臺灣博碩士論文加值系統

1992年物理學家Nagel及Schreckenberg兩人首度將細胞自動機(Cellular Automaton，CA)應用於公路車流行為研究，透過幾個簡單的加減速規則，利用電腦快速運算，讓車輛進行彼此交互作用與規則疊代，呈現出與實測相當之巨觀車流特性，又能描述微觀車流特性。迄今已有相當數量之改良CA模式，惟多針對小客車為研究對象，且對細胞單元之定義均相當粗糙，亦未探討異質(指同類型車種可具不同之速率、加減速、變換車道行為)混合(指同一道路空間可同時運行不同類型車種，如機車、小型車、大型車)車流課題。為更符合實際車流現象，本研究發展精緻型CA模式，並改良傳統CA模式加減速過大之不合理現象，用以探索異質混合車流之時空交通特性。

本研究首先提出一個基礎的異質混合車流細胞自動機模式，該模式比以往細胞自動機模式研究更為精細的「細胞」及「網格」概念，定義「基本單元」(CU)作為衡量車輛及道路空間之共通單位。並進一步以時空網格被車輛細胞移動軌跡所佔用之比例代表佔有率，以車輛細胞每個時階移動的格位數代表速率，每個時階通過的細胞數代表流量，定義一般化佔有率、速率與流量，以精確描述異質混合車流車輛的總體行為。經發展CA基本模式，模擬不同車流密度情況下純車流之時空交通特性，再構建總體交通流量、速率與佔有率的基本關係。惟模擬結果顯示車輛運行過程車速會驟降停止之情形，模式規則待改進。

接著本研究針對前述規則之缺點提出一個修正CA模式，該模式進一步整合駕駛跟車空間預期效應、採取速度相依之隨機項、啟動延遲規則、變換車道與大小車互動規則等。模擬環境設定在二車道的高速公路中進行，模擬情境為在車流中加入慢速車(如同慢速移動瓶頸)與停止車(如同固定地點瓶頸)，探討混合車流之時空交通特性，並進一步探討車流軌跡、流量密度關係與時空車流型態。模擬結果顯示修正CA模式能夠呈現出真實交通環境重要的車流特性與型態。


研究最後針對模擬過程中以往CA模式均未處理之缺點，即車輛在接近前方為停止車輛或固定物時所出現不合理急煞車之情形，提出一個更精緻的CA模式來改善。模式在規則中引入Forbes的跟車概念，利用多段線性速率修正傳統CA模式加減速過大之不合理現象。經高速公路之驗證與測試發現，確能改正車輛速率驟降之缺失，並能顯示Kerner所提出的三相交通現象及其相變。本研究進一步利用此修正CA模式應用在施工區，探討不同速率控制策略對行車效率及安全之影響。

Cellular automata (CA) model was first proposed by Nagel and Schreckenberg in 1992 to simulate the highway traffic. The core logic was to introduce several simple update rules for vehicle movement in computer programs to efficiently simulate the complicated interactive traffic behaviors. A considerable number of revised or extended CA models have been developed to date, most of which only focused on pure traffic with coarse cell units in the simulations. Very little has devoted to the heterogeneous traffic situations and/or mixed traffic contexts, which comprise different types of vehicle. This research aims to develop advanced CA models to simulate the spatiotemporal behaviors under heterogeneous mixed traffic contexts on freeway.

Firstly, a basic CA model is developed to explore the fundamental traffic features. Generalized definitions of traffic variables, in spatiotemporal sense, and a new concept of common unit (CU) for gauging non-identical vehicle sizes and various lane widths are presented. Pure light vehicle and pure heavy vehicle experiments are tested on a two-lane freeway context. Vehicular trajectories, flow-occupancy diagrams, and spatiotemporal traffic patterns under deterministic and stochastic conditions are displayed. The results show that abrupt speed drops occasionally emerge during the simulations.

To resolve this shortcoming, this study continues to propose a revised CA model, which considers the anticipation effect, velocity-dependent randomization, slow-to-start, lane change, and interaction among vehicles. The effects of both stationary and slow-moving bottlenecks on global traffic are examined using this revised CA model. Vehicular trajectories, flow-occupancy, and spatiotemporal traffic patterns are displayed. The results reveal noticeable traffic patterns with free flow, wide moving jam and synchronized flow phases, suggesting that the revised CA model is capable of capturing the essential features of traffic flows.

