. 吴锋，刘方煌，郑应平。混杂系统研究综述。系统工程，1997，15
（2）： 1-8
[4]. M. Athans.Command and Control(C2) Theory: A Challenge to Control
Science, IEEE Transactions on Automatic Control, v AC-32, n 4, Apr,
1987, p 286-293
[5]. 王亦兵，韩曾晋，史其信。高速公路交通流建模。系统工程学报，
1998，13（2）：83-89
[6]. M. Papageorgiou, J.M. Blosseville, H.S. Habib. Macroscopic Modeling
of Traffic Flow on the Boulevard Peripherique in Paris. Transportation
Research, Part B: Methodological, v 23B, n 1, Feb, 1989, p 29-47
[7]. M. Papageorgiou, J.M. Blosseville, H.S. Habib. Modelling and
real-time control of traffic flow on the southern part of Boulevard
Peripherique in Paris. Part I. Modelling. Transportation Research, Part
A: General, v 24A, n 5, Sep, 1990, p 345-359
[8]. M. Papageorgiou. Multilayer Control System Design Applied to
Freeway Traffic. IEEE Transactions on Automatic Control, v AC-29, n
6, Jun, 1984, p 482-490
[9]. M. Papageorgiou. Some Remarks on Macroscopic Traffic Flow
Modeling. Transportation Research, Part A: Policy and Practice, v 32, n
68
参考文献
5, Jun, 1998, p 323-329
[10]. Karmeshu. A stochastic model for highway traffic. Transp. Res.
1981;15B(4):285-294
[11]. Payne H. J Model of Freeway Traffic and Control Simulation Council
Proc. ,Mathematical Models of Public Systems,1971,1:51-61
[12]. Febbraro A D.A new model for an integrated urban transportation
network. The 7th IFAC/IFORS Symp. On Transp. Systems: Theory and
Applications of Advanced Technology,1994
[13]. Bagchi A.Modelling and estimation of traffic flow-A martingale
approach. Intern. J. System Sci.,1980;11(4):429-444
[14]. I. Iwaookutaki. Dynamic Prediction of Traffic Volume Through Kalman
Filtering Theory.Transp.Res.,1984,18(2):1-11.
[15]. Brian L Smith, Michael J., Demertsky. Short Term Traffic Flow
Prediction: Neural Network Approach. Transportation Research Record
1453,Washington,D.C.TRB,1993
[16]. Larry Head K..Event Based Short Term Traffic Flow Prediction Model
Transportation Research Record 1510,Washington, D.C. TRB, 1995
[17]. M.H. Lighthill，G.B. Whitham. On Kinematics Wave：II. A Theory of
Traffic on Long Crowded Roads. Proc. r. Soc. London, 1955. p 317—
345
[18]. 刘智勇，吴今培，万百五。高速公路智能交通控制系统的建模及多
层描述。公路交通科技，1998，15（1）：39-44
[19]. May. A Traffic Flow Fundamentals. New jersey: Prentice Hall Inc. 1990.
p160-190
- 69 -
北京工业大学工学硕士学位论文
[20]. DC. Gazis, R. Herman, R. W. Rothery. Nonlinear Follow-the-leader
Model of Traffic Flow. Operations Research. 1996. 9(4): p913-933
[21]. P.G. Gipps. A Behavioral Car Following Model for Computer
Simulation. Transportation Research. 1981. 15B(2): p105-111
[22]. L. Folorio. Neural Network Classifiction and Forecasting of Freeway
Traffic Flow Stability. The 7th IFAC/IFORS Symp. On Transp. Systems:
Theory and Applications of Advanced Technology, 1994: p1122-1133
[23]. 欧海涛，张卫东，张方渊，许晓鸣。基于多智能体技术的城市智能
交通控制系统。电子学报，2000，28（12）：52-55
[24]. 李作敏，黄中祥。递阶优化模型在道路交通建模中应用评述。公路
交通科技，2000，17（3）：68-70
[25]. A. Gollu, P. Varaiya. Hybrid Dynamical Systems. Proc. of the 28th CDC.
1989, pp. 2708-2712
[26]. R. Alur, D. Dill. The Theory of Timed Automata. Theoretical Computer
Science. 1994. vol. 126, p 3748-3751
[27]. R.L. Grossman, A. Nerode, A.P. Ravn, H. Rischel. Hybrid Systems.
Lecture Notes in Computer Science. Springer-Verlag, vol.736, 1993
[28]. A. van der Schaft, H. Schumacher. An Introduction to Hybrid systems.
