ANALYSIS OF TRAFFIC FLOW ON SELECTED TWO-LANE HIGHWAYS IN IBADAN METROPOLIS BY FOLAKE OLUBUNMI AKINTAYO B.Sc. (Hons.) Civil Engineering (Lagos), M.Sc. Industrial Engineering (Ibadan) A Thesis in the Department of Civil Engineering Submitted to the Faculty of Technology in partial fulfilment of the requirements for the Degree of DOCTOR OF PHILOSOPHY of the UNIVERSITY OF IBADAN SEPTEMBER 2011 CERTIFICATION I certify that this work was carried out by Folake Olubunmi Akintayo in the Department of Civil Engineering, University of Ibadan, Nigeria. -------------------------------------------------------------------- Supervisor Professor Oluwole A. Agbede B.Sc., M.Sc. (Ife), Ph.D. (London) Department of Civil Engineering, University of Ibadan, Nigeria ii DEDICATION This work is dedicated to the: Glory of God; Memories of my late father, Mr. Thomas Adebayo Eludipo; and Prof. Olusegun Adebisi. iii ACKNOWLEDGEMENTS I bless the Almighty God for the successful completion of this work. It started as a dream in 1975 as a beginner in Christ’s School, Ado-Ekiti. After a span of over three decades in many spheres of life, God brought the dream to a fulfilment in due season. Many people were used to achieve this dream, some have gone to the great beyond but many are still alive. To the living (Mamas, uncles, aunties, and mentors) many of whom may not be aware of their positive influences in this African girl-child, I say thank you. I wish to express my heartfelt appreciation to my Supervisor, Prof. O.A. Agbede who was (and still) readily available to show me the goodly and godly way to success. I commend his intervention in my admission for this programme; the story would have been a different one but for his pastoral and fatherly roles. God bless you and your family sir. The useful contributions of my Heads of Department (Dr. B.I.O. Dahunsi, Prof. A.O. Coker, Dr G.A. Alade, Prof. O.A. Agbede and Dr. S.O. Franklin) at different times in the course of this programme are appreciated. I valued the criticism of the work by Dr. K. A. Falade (Sub-Dean Postgraduate of the Faculty of Technology), Dr. G. M. Ayinuola and Dr. F.A. Olutoge, the present and immediate past Postgraduate Coordinator of the Department respectively. I thank Dr. W. K. Kupolati and Dr. Adewumi (Department of Civil Engineering, Obafemi Awolowo University, Ile-Ife) for their sustained interest in the work. I appreciate the concern and support of Prof. Oluwoye of Alabama A&M University, Alabama, USA. The contributions of other lecturers in the Department: Arc. Eugenious Adebamowo, Engrs. W. O. Ajagbe, Oluyemisi Oladejo and Omolara Lade; fellow PG students, Dr. Muhammed, Engr. Lekan Shittu, LAUTECH friends and others too numerous to mention) helped to sharpen my focus and get the work done, thank you sir/ma. I also appreciate the combined positive efforts of the technical staff: Messrs. F. A. Ilugbo, G. N. Okereafor, O. S. Ojo, Oghenejakpor, Oyeleke, Akinyemi, Mrs. Funmi Okoji and Tope Ayodele. I am grateful for the unflinching support and the assistance rendered by the administrative staff: Mrs. Tinuke Muritala, Mrs. Veronica Akpokodje, Mrs. Margaret Olaibi, Mr. Ayobami Olajide and our retirees – Messrs Adeleke and Owolabi. I thank the former departmental library assistant, Mr. D. O. Olaibi for his assistance. I appreciate the good foundations I received for this work from my lecturers in the Department of Civil Engineering, University of Lagos. I am also grateful to my iv lecturers in the Department of Industrial and Production Engineering, University of Ibadan in particular Prof. A.O. Oluleye, Prof. O.E. Charles-Owaba, Dr. F.A. Oyawale, Dr. O.G. Akanbi, Mr. S. O. Oladeji and Prof. A. F. Akinbinu (of blessed memory). I thank Dr. A.O. Owolabi of the Department of Civil Engineering, Federal University of Technology, Akure (FUTA) and bless God for the memory of the late Prof. Olusegun Adebisi. Their joint paper, “Mathematical models for headways in traffic streams” provided an impetus to carry out further research in this area. I am grateful to friends in my former place of work (University of Agriculture, Abeokuta (UNAAB)) for their encouragement to complete this work. I found the various pieces of advice given by my former Dean, Prof. Ayedun and the incumbent Dean, Prof. Ajisegiri during staff seminars very useful in finalising this work. I also appreciate the concern of my Head of Department in UNAAB, Dr. O.S. Awokola, lecturers, staff and students of the Department of Civil Engineering; lecturers, colleagues and friends from other Departments in the College of Engineering. God bless you all. The assistance rendered by Messrs Rotimi and Kazeem in the data collection effort for this work is commendable and appreciated. I appreciate the effort of one of my students, Mr. Seyi Mapaderun in the survey works. I say a big thank you to Dr. Sanya Olubusoye (Statistics Department), in getting suitable statistical software for the analysis of the data. I am grateful to Dr. Tunde Akinkunmi (Computer Science Department) for granting me audience whenever I called upon him. I express my heartfelt gratitude to Dr. Roberts of the Computer Science Department and two of his students (Sina and Leke) who assisted in coding ‘Traffic Flow Simulator’. To members of my families, no word can adequately express my heartfelt appreciation for your understanding and supports all through. You understood the need for me to ‘hibernate’ and get this work completed. I appreciate the spiritual support from my Fathers-in- Lord and Mothers-in Israel. Thank you, Aanuoluwapo for your concern and prayer. I pray God will grant you and my other ‘kids’ the power to surpass this feat in Jesus’ name (amen). To my beloved husband and friend JOA, it is our success. We went through the narrow path to this success together. Vielen Dank zu lieben. “To God be the glory Great things He has done”. v ABSTRACT Traffic congestion is a common feature on highways