Finally, this study further proposes a refined CA model using the rationale of Forbes’ car-following concept with a piecewise-linear movement mechanism, which aims to rectify the common defect of abrupt deceleration existent in most conventional CA models. The proposed CA model is validated in a two-lane freeway mainline context. It shows that this refined CA model can fix the unrealistic deceleration behaviors, thus can reflect the genuine driver behaviors in real world. The model is also capable of revealing Kerner’s three-phase traffic patterns and phase transitions among them. Furthermore, the refined CA model is applied to simulate a highway work zone wherein traffic efficiency (maximum flow rates) and safety (speed deviations) impacted by various control schemes are investigated.

中文摘要 III
ABSTRACT V
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 MOTIVATION 3
1.3 RESEARCH OBJECTIVES 4
1.4 CHAPTERS ORGANIZATION 5
CHAPTER 2 LITERATURE REVIEW 7
2.1 MACROSCOPIC APPROACHES 7
2.2 MICROSCOPIC APPROACHES 11
2.3 RELATED CA APPROACHES 16
2.4 SUMMARY 22
CHAPTER 3 DEFINITIONS 23
3.1 COMMON UNIT FOR CELLS AND SITES 23
3.2 GLOBAL TRAFFIC VARIABLES 24
3.3 LOCAL TRAFFIC VARIABLES 29
3.4 SIMULATION SETTING 30
3.5 SUMMARY 31
CHAPTER 4 BASIC CELLULAR AUTOMATON MODEL 32
4.1 FORWARD RULES 33
4.2 LANE-CHANGING RULES 34
4.3 FRAMEWORK 37
4.4 PURE TRAFFIC SIMULATION RESULTS 37
4.5 SUMMARY 46
CHAPTER 5 REVISED CELLULAR AUTOMATON MODEL 47
5.1 MODIFICATION 47
5.2 VALIDATION 50
5.3 EFFECTS OF STATIONARY AND MOVING BOTTLENECKS 54
5.4 SUMMARY 59
CHAPTER 6 REFINED CELLULAR AUTOMATON MODEL 61
6.1 REFINED RULES 61
6.2 VALIDATION 66
6.3 APPLICATION 73
6.4 TRAFFIC FEATURE EXPLORATIONS 79
6.5 SUMMARY 85
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 86
7.1 CONCLUSIONS 86
7.2 RECOMMENDATIONS 87
REFERENCES 88
APPENDIX 94
VITA 96

