臺灣博碩士論文加值系統

動態車流的研究自從Lighthill 與 Whitham在五十年代提出了以波動方程式來描述交通車流行為的模式，愈來愈多學者投入用數學方程式來描述交通車流行為的研究。且根據不同之交通現象與道路狀況所建立的相關模式與研究也被陸續提出。
動態車流模式可概略分為三大類，巨觀、微觀和本研究所欲探討的中觀車流模式。最先提出中觀車流模式的是Prigogine和Andrews兩位學者。他們修改了一些在氣體動力學中的概念，導出一描述車流行為的似波茲曼方程式。本研究將提出一個新的交通波茲曼方程式，利用速度分佈函數來描述動態車流。在此交通波茲曼方程式，我們考慮車子受漂移、交通場、加減速和換車道所控制。由於波茲曼方程式是個高度複雜的方程式，本研究將使用蒙地卡羅模擬法來求解。
蒙地卡羅模擬法是利用隨機的方法來模擬一個系統。在本研究中，蒙地卡羅模擬法乃是利用電腦對車子的運動做直接的物理模擬(direct physical simulation)，而非去解車流運動數學模型的數值解。雖然蒙地卡羅模擬法較精確的描述車子運動行為，但其在模擬的效率上來說並不是很好。所以最後我們就將利用個人電腦叢集計算的技術來改善蒙地卡羅模擬效率。

Lighthill and Whitham proposed their kinematic traffic flow model five decades ago, then the mathematical description of traffic flow operations has been a lively subject of research and debate for traffic scientists. There were a wide range of traffic flow theories and models, which were developed to describe traffic flow operations.
In this study, we focus on mesoscopic traffic flow model. The gas-kinetic traffic flow model of Prigogine and Andrews, one of mesoscopic traffic flow model, was developed during 1960’s. They modified some of the key concepts in the kinetic theory of gases and wrote down an equation alike to the Boltzmann transport equation. We present a new traffic Boltzmann transport equation describes the dynamics of the velocity distribution functions of vehicles in the traffic flow. From the traffic Boltzmann transport equation, we consider the vehicles governed by drift, traffic field, deceleration, and lane-changing. The Monte Carlo simulation technique plays an important role in solving the complex equation.
The name of Monte Carlo simulation technique is usually given to stochastic methods that employ a stochastic process to simulate a system. In this study, Monte Carlo simulation technique is introduced to directly solve the traffic Boltzmann transport equation by direct physical simulation. Monte Carlo simulation technique offers an accurate description of transport, but it requires intensive computation and hence has not found wide use for traffic flow applications. Then we introduce the parallel Monte Carlo simulation technique used for improving the drawback of Monte Carlo simulation. Finally, comparison the simulation results with real VD data is discussed.

Contents
Abstract
Contents
List of Figures
List of Tables
Chapter 1 Introduction
1.1 Motivation and Objective
1.2 Study Procedure
1.3 Outline of Thesis
Chapter 2 Literatures review
2.1 A Review on Dynamic Traffic Flow Model
2.1.1 Macroscopic Traffic Flow Models
2.1.2 Microscopic Traffic Flow Models
2.1.2.1 Car-following models
2.1.2.2 Cellular Automaton Models
2.1.3 Mesoscopic Traffic Flow Models
2.2 A Review on the Computational Methods for the Boltzmann Transport Equation
2.3 Introduction to the development of Message Passing Interface
Chapter 3 Traffic Boltzmann Transport Equation
3.1 Boltzmann Transport Equation for mesoscopic traffic flow
3.2 Scattering Mechanisms
Chapter 4 Monte Carlo Simulation Technique
4.1 A Short History of Monte Carlo
4.2 Pseudorandom number generators
4.3 Procedure of Monte Carlo Simulation Technique
4.4 Technique in Parallel Computing
Chapter 5 Numerical Simulation of Freeway Traffic Flow
5.1 Numerical Results of Some Examples
5.2 Comparison with Real Data
5.2.1 Space Mean and Time Mean Speed
5.2.2 Simulation Results
5.3 Result of Parallel Monte Carlo Simulation Technique
Chapter 6 Conclusions and Future Works
6.1 Conclusions
6.2 Future Works
References

[1] Lighthill, M. J., and G. B Whitham, “ On Kinematics Waves II. A Theory of Traffic Flow on Long Crowded Road “, London, Proceedings Royal Society, A229, pp.317-345, 1955.