in many cities of the world, including Ibadan, Nigeria. Previous studies have shown that several mathematical traffic flow models developed to analyse congestion cannot be easily generalised or adapted to varying situations. In addition, validation errors of some models are as high as 60.0 %. In pursuit of the objective of minimising traffic congestion in parts of the Ibadan metropolis, headway simulation models were developed for the analysis of flow on some selected two-lane highways characterised by heavy traffic. Traffic survey was conducted on three purposively selected heavily-trafficked two-lane highways (Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona-Apata) in the Ibadan metropolis. Headway modelling approach incorporating the prevailing roadway, traffic and control conditions was developed. Field data were captured on the three roads with a camcorder between 7.00 a.m. and 6.00 p.m. for a period of six months as specified in the Highway Capacity Manual. Comparison of the modelling result and field headway data were carried out using Kolmogorov-Smirnov (KS) test (p = 0.05). A traffic flow simulator was developed to simulate the different congestion scenarios by varying the minimum and maximum headways. Capacity analysis and validation of the results were carried out using ANOVA methods. Average vehicular flow of 715 ± 3, 970 ± 5 and 1118 ± 9 vph per lane on Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona-Apata roads respectively. Eighteen hyperbolic headway scenarios were produced and the highest coefficient of 2 correlation (R = 0.92) was recorded at 90 percentile while 0.18, 0.36, 0.50, 0.71, 0.82, and 0.79 were obtained at 1, 10, 30, 50, 70, and 100 percentiles respectively. There was no significant difference between theoretical and field data using Kolmogorov- Smirnov (KS) test (p < 0.05). Also, a total number of 171 congestion scenarios were generated using the traffic flow simulator. Traffic flow varied between 204 and 2376 pcu per lane while headways varied between 1 and 18 seconds. The capacity analysis produced approximated maximum flow rates of 1850, 2865 and 2881 pcu in the two directions of travel for Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona- Apata roads respectively. The capacity of Total Garden-Agodi Gate was within the recommended maximum value of 2800 pcu in the two directions of travel for two-lane highways. The results for J Allen-Oke Bola and Odo Ona-Apata roads showed that an vi additional lane will be required in each direction of travel. The validation of the models on the dualised J Allen-Oke Bola road showed that congestion can be reduced by about 55.0 %. A maximum validation error of 35.0 % was obtained. The traffic flow simulator developed successfully simulated the traffic situations on the selected highways. The analysis of the flow yielded results that could ameliorate traffic congestion on the selected two-lane highways in the Ibadan metropolis. Keywords: Traffic flow, Two-lane highways, Headway simulation models, Traffic congestion, Capacity analysis. Word Count: 469 vii TABLE OF CONTENTS Page Certification ii Dedication iii Acknowledgements iv Abstract vi Table of Contents viii List of Figures xi List of Plates xiii List of Tables xiv Notation xv Chapter 1 INTRODUCTION 1 1.1 Background 1 1.2 Research Problem 4 1.3 Study Area 5 1.4 Aim and Objectives 5 1.5 Justification 10 Chapter 2 LITERATURE REVIEW 2.1 Traffic Flow 11 2.1.1 Traffic flow parameters 11 2.1.2 Measurement of Traffic Flow 12 2.1.3 Traffic Flow Regimes 12 2.2 Traffic congestion 13 2.2.1 Causes of traffic congestion 13 2.2.2 Negative Impacts of traffic congestion 13 2.2.3 Congestion reduction strategies 14 2.2.4 Analysis of congested flow 16 2.3 Traffic flow modelling 17 2.3.1 Types of models 17 2.3.2 Criteria for model selection 18 2.3.3 Traffic simulation 21 2.3.4 Traffic simulation models 21 viii Page 2.3.5 Classification of traffic simulation models 22 2.3.6 Traffic simulation model building 24 2.3.7 Vehicle generation algorithm 25 2.4 Headway Distribution Models 26 2.4.1 Headway distribution models for free flow 27 2.4.2 Headway distribution models for constrained flow 28 2.4.3 Parameter estimation and calibration of headway models 29 2.5 Highway Capacity 32 2.5.1 Factors affecting capacity 32 2.5.2 Need for highway capacity analysis 34 2.5.3 Capacity analysis methods 35 2.5.3.1 The Highway Capacity Manual method 35 2.5.3.2 The British Standard Approach 36 2.5.3.3 Statistical method 38 2.5.3.4 Dynamic highway capacity estimation method 38 2.5.3.5 Safety-based capacity analysis 38 2.5.4 Level of Service 38 2.5.5 Acceptable degrees of congestion 40 2.5.6 Design hourly volume 41 2.5.7 Capacity of two-lane highways 41 2.5.8 Capacity analysis of two-lane highways 42 Chapter 3 METHODOLOGY 44 3.1 Traffic Survey 44 3.2 Traffic Data collection 44 3.2.1 Headway data capturing and extraction 45 3.3 Headway Modelling Process 45 3.3.1 Theoretical headway generation algorithm 45 3.3.2 Hyperbolic headway distribution models 47 3.4 Traffic Flow Simulator (TRAFLOS) 48 3.4.1 TRAFLOS algorithm 48 3.5 Experimental Design of Congestion Scenarios 50 3.6 Practical Capacity of Selected Roads 52 ix Page 3.6.1 Determination of adjustment factors 52 3.7 Statistical Analysis 53 Chapter 4 RESULTS AND DISCUSSIONS 55 4.1 Traffic Survey Results 55 4.1.1 General summary 55 4.1.2 Average traffic flow 57 4.1.3 Field headways 58 4.2 Headway Modelling Output 61 4.2.1 Vehicular interaction 61 4.2.2 Comparison of theoretical and field headways 67 4.3 Traffic Flow Analysis 68 4.3.1 Simulated traffic flows 68 4.3.2 Congestion factors 72 4.3.3 Capacity adjustment 75 4.3.4 Capacity analysis for different congestion scenarios 75 4.3.5 Results of the analysis of variance test 82 4.3.6 Validation of models for J Allen Oke-Bola road 83 4.3.7 Validation errors 84 Chapter 5 CONCLUSION AND RECOMMENDATION 85 5.1 Conclusions 85 5.2 Recommendation 85 REFERENCES 86 