Springer-Verlag, 2000
[29]. R. David. Modeling of Hybrid Systems Using Continuous and Hybrid
Petri nets. International Workshop on Petri Nets and Performance
Models, 1997, p 47-58
[30]. R. David, H. Alla. On Hybrid Petri Nets. Discrete Event Dynamic
Systems: Theory and Applications, v 11, n 1-2, Jan, 2001, p 9-40
70
参考文献
[31]. G. Horton, V.G. Kulkarni, D.M. Nicol, K.S. Trivedi. Fluid stochastic
Petri nets: theory, applications and solution techniques. European
Journal of Operational Research, v 105, n 1, Feb 16, 1998, p 184-201
[32]. C. Valantin-Roubinet. Modeling of Hybrid Systems: DAE Supervised
by Petri Nets. The Example of a Gas Storage. Proc. of 3rd Int. Cont. On
Automation of Mixed Process. ADPM98 Reims, France. 1998, p
142-149
[33]. R. Champagnat, P. Esteban, H. Pingaud, R. Valette. Petri Net Based
Modeling of Hybrid Systems. Computers in Industry, v 36, n 1-2, Apr
30, 1998, p 139-146
[34]. A. Giua, E. Usai. High-level Hybrid Petri Nets: a Definition.
Proceedings of the 35th Conference on Decision and Control, 1996, p
148-150
[35]. I. Demongodin, N. Audry, F. Prunet. Batches Petri nets. Proceedings of
the IEEE International Conference on Systems, Man and Cybernetics, v
1, 1993, p 607-616
[36]. J.A. Stiver, P.J. Antsaklis. Modeling and Analysis of Hybrid Dynamical
Systems. Proc. of the 31st CDC. 1992,p 3748-3751
[37]. 谢广明，郑大钟. 一类线性切换系统能控性和能达性的充要条件. 控
制与决策. 2001, 16(2): p 248-253
[38]. I. Kolmanovsky, E.G Gilbert. Multimode Regulators for Systems with
State and Control Constraints and Disturbance Inputs. Control Using
Logic Based Switching – Lecture Notes in Control and Information
Science. Berlin: Springer-Berlag, 1996. p 105-117
- 71 -
北京工业大学工学硕士学位论文
[39]. 孙洪飞，赵军，高晓东. 带有时滞摄动的线性切换系统的稳定性. 控
制与决策. 2002, 16(2): p 431-434
[40]. A. Bemporad, M. Morari. Control of systems integrating logic,
dynamics, and constraints. Automatica, v 35, n 3, Mar, 1999, p 407-427
[41]. M.D. Lemmon, K.X. He, I. Markovsky. Supervisory Hybrid Systems[J].
IEEE Control Systems Magazine,1999,19(4): p 42-55.
[42]. J. Lygeros, D. N. Godbole, and S. Sastry, “Multiagent hybrid system
design using game theory and optimal control,” in IEEE Conference on
Decision and Control, pp. 1190--1195, Kobe,Japan, December 11-13
1996.
[43]. J. Lygeros and D. Godbole, “An interface between continuous and
discrete event controllers for vehicle automation,” in American Control
Conference, pp. 801--805, Baltimore, Maryland, USA,June 29-July 1
1994.
[44]. J. Lygeros, D. N. Godbole, and S. Sastry, “Optimal control approach to
multi-agent, hierarchical system verification,” in IFAC World Congress,
pp. 389--394, San Fransisco, California, USA,June 30-July 5 1996.
[45]. J. Lygeros, C. Tomlin, and S. Sastry, ”Multi-objective hybrid controller
synthesis,” in Proceedings of HART97 (O.Maler, ed.), no.1201 in
LNCS, pp. 109--123, Berlin: Springer-Verlag,1997.
[46]. J. Lygeros, D. N. Godbole, and S. Sastry,” Simulation as a tool for
hybrid control,” in Proceedings of the Fifth IEEE conference on AI,
Simulation and Planning in High-Autonomy Systems, Gainesville,
Florida, USA, December 7-9 1994.