[2] May, A. D., Traffic Flow Fundamentals, Prentice Hall, Englewood Cliffs, NJ, 1990.
[3] Payne, H. J., “Freflo: A Macroscopic Simulation Model of Freeway Traffic”, Transportation Research Record, No.722, 1979.
[4] Prigogine, I., and F. C. Andrews, ”A Boltzmann-Like Approach For Traffic Flows”, Operations Research, Vol. 8, pp.789-797, 1960.
[5] Prigogine, I., and R. Herman, Kinetic Theory of Vehicular Traffic, American Elsevier Publishing Company, 1971.
[6] Reuschel, A., “Vehicles Moves in a Platoon”, Oesterreichisches Ingenieur-Archir, Vol. 4, pp.193-215, 1950.
[7] Chandler, R. E., R. Herman, and E. W. Montroll, “Traffic Dynamics: Studies In Car Following”, Operations Research, Vol. 6, pp.165-184, 1958.
[8] Gazis, D. C., R. Herman, and R. B. Potts, “Car-Following Theory Of Steady-State Traffic Flow”, Operations Research, Vol. 7, pp.499-505, 1959.
[9] Herman, R., E. W. Montroll, R. B. Potts, and R. W. Rothery, “Traffic Dynamics: Analysis Of Stability In Car Following”, Operations Research, Vol. 7, pp.499-505, 1959.
[10] Cho, H. J., S. C. Lo, “Modeling of Self-Consistent Multi-Class Dynamic Traffic Flow Model”, to appear Physica A,2002.
[11] Helbing, D., “Gas-kinetic derivation of Navier-Stokes-like traffic equation”, Physical Review E, Vol. 53, No. 3, pp.2266-2381, 1996.
[12] Pipes, L. A., “An Operational Analysis of Traffic Dynamics”, Journal of Applied Physics, Vol. 24, No. 3, pp.274-287, 1953.
[13] Newell, G. F., “Nonlinear Effects In The Dynamics Of Car Following”, Operations Research, Vol. 9, pp.209-229, 1961.
[14] Todosiev, E. P., and L. C. Barbosa, “A Proposed Model for the Driver-Vehicle System”, Traffic Engineering, Vol. 34, pp.17-20, 1964.
[15] Wiedemann, R., Simulation des strabβenverkehrsfluβes, Technical Report, Institute for Traffic Engineering, University of Karlsrühe (in German), 1974.
[16] Nagel, K., “Particle Hopping Models and Traffic Flow Theory”, Physical Review E, Vol. 53, pp.4655-4672, 1996.
[17] Nagel, K., “From Particle Hopping Models and Traffic Flow Theory”, Transportation Research Record, No. 1644, pp.1-9, 1998.
[18] Anderson, R. L., R. Herman, and I. Prigogine, “On The Statistical Distribution Function Theory Of Traffic Flow”, Operations Research, Vol. 10, pp.180-196, 1962.
[19] Herman, R., and T. Lam, “On The Mean Speed In The ‘Boltzmann-Like’ Traffic Theory: Analytical Derivation”, Transportation Science, Vol. 5, No. 3, pp.314-326, 1971.
[20] Paveri-Fontana, S. L., “On Boltzmann-Like Treatments for Traffic Flow: A Critical Review of the Basic Model and An Alternative Proposal for Dilute Traffic Analysis”, Transportation Research, Vol. 9, pp.225-235, 1975.
[21] Edie, L. C., R. Herman, and T. N. Lam, “Observed Multilane Speed Distribution And The Kinetic Theory Of Vehicular Traffic”, Transportation Science, Vol. 14, No. 1, pp.55-76, 1980.
[22] Lampis, M., “On The Kinetic Theory Of Traffic Flow In The Case Of A Nonnegligible Number Of Queueing Vehicles”, Transportation Science, Vol. 12, No.1, pp.16-28, 1978.
[23] Nelson, P., “A Kinetic Theory of Vehicular Traffic and its Associated Bimodal Equilibrium Solutions”, Transport Theory and Statistical Physics, Vol. 24, pp.383-409, 1995.
[24] Nelson, p., D. D. Bui., and A. Sopasakis, “A Novel Traffic Stream Model Deriving from a Bimodal Kinetic Equation”, Proceedings of the IFAC conference, pp.799-804, 1997.