APPENDICES 96 Appendix A1: SONY camcorder operating guide 97 Appendix A2: Extracted field headway data set 105 Appendix B: Headway modelling output 112 Appendix C: Kolmogorov-Smirnov test 135 Appendix D: Traffic flow simulator output 150 Appendix E: One-way ANOVA test 192 x LIST OF FIGURES Page Fig. 1.1: Nigeria’s road network 6 Fig. 1.2: Ibadan metropolitan area’s road network 7 Fig. 1.3: Network of some principal roads in Ibadan metropolis 8 Fig. 2.1: Model usage flow chart 19 Fig. 3.1: Theoretical headway generation algorithm flowchart 46 Fig. 3.2: Traffic flow simulator flowchart 49 Fig. 4.1: Distribution of field headways for flows between 700 to 1200vph 60 Fig. 4.2: Cumulative headway distribution for flows between 700 to 1200vph 66 Fig. 4.3: Distribution of simulated flows with minimum headway of 1 second 71 Fig. 4.4: Congestion factors for simulated flows 74 Fig. B2.1: Hyperbolic model at 1 percentile vehicular interaction 117 Fig. B2.2: Hyperbolic model at 2 percentile vehicular interaction 118 Fig. B2.3: Hyperbolic model at 3 percentile vehicular interaction 119 Fig. B2.4: Hyperbolic model at 4 percentile vehicular interaction 120 Fig. B2.5: Hyperbolic model at 5 percentile vehicular interaction 121 Fig. B2.6: Hyperbolic model at 10 percentile vehicular interaction 122 Fig. B2.7: Hyperbolic model at 20 percentile vehicular interaction 123 Fig. B2.8: Hyperbolic model at 30 percentile vehicular interaction 124 Fig. B2.9: Hyperbolic model at 40 percentile vehicular interaction 125 Fig. B2.10: Hyperbolic model at 50 percentile vehicular interaction 126 Fig. B2.11: Hyperbolic model at 60 percentile vehicular interaction 127 Fig. B2.12: Hyperbolic model at 70 percentile vehicular interaction 128 Fig. B2.13: Hyperbolic model at 80 percentile vehicular interaction 129 Fig. B2.14: Hyperbolic model at 90 percentile vehicular interaction 129 Fig. B2.15: Hyperbolic model at 95 percentile vehicular interaction 130 Fig. B2.16: Hyperbolic model at 98 percentile vehicular interaction 131 Fig. B2.17: Hyperbolic model at 99 percentile vehicular interaction 132 Fig. B2.18: Hyperbolic model at 100 percentile vehicular interaction 133 xi Page Fig. C1.1: Comparison of field and simulated headways for flow rate of 700 vph 145 Fig. C1.2: Comparison of field and simulated headways for flow rate of 800 vph 146 Fig. C1.3: Comparison of field and simulated headways for flow rate of 900 vph 147 Fig. C1.4: Comparison of field and simulated headways for flow rate of 1000 vph 148 Fig. C1.5: Comparison of field and simulated headways for flow rate of 1100 vph 149 xii LIST OF PLATES Page Plate 1.1: Traffic stream on Obafemi Awolowo road (before dualisation) 9 Plate 1.2: Traffic stream on Odo Ona-Apata road 9 Plate 3.1: Sony HDR-HC3 Camcorder 54 Plate 3.2: Traffic Flow Simulator screen 55 xiii LIST OF TABLES Page Table 2.1: Overview of traffic flow models 20 Table 2.2: Comparison of headway distribution models 30 Table 2.3: Recommended design flows for two-way urban roads 37 Table 2.4: Level of service characteristics 39 Table 2.5: Guide for selection of design levels of service 41 Table 2.6: Maximum service volumes under ideal conditions 43 Table 3.1: Congestion scenarios design template 51 Table 4.1: Summary of preliminary traffic study 56 Table 4.2: Average traffic flow on selected roads 57 Table 4.3: Minimum and maximum values of headway 58 Table 4.4: Percentage composition of field headway per flow regime 59 Table 4.5: Hyperbolic headway simulation models 62 Table 4.6: Hyperbolic model adjustment factors 63 Table 4.7: Cumulative headway distribution spreadsheet for flows between 700 to 1200 vph 64 Table 4.8: Kolmogorov-Smirnov test result 67 Table 4.9: Simulated traffic volume for different congestion scenarios 69 Table 4.10: Computed flow rates for different congestion scenarios 70 Table 4.11: Computed congestion factors for different congestion scenarios 73 Table 4.12: Congestion factors and equivalent level of service 74 Table 4.13: Capacity adjustment factors 75 Table 4.14: Capacity analysis of Total Garden-Agodi Gate road for kc=1 76 Table 4.15: Capacity analysis of J Allen-Oke Bola road for kc=1 77 Table 4.16: Capacity analysis of Odo Ona-Apata road for kc=1 78 Table 4.17: Simulated capacities at different congestion levels for Total Garden-Agodi Gate road 79 Table 4.18: Simulated capacities at different congestion levels for J Allen-Oke Bola road 80 Table 4.19: Simulated capacities at different congestion levels for Odo Ona-Apata road 81 Table 4.20: ANOVA test result for field and simulated capacities 82 Table 4.21: Capacity adjustment factors for dualised J Allen-Oke Bola road 83 Table 4.22: Capacity analysis of dualised J Allen-Oke Bola Road 84 xiv NOTATION A = cumulative headway adjustment factor C = basic capacity Cp = practical capacity ei = lower boundary limit of headways in Gi di = upper boundary limit of headways in Gi f (x) = probability density function of x fi = adjustment factor Gi = headway group i h = headway h1 = minimum headway h2 = maximum headway H = cumulative headway k = traffic density kc = congestion factor ki = headway group composition factor i q = flow (vehicles arrival rate) Rn = random number 2 R = coefficient of correlation T = total time/total headway v = mean (average) speed V = traffic volume VR = number of vehicles released per simulation run xv Chapter 1 INTRODUCTION 1.1 Background The highway network is an important component of the transportation system. In Nigeria, it is the principal means of transportation facilitating the socioeconomic activities of the people. Two-lane highways (single carriageway) formed the main component of this system at the local, state and federal levels. Efficient and effective flow of traffic is desirable for the highway system to operate optimally at designed capacity and for favourable level of service. Traffic flow represents the interaction between vehicles, drivers and infrastructure. Traffic