Bando, M., Hasebe, K., Nakayama, A., Shibata, A., and Sugiyama. Y., (1994). Structure stability of congestion in traffic dynamics. Jpn. J. Ind. Appl. Math. 11, pp. 203–223.
Bando, M., Hasebe, K., Nakayama, A., Shibata, A., and Sugiyama. Y., (1995). Dynamic model of traffic congestion and numerical simulation. Physical Review E, volume 51(2), pp. 1035–1042.
Barlović, R., Santen, L., Schadschneider, A., and Schreckenberg, M. (1998). Metastable states in cellular automata for traffic flow. European Physical Journal B 5, pp. 793–800.
Barlović, R., (2003). Traffic Jams – Cluster formation in low-dimensional cellular automata models for highway and city traffic. Ph.D. thesis, University at Duisburg-Essen, Standort Duisburg.
Benjamin, S. C., Johnson, N. F. and Hui, P., (1996). Cellular automata models of traffic flow along a highway containing a junction. Journal of Physics A: Mathematical and General, Vol. 29, pp. 3119–3127.
Bham, G.H. and Benekohal, R.F., (2004). A high fidelity traffic simulation model based on cellular automata and car-following concepts. Transportation Research C 12, pp. 1-32.
Brackstone, M. and M. McDonald., (1999). Car-following: a historical review. Transportation Research F, Vol. 2, pp. 181-196.
Brilon, W. and Wu, N., (1999). Evaluation of cellular automata for traffic flow simulation on freeway and urban streets, Traffic and Mobility: Simulation-Economics-Environment, Institut für Kraftfahrwesen, RWTH Aachen, Duisburg, pp.163-180.
Chakroborty, P. and S. Kikuchi., (1999). Evaluation of the general motors based car-following models and a proposed fuzzy inference model. Transportation Research C, Vol. 7, pp. 209-235.
Chandler, R.E., Herman, R., Montroll, E., (1958). Traffic dynamics: Studies in car following. Operations Research 6, pp. 165–184.
Chowdhury, D., Wolf, D.E. and Schreckenberg, M., (1997). Particle-hopping models for two-lane traffic with two kinds of vehicles: effects of lane-changing rules. Physica A 235, pp. 417-439.
Chowdhury, D., Santen, L., and Schadschneider, (2000). A. Statistical physics of vehicular traffic and some related systems. Physics Reports, Vol. 329, pp. 199-329.
Daganzo, C. F., (1997). Fundamentals of Transportation and Traffic Operations. Elsevier Science Ltd. Pergamon.
Daganzo, C. F., (1994). The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research B, Vol. 28, pp. 269-287.
Daganzo, C.F., (1995). A finite difference approximation of the kinematic wave model of traffic flow. Transportation Research Part B, Vol. 29B, pp. 261-276.
Daganzo, C.F., (1999). The lagged cell-transmission model. International Symposium on Transportation and Traffic Theory, Ceder, A. (Ed.), New York, Pergamon.
Daganzo, C. F., (2002). A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections. Transportation Research B, Vol. 36, pp. 131-158.
Daganzo, C. F., (2002). A behavioral theory of multi-lane traffic flow. Part II: Merges and the onset of congestion. Transportation Research B, Vol. 36, pp. 159-169.
Ebersbach, A., Schneider, J., Morgenstern, I. and Hammwohner, R., (2000). The influence of trucks on traffic flow an investigation on the Nagel-Schreckenberg model, International Journal of Modern Physics C 11 (4), pp. 837-842.
Emmerich, H. and Rank, E., (1997). An improved cellular automaton model for traffic flow simulation, Physica A, Vol.234, pp. 676-686.
Ez-Zahraouya, H., Jetto, K. and Benyoussef, A., (2004). The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton, European Physical Journal B 40, pp. 111-117.
Forbes, T.W., Zagorski, H.J., Holshouser, E.L. and Deterline, W.A., (1958). Measurement of driver reactions to tunnel conditions. Highway Research Board, Proceedings 37, pp. 345-357.
Forbes, T.W., (1963). Human factor considerations in traffic flow theory. Highway Research Record 15, pp.60-66.
Gazis, D.C., Herman, R., Potts, R.B., (1959). Car-following theory of steady-state traffic flow. Operations Research 7, pp. 499–505.
Gazis, D.C., Herman, R., Rothery, R.W., (1961). Nonlinear follow-the-leader models of traffic flow. Operations Research 9, pp. 545–567.
Hamed, M.M., Easa, S.M., and Batayneh, R.R., (1997). Disaggregate Gap-Acceptance Model for Unsignalized T-Intersections. J. Transportation. Engineering, Vol. 123, pp. 36-42.
Helbing, D. and Schreckenberg M., (1999). Cellular automata simulating experimental properties of traffic flow, Physical Review E, Vol.59, pp. 2505-2508.
Helbing, D., (2001). Traffic and related self-driven many particle systems. Reviews of Modern Physics, 73, pp. 1067-1141.