[25] Helbing, D. and A. Greiner, “Modeling and Simulation of Multilane Traffic Flow”, Physical Review E, Vol. 55, No. 5, pp.5498-5508, 1997.
[26] Klar, A., and R. Wegener, “A Hierarchy of Models for Multilane Vehicular Traffic I & II: Modeling”, SIAM Journal of Applied Mathematics, 1998.
[27] Hoogendoorn, S. P. and P. H. L. Bovy, “Modeling Multiple User-Class Traffic”, Transportation Research Record, No. 1644, pp.57-70, 1998.
[28] Hoogendoorn, S. P. and P. H. L. Bovy, “Continuum Modeling of Multiclass Traffic Flow”, Transportation Research Part B, Vol. 34, pp.123-146, 2000.
[29] Cho, H. J. and S. C. Lo, “Numerical Simulation of the Multilane Traffic Dispersion”, Applied Physics Letter, 2001.(submitted paper)
[30] Cho, H. J. and S. C. Lo, “Modeling of Nonlinear Mixed Traffic Dispersion”, the Networks and the Spatial Economics, 2001.(submitted paper)
[31] Bellomo, N., Lecture notes on the mathematical theory of the Boltzmann equation, World Scientific, 1995.
[32] Nordsiech, A., B. L. Hicks., “Monte Carlo evaluation of the Boltzmann collision integral”, in Proc. 5-th Intern. Symp. On RGD, C. L. Brundin Ed., Academic Press, Vol. 1, pp.695-710, 1967.
[33] Aristov, V. V., “On solution of the Boltzmann equation for discrete velocities,” Dokl. Akad. Nauk USSR, Vol. 283, No. 4, pp831-834, 1985.
[34] Tan, Z., Y. K. Chen, P. L. Varghese and J. R. Howell, “New numerical strategy to evaluate the collision integral of the Boltzmann equation,” in Proc. 16th Intern. Symp. On RGD, Progress in Aeronaut. And Astronaut, pp.359-373, 1989.
[35] Bird, G. A., “Direct simulation and the Boltzmann equation”, Phys.l Fluids, Vol. 13, No. 11, pp-2676-2681, 1970.
[36] Nanbu, K., “Direct simulation scheme derived from the Botzmann equation. I. Monocomponent gases,” J. Phys. Soc. Japan, Vol. 49, No. 5, pp.2042-2049, 1980.
[37] Nanbu, K., “Direct simulation scheme derived from the Botzmann equation. II. Multicomponent gases mixtures,” J. Phys. Soc. Japan, Vol. 49, No. 5, pp.2050-2054, 1980.
[38] Nanbu, K., “Direct simulation scheme derived from the Botzmann equation. III. Rough sphere gases,” J. Phys. Soc. Japan, Vol. 49, No. 5, pp.2055-2058, 1980.
[39] Nanbu, K., “Direct simulation scheme derived from the Botzmann equation. IV. Correlation of velocity,” J. Phys. Soc. Japan, Vol. 50, No. 9, pp.2829-2836, 1981.
[40] Babovsky, H., “On a simulation scheme for the Boltzmann equation”, Math. Methods Appl. Sci., Vol. 8, pp.223-233, 1986.
[41] William, G., L. Ewing, and S. Anthony, Using MPI-Portable Parallel Programming with the Message Passing Interface, The MIT Press, Cambridge, Masachusetts, London, England.
[42] Bellomo, N. and M. L. Schiavo, “From the Boltzmann Equation to Generalized Kinetic Models in Applied Science”, Mathematical and Computer Modelling, Vol. 26, No. 7, pp.43-76, 1997.
[43] Yang, Q. and H. N. Koutsopoulos, “A Microscopic Traffic Simulator for Evaluation of Dynamic Traffic Management Systems,” Transportation Research Port C, Vol. 4, No. 3, pp.113-129, 1996.
[44] Kalos, M. H. and P. A. Whitlock, Monte Carlo Methods Volume I: Basics, John Wiley & Sons, Inc., 1986.
[45] Duke, Schofer, and May, “A Statistical Analysis of Speed-Density Hypotheses,” Highway Research Record 154, Transportation Research Board, Washington, DC, 1967.
[46] Gerlough, D. L. and M. J. Huber, Traffic Flow Theory: A Monograph, Transportation Research Board National Research Council, Washington, D.C., 1975.