flow can be either free or constrained (Helbing, 2001; and Nagatani, 2002). In free flow conditions, drivers can choose their own speed or constrained to car-following system. Kerner (2004) classified the congestion regime into two distinct phases: synchronized flow and wide moving jams. In synchronized flow, the speeds of the vehicles are low and vary quite a lot between vehicles, but the traffic flow remains close to free flow. In wide moving jams, vehicle speeds are more equal and lower, and time delays can be quite large. Traffic congestion is a road condition characterised by speeds slower than free flow speeds, resulting in longer travel times and increased queuing (Aworemi et al., 2009; Hook 1995). It occurs when traffic demand is greater than the capacity of a road (Lee et al., 2008). Traffic jam is extreme traffic congestion where vehicles are fully stopped for periods of time (Abul-Magd, 2007). Traffic congestion is considered one of the main urban transportation problems, particularly in developing countries where vehicle ownership is growing geometrically without corresponding sustainable land use patterns and transportation schemes (Tugbobo, 2009). Traffic congestion leads to increased travel time, air pollution and fuel consumption. Providing additional lanes to existing highways and building new ones have been the traditional response to congestion (FHW 2005). However, the data collection effort for this exercise is great. Consequently, transportation engineers and researchers are increasingly developing simulation models to analyse traffic flows on highways. 1 Capacity expansion is one of the strategies usually adopted in both developed and developing countries to mitigate traffic congestion. Expanded highways improve traffic flow and reduce congestion. Capacity is the maximum number of vehicles that can pass a given point on a roadway or in a designated lane during one hour without the traffic density being so great as to cause unreasonable delay, hazard, or restriction to the drivers’ freedom to manoeuvre under the prevailing roadway and traffic conditions (TRB, 2000). Major attention has been given to capacity analysis methodology, because capacity estimates have a central role in the estimation of other highway performance measures (Luttinen, 2004). False estimation pollutes other reasonable traffic studies. Errors caused by inaccurate or wrong estimation of highway capacity can easily affect the results of other studies (Hwang et al., 2005). Zang (2010) developed an improved highway capacity model that is feasible and can reflect the actual traffic flow characteristics; Yao et al. (2009) developed optimisation procedure that produced good estimates of the roadway capacity and other traffic stream parameters. Tanyel et al. (2005) showed that further studies should be made to develop a more reliable capacity and performance models for Turkey. Chang and Kim (2000) presented a quantitative method for highway capacity determination by evaluating alternative approaches in developing capacity from the statistical distribution of observed headways of traffic flow in Korea. Approximated headway distribution models of free-flowing traffic on Ohio Freeways was developed by Zwahlen et al. (2007) to simulate queue buildup and delay times under congested traffic conditions. Traffic flow is a complex phenomenon and quite difficult to completely understand. Over the last fifty years, several modelling methods have been developed for vehicular traffic flow and categorised based on applicability, generability and accuracy (Hoogendoorn and Bovy, 2001). Lu (1990) also emphasised the importance of the accuracy of models for traffic flow simulation. Brockfield et al. (2004) reported that the most difficult stage in the development and use of traffic flow models is the calibration and validation stage. Validation errors of some models are as high as 60 %. The difficulty is due to lack of suitable methods for adapting the models to empirical data. Headway modelling is useful in the analysis of flow in a traffic stream (Chandra & Kumar, 2001). Highway capacity is usually determined by the minimum acceptable mean headway (Zhang et al., 2007 and Arasan and Koshy, 2003). 2 Headway is defined as the time between successive vehicles as they pass a point on a lane (Banks, 2003; Kyte & Teplay, 1999; Owolabi and Adebisi, 1996). It is usually measured in seconds. Headway measurement can be performed manually with a stopwatch and automatically with any presence-type detector or with video image processors (Salter, 1990). Headways are affected by such factors as traffic volume, ratio of large sized vehicles, road structure, daytime or night-time, and weather (Daisuke et al., 1999). Several studies have been carried out using headway modelling to analyse and solve specific traffic problems on highways (Akintayo and Agbede, 2009); Onibere et al. (1987); and Ovuworie (1980). Hoogendoorn (2005) presented a new approach to estimating the distribution of free speeds using a composite time headway distribution model. Haight et al. (1961) proposed a new statistical method for describing headway distribution of cars by classifying them as random, regular (equally spaced) or intermediate. Hossain and Iqbal (1999) found that in the flow range of 200-640 vph the exponential and log-normal distributions can best describe the headway pattern on two-lane, two-way highways. Owolabi and Adebisi (1993) found the composite exponential model to be a sound descriptor of observed headways along Zaria-Sokoto Road, Nigeria for flows ranging from 170 vph to 750 vph irrespective of whether or not motorcycles were in the traffic stream. Dawson and Chimini (1968) developed a generalised type headway model for single lane traffic flows on two-lane, single carriageways. Bham and Ancha (2006) proposed two shifted continuous distribution models, the lognormal and gamma models for preferred time