Hsu, C.C., Lin, Z.S., Chiou, Y.C. and Lan, L.W., (2007). Exploring traffic features with stationary and moving bottlenecks using refined cellular automata. Journal of the Eastern Asia Society for Transportation Studies 7, pp. 2246-2260.
Jiang, R. and Wu, Q.S., (2003). Cellular automata models for synchronized traffic flow, J. Phys. A: Math. Gen. 36, pp. 381–390.
Jiang, R. and Wu, Q.S., (2004). Spatial–temporal patterns at an isolated on-ramp in a new cellular automata model based on three-phase traffic theory. Journal of Physics A: Mathematical & General 37, pp. 8197–8213.
Jiang, R., Mao-Bin H., Bin, J., Ruili, W. and Wu, Q.S., (2008). Enhancing highway capacity by homogenizing traffic flow. Transportmetrica, Vol. 4, No. 1, pp. 51-61
Kerner, B.S., Rehborn, H., (1996). Experimental features and characteristics of traffic jams. Physical Review E 53, pp. R1297-R1300.
Kerner, B. S., (1998). Experimental features of self-organization of traffic flow. Physical Review Letter, Vol. 81, 1998, pp. 3797-3800.
Kerner, B.S., Klenov, S.L., (2002). A microscopic model for phase transitions in traffic flow. Journal of Physics A 35, pp. L31-L43.
Kerner, B.S., Klenov, S.L., Wolf, D.E., (2002). Cellular automata approach to three-phase traffic theory. Journal of Physics A 35, 9971-10013.
Kerner, B.S. and Klenov, S.L., (2003). Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks, Physical Review E, Vol.68, pp. 036130.
Kerner, B.S., Klenov, S.L., (2004). Spatio-temporal patterns in heterogeneous traffic flow with variety of driver behavioural characteristics and vehicle parameters. Journal of Physics A 37, pp. 8753-8788.
Kerner, B.S., Rehborn, H., Aleksic, M. and Haug, A., (2004). Recognition and tracking of spatial–temporal congested traffic patterns on freeways, Transportation Research Part C, Vol.12, pp. 369-400.
Kerner, B.S., (2004). The physics of traffic, Springer-Verlag Berlin Heidelberg.
Kerner, B. S., (2005). Control of spatiotemporal congested traffic patterns at highway bottlenecks. Physica A, Vol. 355, pp. 565-601.
Kerner, B.S., Klenov, S.L., Hiller, A., and Rehborn, H., (2006). Microscopic features of moving traffic jams, Physical Review E, Vol.73, pp. 046107.
Knospe, W., Santen, L., Schadschneider, A. and Schhreckenberg, M., (2000). Towards a realistic microscopic description of highway traffic. Journal of Physics A 33, pp. 477-485.
Knospe, W., Santen, L., Schadschneider, A. and Schreckenberg, M., (1999). Disorder effects in cellular automata for two-lane traffic, Physica A 265, pp. 614-633.
Koshi, M., Iwasaki, M., Ohkura, I., (1983). Some findings and an overview on vehicular flow characteristics. In: Hurdle, V., Hauer, E., Stuart, G. (Eds.), Proceedings, 8th International Symposium on Transportation and Traffic Flow Theory, pp. 403-426.
Krauss S. and Wagner, P., (1997). Metastable states in a microscopic model of traffic flow. Physical Review E 55(5), pp. 5597-5602.
Kühne, R. in: Gartner, N. Messner, C.J. and Rathi, A.J. (eds.), (1998). Traffic Flow Theory, 2nd ed. Transportation Research Board, Special Report 165.
Lan, L. W. and H. H. Yeh., (2001). Car following behavior for drivers with non-identical risk aversion: ANFIS approach. Journal of the Chinese Institute of Civil and Hydraulic Engineering, Vol. 13, No. 2, 2001, pp. 427-434.
Lan, L.W. and Chang, C.W., (2003). Moving behaviors of motorbikes in mixed traffic: particle hopping model, Journal of the Eastern Asia Society for Transportation Studies, Vol. 5, pp. 23-37.
Lan, L.W. and Chang, C. W., (2005). Inhomogeneous cellular automata modeling for mixed traffic with cars and motorcycles, Journal of Advanced Transportation 39 (3), pp. 323-349.
Lan, L. W. and Hsu, C. C., (2005). Using cellular automata to explore spatiotemporal traffic patterns, Proceedings, 10th International Conference of Hong Kong Society for Transportation Studies, pp. 210-219.
Lan, L. W. and Hsu, C. C., (2006). Formation of spatiotemporal traffic patterns with cellular automaton simulation, Transportation Research Board, 85th Annual Meeting, Washington, DC, in CD-ROM.
Lan, L.W., Chiou, Y.C., Hsu, C.C. and Lin, Z.S., (2007). Spatiotemporal mixed traffic patterns with revised cellular automaton simulation. Proceedings, 12th International Conference of Hong Kong Society for Transportation Studies, pp. 133-142.
Lan, L.W., Chiou, Y.C., Lin, Z.S. and Hsu, C.C., (2008). A new cellular automaton model in traffic simulation at a highway work zone. Proceedings, 10th International Conference on Applications of Advanced Technologies in Transportation. Athens, Greece.