72
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hybrid systems. IEEE Transactions on Automatic Control, v 46, n 3,
March, 2001, p 398-415
[48]. 郑大钟 赵千川。离散事件动态系统。北京：清华大学出版社，2001
[49]. 李增中，韩兵。基于 HPN 仿真的混杂系统分层调度方案。微电脑应
用，2001，17（7）：22-25
[50]. D. Lefebvre. About numerical methods for timed and continuous Petri
nets. Proceedings of the IEEE International Conference on Systems,
Man and Cybernetics, v 4, 2002, p 411-416
[51]. 何贤会，高春华，王慧。基于混杂 Petri 网的混杂系统建模方法。机
电工程，2000，17（2）：69-72
[52]. A. Tzes, S. Kim, W. R. McShane. Applications of Petri Networks to
Transportation Network Modeling. IEEE Transactions on Vehicular
Technology, v 45, n 2, May, 1996, p 391-400
[53]. R. Fernandez, N. Zerhouni. Modeling and Analysis of Disassembly
Systems Using Continuous Petri Nets. Proceedings of the IEEE
International Symposium on Assembly and Task Planning, 2001, p
232-237
[54]. M. Silva, L. Recalde. Petri nets and integrality relaxations: A view of
continuous petri net models. IEEE Transactions on Systems, Man and
Cybernetics Part C: Applications and Reviews, v 32, n 4, November,
2002, p 314-327
[55]. I. Demongodin, N.I. Koussoulas. Differential Petri Nets: Representing
Continuous Systems in a Discrete-Event World. IEEE Transactions on
- 73 -
北京工业大学工学硕士学位论文
Automatic Control. 1998, 43(4): p 573-579
[56]. http://www.simulaworks.com/
通运输工程学报，2002，2（1）：74-79
[2]. 荆便顺. 道路交通控制工程. 人民交通出版社，1995：1-130
[3]. 吴锋，刘方煌，郑应平。混杂系统研究综述。系统工程，1997，15
（2）： 1-8
[4]. M. Athans.Command and Control(C2) Theory: A Challenge to Control
Science, IEEE Transactions on Automatic Control, v AC-32, n 4, Apr,
1987, p 286-293
[5]. 王亦兵，韩曾晋，史其信。高速公路交通流建模。系统工程学报，
1998，13（2）：83-89
[6]. M. Papageorgiou, J.M. Blosseville, H.S. Habib. Macroscopic Modeling
of Traffic Flow on the Boulevard Peripherique in Paris. Transportation
Research, Part B: Methodological, v 23B, n 1, Feb, 1989, p 29-47
[7]. M. Papageorgiou, J.M. Blosseville, H.S. Habib. Modelling and
real-time control of traffic flow on the southern part of Boulevard
Peripherique in Paris. Part I. Modelling. Transportation Research, Part
A: General, v 24A, n 5, Sep, 1990, p 345-359
[8]. M. Papageorgiou. Multilayer Control System Design Applied to
Freeway Traffic. IEEE Transactions on Automatic Control, v AC-29, n
6, Jun, 1984, p 482-490
[9]. M. Papageorgiou. Some Remarks on Macroscopic Traffic Flow
Modeling. Transportation Research, Part A: Policy and Practice, v 32, n
68
参考文献
5, Jun, 1998, p 323-329
[10]. Karmeshu. A stochastic model for highway traffic. Transp. Res.
1981;15B(4):285-294
[11]. Payne H. J Model of Freeway Traffic and Control Simulation Council
Proc. ,Mathematical Models of Public Systems,1971,1:51-61
[12]. Febbraro A D.A new model for an integrated urban transportation
network. The 7th IFAC/IFORS Symp. On Transp. Systems: Theory and
Applications of Advanced Technology,1994
[13]. Bagchi A.Modelling and estimation of traffic flow-A martingale
approach. Intern. J. System Sci.,1980;11(4):429-444
[14]. I. Iwaookutaki. Dynamic Prediction of Traffic Volume Through Kalman
Filtering Theory.Transp.Res.,1984,18(2):1-11.
[15]. Brian L Smith, Michael J., Demertsky. Short Term Traffic Flow
Prediction: Neural Network Approach. Transportation Research Record
1453,Washington,D.C.TRB,1993
[16]. Larry Head K..Event Based Short Term Traffic Flow Prediction Model
Transportation Research Record 1510,Washington, D.C. TRB, 1995
[17]. M.H. Lighthill，G.B. Whitham. On Kinematics Wave：II. A Theory of
Traffic on Long Crowded Roads. Proc. r. Soc. London, 1955. p 317—
345
[18]. 刘智勇，吴今培，万百五。高速公路智能交通控制系统的建模及多
层描述。公路交通科技，1998，15（1）：39-44
[19]. May. A Traffic Flow Fundamentals. New jersey: Prentice Hall Inc. 1990.