headway and time headway of drivers in steady state car-following. Yuichi and Shizuma (1989) presented a practical method for estimating the headway distribution based on the experimentally observed data of the number of vehicles passing in a certain time interval theoretically as a general case of gamma-type headway distribution model. Parameters of headway distribution models are usually estimated from the field data. The field data must be reliable and the parameters must be properly estimated before the models can be applied. Hagring (2000) highlighted three techniques usually employed in headway parameters estimation: the method of moments, the maximum-likelihood method and the least-squares method. As highlighted earlier, several researchers have used these techniques to develop simple mathematical models based on Poisson and Erlang distributions to estimate headway parameters for flows at low levels. Complex mathematical headway distribution models such as Log- 3 normal, Pearson Type III and Hyperlang have been employed in parameter estimation of moderate and high traffic flow levels. However, for cases in which the random traffic-based Poisson does not hold or other mathematical headway distributions require great field measurements or do not fit the real-world data closely, researchers are increasingly developing simulation models to analyse and solve complex flow problems in engineering (Agbede, 1995; Kosonen, 1999). Brockfield et al. (2007) reported that simulation models are becoming increasingly important tools in modelling transportation systems. Metcalfe (1997) explained that simulation techniques are useful in complex situations for which appropriate formulae are not known although they are far less convenient than mathematical models. It is also important to apply appropriate and reasonable initial and boundary conditions to the simulation models to ensure reliability of output results (Agbede and Adegbola, 2003) Lee et al. (2008) developed a simulation tool using stand-alone application which adopts object-oriented approach and JAVA as the main application programming interface (API) to forecast traffic congestion level. Zwahlen et al. (2007) suggested that it would be advantageous to convert hourly traffic counts into corresponding cumulative headway using the least-squares method. They employed this method to generate hyperbolic fit models to approximate headway distributions of free-flowing traffic on Ohio Freeways for work zone traffic simulations. 1.2 Research Problem In spite of the global economic recess, vehicle ownership is continuing to increase in cities of the world including Nigeria. The consequences of this in Ibadan metropolis, where there is no corresponding sustainable land use patterns and transportation schemes is traffic congestion. Dynamic traffic data capturing and analysis systems are necessary to assist the civil engineers on the improvement schemes to ameliorate the problem. However, the challenges and cost of these systems are enormous for Oyo State and the eleven Local Government Areas constituting the Ibadan metropolis. Previous studies have shown that several mathematical traffic flow models developed to analyse congestion cannot be easily generalised or adapted to varying roadway, traffic and control conditions. In addition, validation errors of some models are as high as 60.0 %. In pursuit of the objective of minimising traffic congestion in 4 parts of the Ibadan metropolis, headway simulation models were developed for the analysis of flow on some selected two-lane highways characterised by heavy traffic. 1.3 Study Area Nigeria is connected by a network of roads as shown in Fig. 1.1. The two-lane roads form its major component particularly in Oyo State. Ibadan is the capital of Oyo State, one of the thirty-six states in Nigeria. The metropolitan area of Ibadan is o o o approximately on Latitudes 7 15'and 7 30' North of the Equator; and Longitudes 3 o 45' and 4 00' East of the Greenwich Meridian (Ayeni, 2002). The road network connecting the eleven Local Government Areas in the metropolis (Fig. 1.2) is vast and central to the socioeconomic activities of the people. A network of the roads studied (Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona-Apata) and some other principal roads in the metropolis are shown in Fig. 1.3. Two of the roads studied, J Allen-Oke Bola and Odo Ona-Apata are sections of Obafemi Awolowo (formerly Lagos By-pass) and Ibadan-Abeokuta roads respectively. These roads are under the jurisdiction of the federal government. The Odo Ona-Apata road serves as a link to the Nigerian National Petroleum Corporation (NNPC) depot in Ibadan. The road also connects Ibadan to Abeokuta, the Ogun State capital. The J Allen-Oke Bola is a link road to the Central Business District (CBD) of the metropolis (Dugbe and environs). The third road, Total Garden-Agodi Gate is under the purview of the Oyo State government. It links some areas in the metropolis with the University Teaching Hospital (UCH) and the Oyo State Secretariat. Traffic streams on J Allen-Oke Bola and Odo Ona-Apata roads are shown in Plates 1.1 and 1.2 respectively. 1.4 Aim and Objectives The aim of this study is to formulate a rational procedure for minimising highway traffic congestion using germane traffic parameters such as headway and flow. The objectives of this study are as follows: i. To determine the parameters that contribute to congestion of purposively selected roads in Ibadan metropolis. ii. To develop models for representing and replicating the parameters. 