Lárraga, M.E., del Río, J.A., Alvarez-lcaza, L., (2005). Cellular automata for one-lane traffic flow modeling. Transportation Research C 13, pp. 63-74.
Lee, H.K., Barlovic, R., Schreckenberg, M. and Kim, D., (2004). Mechanical restriction versus human overreaction triggering congested traffic states. Physical Review Letter, 92(23), pp. 238702-1~238702-4.
Lighthill, M. H. and G. B. Whitham., (1955), On kinematic waves: a theory of traffic flow on long crowed roads, Proceedings of the Royal Society, Series A, No. 229, pp. 317-345.
Liu, G., A. S. Lyrintzis, and P. G. Michalopoulus., (1998). Improved high-order model for freeway traffic flow. Transportation Research Record, No. 1644, pp. 37-46.
Mahmassani, H., and Sheffi, Y., (1981). Using gap sequences to estimate gap acceptance functions. Transportation Research Part B, Vol. 15, pp. 143-148.
May, A. D., (1990). Traffic Flow Fundamentals. Prentice-Hall Inc., New Jersey.
Meng, J. P., Dai, H. Q., Dong, L. Y. and Zhang, J. F., (2007). Cellular automaton model for mixed traffic flow with motorcycles. Physica A 380, Mathematical & General, pp. 470-480.
Nagel, K. and Schreckenberg, M., (1992). A cellular automaton model for freeway traffic. Physics I 2, pp. 2221-2229.
Nagel, K., (1996). Particle-hopping models and traffic flow theory. Physical Review E 53, pp. 4655-4672.
Nagel, K., (1998). From particle-hopping models to traffic flow theory, Transportation Research Record 1644, pp. 1-9.
Nagel, K., Wolf, D. E., Wagner, P. and Simon, P., (1998). Two-lane traffic rules for cellular automata: A systematic approach. Physical Review E 58, pp. 1425-1437.
Nakanishi, K., Itoh, K., Igarashi, Y., Bando, M., (1997). Solvable optimal velocity models and asymptotic trajectory. Physical Review E, volume 55, pp. 6519–6532.
Newell, G.F., (1965). Instability in dense highway traffic, a review. In: Almond, J. (Ed.), Proceedings of 2nd International Symposium on the Theory of Road Traffic Flow, pp. 73–83.
Payne, H. J., (1971). Model of freeway traffic and control. Mathematics of Public Systems, Vol. 1, pp. 51-61.
Pipes, L.A., (1953). An operational analysis of traffic dynamics. Journal of Applied Physics, Vol. 24 (3), pp. 74–281.
Polus, A., Shmueli-Lazar, S., and Livneh, M., (2003). Critical gap as a function of waiting time in determining roundabout capacity. Journal of Transportation Engineering, 129(4), pp.504-509.
Pottmeier, A., Barlovic, R., Knospe, W. and Schadschneider, A., (2002). Localized defects in a cellular automaton model for traffic flow with phase separation, Physica A, 308, pp. 471-482.
Richards, P. I., (1956). Shock waves on highway. Operations Research, Vol. 4, No. 1, pp. 42-51.
Rickert, M., Nagel, K., Schreckenberg, M. and Latour, A., (1996). Two lane traffic simulations using cellular automata, Physica A, 231, pp. 534-550.
Rothery, R.W. in: Gartner, N. Messner, C.J. and Rathi, A.J. (eds.), (1998). Traffic Flow Theory, 2nd ed. Transportation Research Board, Special Report 165.
Sheu, J.B., (2008). A quantum mechanics-based approach to model incident-induced dynamic driver behavior, Physica D, Vol. 237, pp. 1800-1814.
Sugiyama, Y., Yamada, H., (1997). Simple and exactly solvable model for queue dynamics, Physical Review E 55, pp. 7749-7752.
Transportation Research Board, (2000). Highway Capacity Manual, National Research Council, Washington D.C.
Treiterer, J., Myers, J.A., (1974). The hysteresis phenomenon in traffic flow. In: Buckhy, D.J. (Ed.), Proceedings of 6th International Symposium on Transportation and Traffic theory, pp. 13–38.
Wang, R., Jiang, R., Wu, Q.S. and Liu, M., (2007). Synchronized flow and phase separations in single-lane mixed traffic flow, Physica A, 378, pp. 475-484.
Wang, B.H., Wang, L., Hui, P.M. and Hu, B., (2000). The asymptotic steady states of deterministic one-dimensioned traffic flow models, Physica B, 27, pp. 237-239.
Wolfram, S., (1986). Theory and Applications of Cellular Automata. Word Scientific, Singapore.
Wolf, D.E., (1999). Cellular automata for traffic simulations, Physica A, 263, pp. 438-451.
Wong, G. C. K. and S. C. Wong., (2002). A multi-class traffic flow model – an extension of LWR model with heterogeneous drivers. Transportation Research A, Vol. 36, pp. 827-841.

Zhang, H. M., (1998). A theory of nonequilibrium traffic flow. Transportation Research B, Vol. 32, pp. 485-498.
Zhang, H. M. and T. Kim., (2005). A car-following theory for multiphase vehicular traffic flow. Transportation Research B, Vol. 39, pp. 385-399.
Zhu H.B., L. Lei, and S.Q. Dai., (2009). Two-lane traffic simulations with a blockage induced by an accident car, Physica A, Vol. 388, pp. 2903-2910.