p160-190
- 69 -
北京工业大学工学硕士学位论文
[20]. DC. Gazis, R. Herman, R. W. Rothery. Nonlinear Follow-the-leader
Model of Traffic Flow. Operations Research. 1996. 9(4): p913-933
[21]. P.G. Gipps. A Behavioral Car Following Model for Computer
Simulation. Transportation Research. 1981. 15B(2): p105-111
[22]. L. Folorio. Neural Network Classifiction and Forecasting of Freeway
Traffic Flow Stability. The 7th IFAC/IFORS Symp. On Transp. Systems:
Theory and Applications of Advanced Technology, 1994: p1122-1133
[23]. 欧海涛，张卫东，张方渊，许晓鸣。基于多智能体技术的城市智能
交通控制系统。电子学报，2000，28（12）：52-55
[24]. 李作敏，黄中祥。递阶优化模型在道路交通建模中应用评述。公路
交通科技，2000，17（3）：68-70
[25]. A. Gollu, P. Varaiya. Hybrid Dynamical Systems. Proc. of the 28th CDC.
1989, pp. 2708-2712
[26]. R. Alur, D. Dill. The Theory of Timed Automata. Theoretical Computer
Science. 1994. vol. 126, p 3748-3751
[27]. R.L. Grossman, A. Nerode, A.P. Ravn, H. Rischel. Hybrid Systems.
Lecture Notes in Computer Science. Springer-Verlag, vol.736, 1993
[28]. A. van der Schaft, H. Schumacher. An Introduction to Hybrid systems.
Springer-Verlag, 2000
[29]. R. David. Modeling of Hybrid Systems Using Continuous and Hybrid
Petri nets. International Workshop on Petri Nets and Performance
Models, 1997, p 47-58
[30]. R. David, H. Alla. On Hybrid Petri Nets. Discrete Event Dynamic
Systems: Theory and Applications, v 11, n 1-2, Jan, 2001, p 9-40
70
参考文献
[31]. G. Horton, V.G. Kulkarni, D.M. Nicol, K.S. Trivedi. Fluid stochastic
Petri nets: theory, applications and solution techniques. European
Journal of Operational Research, v 105, n 1, Feb 16, 1998, p 184-201
[32]. C. Valantin-Roubinet. Modeling of Hybrid Systems: DAE Supervised
by Petri Nets. The Example of a Gas Storage. Proc. of 3rd Int. Cont. On
Automation of Mixed Process. ADPM98 Reims, France. 1998, p
142-149
[33]. R. Champagnat, P. Esteban, H. Pingaud, R. Valette. Petri Net Based
Modeling of Hybrid Systems. Computers in Industry, v 36, n 1-2, Apr
30, 1998, p 139-146
[34]. A. Giua, E. Usai. High-level Hybrid Petri Nets: a Definition.
Proceedings of the 35th Conference on Decision and Control, 1996, p
148-150
[35]. I. Demongodin, N. Audry, F. Prunet. Batches Petri nets. Proceedings of
the IEEE International Conference on Systems, Man and Cybernetics, v
1, 1993, p 607-616
[36]. J.A. Stiver, P.J. Antsaklis. Modeling and Analysis of Hybrid Dynamical
Systems. Proc. of the 31st CDC. 1992,p 3748-3751
[37]. 谢广明，郑大钟. 一类线性切换系统能控性和能达性的充要条件. 控
制与决策. 2001, 16(2): p 248-253
[38]. I. Kolmanovsky, E.G Gilbert. Multimode Regulators for Systems with
State and Control Constraints and Disturbance Inputs. Control Using
Logic Based Switching – Lecture Notes in Control and Information
Science. Berlin: Springer-Berlag, 1996. p 105-117
- 71 -
北京工业大学工学硕士学位论文
[39]. 孙洪飞，赵军，高晓东. 带有时滞摄动的线性切换系统的稳定性. 控
制与决策. 2002, 16(2): p 431-434
[40]. A. Bemporad, M. Morari. Control of systems integrating logic,
dynamics, and constraints. Automatica, v 35, n 3, Mar, 1999, p 407-427
[41]. M.D. Lemmon, K.X. He, I. Markovsky. Supervisory Hybrid Systems[J].
IEEE Control Systems Magazine,1999,19(4): p 42-55.
[42]. J. Lygeros, D. N. Godbole, and S. Sastry, “Multiagent hybrid system
design using game theory and optimal control,” in IEEE Conference on
Decision and Control, pp. 1190--1195, Kobe,Japan, December 11-13
1996.
[43]. J. Lygeros and D. Godbole, “An interface between continuous and
discrete event controllers for vehicle automation,” in American Control
Conference, pp. 801--805, Baltimore, Maryland, USA,June 29-July 1
1994.
[44]. J. Lygeros, D. N. Godbole, and S. Sastry, “Optimal control approach to
multi-agent, hierarchical system verification,” in IFAC World Congress,
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