5 iii. To evolve mechanisms for traffic flow enhancement and congestion reduction on the roads under study. Fig. 1.1. Nigeria's road network Source: GEOATLAS (2011) 6 Fig. 1.2. Ibadan metropolitan area’s road network Source: Ayeni (2002) 7 1 3 2 Fig. 1.3. Network of some principal roads in Ibadan metropolis Source: Tele Atlas Africa (2007) 1 Total Garden-Agodi Gate road 2 J Allen-Oke Bola road 3 Odo Ona-Apata road 8 Plate 1.1. Traffic stream on J Allen-Oke Bola road (14 January, 2009; before dualisation of the road) Plate 1.2. Traffic stream on Odo Ona-Apata road (23 April, 2009; 10:12 a.m.) 9 1.5 Justification Traffic congestion is a common feature on highways in many cities of the world including Ibadan, Nigeria. Previous studies have shown that several mathematical traffic flow models developed to analyse congestion cannot be easily generalised or adapted to varying situations. In addition, validation errors of some models are as high as 60.0 %. There is therefore a need to formulate a rational procedure for minimising highway traffic congestion using germane traffic parameters such as headway and flow. The mechanisms should be able to enhance traffic flow and reduce congestion on the two-lane highways under study in Ibadan, Nigeria. The system should also be replicable and adaptable for efficient and effective management of other two-lane highways in many cities of the world. 10 CHAPTER 2 LITERATURE REVIEW 2.1 Traffic Flow The scientific study of traffic flow had its beginning in the 1930s with the application of probability theory to the description of road traffic (Adams, 1936). However, the evolving discipline now known as traffic flow theory was instigated in the 1950s by the works of many researchers: Wardrop (1952), Pipes (1953), Lighthill and Whitham (1955), Newell (1955), Webster (1957), Edie and Foote (1958) and Chandler et al. (1958). With the advent of personal computers, the research and application of traffic flow theory continues: Bagchi and Maarseveen (1980); Cremer and Papageorgiou (1981); Junevicius and Bogdevicius (2009); Arasan and Arkatkar (2010); Mallikarjuna and Rao (2010). Traffic flow phenomena are associated with a complex dynamic behaviour of spatiotemporal traffic patterns. A spatiotemporal traffic pattern is a distribution of traffic flow variables in space and time. As a result, measurement of the variables of interest for traffic flow theory is in fact the sampling of a random variable (Hall, 1997). Therefore, only through a spatiotemporal analysis of real measured traffic data the understanding of features of real traffic is possible (Kerner, 2009). Traffic flow theories seek to describe in a precise mathematical way the interactions between the vehicles and their operators and the infrastructure. The inclusion of human factors into road traffic flow modelling equations has further increased the complexity associated with traffic flow analysis (Maerivoet and Moor, 2005); Akanbi et al., 2009). The theories are an indispensable construct for all models and tools that are being used in the design and operation of highways (Gartner et al., 1997). 2.1.1 Traffic Flow Parameters Traffic flow can generally be described in terms of three parameters: the mean speed v, the traffic flow rate q, and the traffic density k (Payne, 1979; Wu, 2002). The three parameters are associated with each other by the equilibrium relationship:    (2.1) The speed and the density describe the quality of service experienced by the traffic stream while the flow rate (often shortened as flow) measures the quantity of the 11 stream and the demand on the highway facility (Salter and Hounsell, 1996; May, 2001). 2.1.2 Measurement of Traffic Flow Measurement at a point, by hand tallies or pneumatic tubes, was the first procedure used for traffic data collection. This method is easily capable of providing volume counts and therefore flow rates directly, and with care can also provide time headways. The technology for making measurements at a point on freeways changed over 30 years ago from using pneumatic tubes placed across the roadway to using point detectors (May et al. 1963; Athol 1965). The most commonly used point detectors are based on inductive loop technology, but other methods in use include microwave, radar, photocells, ultrasonics, and television camera. Traffic flow rate, often shortened as flow, is simply defined as the number of vehicles passing some designated highway point in a given time interval (Mannering and Kilareski, 1997). It is typically expressed as an hourly rate, that is, in number of vehicles per hour. Flow rates are collected directly through point measurements, and by definition require measurement over time. They cannot be estimated from a single snapshot of a length of road. Flow rates are usually expressed in terms of vehicles per hour, although the actual measurement interval can be much less. Concern has been expressed, however, about the sustainability of high volumes measured over very short intervals (such as 30 seconds or one minute) when investigating high rates of flow. The 1985 Highway Capacity Manual (HCM 1985) suggests using at least 15- minute intervals, although there are also situations in which the detail provided by five minute or one minute data is valuable. 2.1.3 Traffic Flow Regimes Flow regimes (phases and states) are used to describe operational characteristics of flow in a traffic stream. The regimes are generally classified into two (Colombo, 2002): 1. Free-flow traffic occurs at low densities and as such vehicles are able to freely travel at their desired speed. The traffic flow is unrestricted, that is, no significant delays are introduced due to possible overtaking manoeuvres. The flow is said to be stable since the effects of small and local disturbances in the temporal and spatial patterns of the traffic stream are insignificant. 12 2. Congested flow is characterized by the decrease in speed, the increase in travel time and the increase of vehicle’s queue on the road (Lee et al., 2008). The congested flow may further be classified into two phases based on the empirical findings of Kerner and Rehborn (1996): i. Synchronised flow, also called capacity flow by Maerivoet and Moor (2005). It is characterised by low speed but high continuous flow. In this state, the average headway is minimal and maximum flow is attained. ii. Wide-moving jam describes low speeds and low flows. 2.2 Traffic Congestion Generally, traffic congestion occurs when traffic demand is greater than the capacity of the road. Traffic congestion is considered to be at extreme level when vehicles are fully stationary for long periods of time (Lee et al., 2008). Traffic congestion can be characterised based on three factors: • Slower speed of vehicles • Longer travel times • Increased queuing 2.2.1 Causes of Traffic Congestion The US Federal Highway Administration (FHWA, 2005) has classified seven main causes of traffic congestion as: • physical bottlenecks/ capacity • traffic incidents • work zones • weather • traffic control devices • special events and • fluctuation in normal traffic 2.2.2 Negative impacts of Traffic congestion Andrew (2004) opined that traffic congestion has a number of negative effects which include: 13 i. Wasting time of motorists and passengers ("opportunity cost"). As a non- productive activity for most people, congestion reduces regional economic health. ii. Delays, which may result in late arrival for employment, meetings, and education, resulting in lost business, disciplinary action or other personal losses. iii. Inability to forecast travel time accurately, leading to drivers allocating more time to travel "just in case", and less time on productive activities. iv. Wasted fuel increases air pollution and carbon dioxide emissions (which may contribute to global warming) owing to increased idling, acceleration and braking. Increased fuel use may also in theory cause a rise in fuel costs. v. Wear and tear on vehicles as a result of idling in traffic and frequent acceleration and braking, leading to more frequent repairs and replacements. vi. Stressed and frustrated motorists, encouraging road rage and reduced health of motorists. vii. Emergencies: blocked traffic may interfere with the passage of emergency vehicles travelling to their destinations where they are urgently needed. viii. Spill over effect from congested main arteries to secondary roads and side streets as alternative routes are attempted ('rat running'), which may affect neighbourhood amenity and real estate prices. 2.2.3 Congestion reduction strategies Aworemi et al. (2009) came up with the following strategies to ameliorate traffic congestion on Nigerian roads. i. Enhanced transport coordination: the various modes of public transport including intermediate public transport have to work in tandem. They should complement rather than involve themselves in cutthroat competition. Therefore there is an urgent need for a transportation system that is seamlessly integrated across all modes in Lagos State. Since the ultimate objective is to provide an adequate and efficient transport system, there is a need to have a coordinating authority with the assigned role of coordinating the operations of various modes (Sanjay, 2005). This coordinating authority may be appointed by the state of federal government and may have representatives from various stakeholders such as private taxi operators, bus operators, railways and the government. The key objective should be to attain the integration of different modes of transport to improve the efficiency of service delivery and comfort for commuters, which in turn can 14 dissuade the private car owners from using their vehicles and thereby reducing the number of cars on the roads which can eventually lead to congestion reduction. ii. Road Capacity Expansion: road widening is often advocated as ways to reduce traffic congestion. However it tends to be expensive and may provide only modest congestion reduction benefits over the long run, since a significant portion of added capacity is often filled with induced peak period vehicle traffic. A large amount of additional capacity would be needed to reduce urban traffic congestion. Some research indicates that roadway capacity expansion provides only slight reductions in urban traffic congestion (Texas Transportation Institute, 2009). iii. Improved road infrastructure: this include, • Junction improvement • Grade separation using bridges (or, less often tunnels) freeing movements from having to stop for other crossing movement • R eversible lanes, where certain sections of highway operate in the opposite direction on different times of the day or days of the week, to match asymmetric demand. This may be controlled by variable message signs or by movable physical separation. • Bus lanes, for example, the Bus Rapid Transit (BRT) • Separate lanes for specific user groups (usually with the goal of higher people throughput with fewer vehicles). iv. Supply and demand: congestion can be reduced by either increasing road capacity (supply) or by reducing traffic (demand). Capacity can be increased in a number of ways, but needs to take account of latent demand otherwise it may be used more strongly than anticipated (Hermann, 2006). Increased supply can include, adding more capacity over the whole of a route or at bottlenecks, creating new routes, and traffic management improvements. Reduction of demand can include, parking restriction, park and ride, reduction of road capacity, congestion pricing, road space rationing, and incentives to use public transport, telecommuting, and online shopping. v. Intelligent transportation system: intelligent transportation systems include the application of a wide range of new technologies, including traffic reporting via 15 radio or possibly mobile phones, parking guidance and information, automated highway systems, traffic counters, navigation systems, transit improvement and electronic charging. These can provide great reduction in congestion as well as variety of transportation improvements. (Ogilvie et al., 2004). vi. Encouraging “Green Modes”: any traffic congestion reduction strategy in Lagos should encourage development of “green modes” such as bicycles, cycle rickshaws and pedestrians (Sanjay, 2005). First of all, the safety concerns of cyclists and pedestrians have to be addressed adequately. For this purpose, there has to be a segregated right-of-way for bicycles and pedestrians. Apart from reducing congestion, it will also help improve safety, increase the average speed of traffic and reduce emissions resulting from slow speeds. To enable longer trip lengths on bicycles, bicycle technology should be improved. vii. Drivers’ enlightenment: there should be proper and adequate enlightenment for the drivers on the dangers inherent in congestion, and also dissuading them from certain congestion-causing habit such as wrong overtaking, one way driving, disobey of traffic signals and traffic wardens. 2.2.4 Analysis of Congested Flow Traffic congestion can be measured in various ways, including roadway Level of Service (LOS), average traffic speed, and average congestion delay compared with free-flowing traffic (Litman, 2005). Some researchers however claimed that there is no standard way of measuring road congestion. They described traffic congestion as a subjective quantity as perceived by road users. In the same road condition, some may feel that the road is heavily congested, while some others may feel that the road is only slightly congested (Pongpaibool et al., 2007). Kerner (2004) distinguished several congestion patterns with respect to traffic flows as: Synchronised (SP) which is further subdivided into Moving Synchronised (MSP), Widening Synchronised (WSP), Localised Synchronised (LSP). A General Pattern (GP) contains both synchronised flow and wide –moving jams. The different types of GP are Dissolving GP (DGP), a GP under weak congestion, and a GP under strong congestion. An Expanded Pattern (EP) occurs when two bottlenecks are spatially close to each other. In order to accurately estimate, automatically track, and reliably predict the above identified congested traffic patterns, Kerner et al. (2001) 16 have developed two models: Forecasting of Traffic Objects (FOTO) and Automatische StauDynamik Analyse (ASDA) Posawang et al. (2009) used artificial neural network (ANN) model that classify velocity and traffic flow into three congestion levels: light, heavy, and jam in service in the Bangkok Metropolitan Area. Duan et al. (2009) used floating car data to analyse the spatio-temporal characteristics of Shanghai traffic congestion. Aworemi et al. (2009) employed research questions to design ameliorative measures of road traffic congestion in Lagos metropolis. 2.3 Traffic Flow Modelling Generally, models are tools designed to represent a simplified version of reality (Wang and Anderson, 1982; Ackoff and Sasieni, 1986). Neelamkavil (1987) defined a model as a simplified representation of a system intended to enhance our ability to understand, explain, change, preserve, predict, and possibly control, the behaviour of a system. Eisner (1988) described models as quantitative representative of a system. A model is also regarded as an object or concept which is used to represent something else that is reality converted to a comprehensive form (Meyer, 1985). 2.3.1 Types of Models According to Ackoff and Sasieni (1986), three types of models are commonly used in science and engineering: iconic, analogue, and symbolic. i. Iconic models are images of the physical system they represent. They are either scale down (photographs, drawings, maps) or scaled up as in molecular structures. Iconic models are generally specific, concrete, and difficult for experimental purposes. ii. Analogue models are dynamic in character. Analogues use one set of properties to represent another set of properties. For example, contour lines on a map are analogues of elevation, and graphs are analogues that use geometrical magnitude and location to represent a wide variety of variables and the relationships between them. Analogue models are less concrete, but easier to manipulate than iconic models. iii. Symbolic (Mathematical) models use letters, numbers, and other types of symbols to represent variables and the relationships between them. They are the 17 most general and abstract type of models and the easiest to manipulate experimentally. Symbolic models take the form of mathematical relationships that reflect the structure of thta which they represent. When the relationships are given for steady state only, the model has static character and is described with algebraic equations only. However, dynamic mathematical models include transient as well as the steady state behaviour of a system, and are described by set of differential equations and by a set of boundary conditions. 2.3.2 Criteria for Model Selection For models to be very useful, Wilson (1968) suggested that they should be: • Small • Modular • Well documented • Use very common languages • Deal with specific rather than generalised problems. Generalised models are rarely suitable or efficient for specific use. • Avoid complex techniques, except in the case of most technical problems having little social or political content. • Provide for substantial user ability to see intermediate results, to modify the data prior to the next step, and generally intervene in the overall process of model use. Agbede (1996) also suggested the following criteria in the choice of the most appropriate model for any given system. i. It should be sufficiently simple so as to be amenable to mathematical treatment. ii. It should not be too simple so as to exclude those features which are of interest to the system under study. iii. There must be information available for model calibration. iv. The model should be the most economic one for solving the problem. A flow chart showing model usage for any typical engineering system is shown in figure 2.1. An overview of traffic flow models by Hoogendoorn and Bovy (2001) is presented in Table 2.1. 18 Collect data and observe system Compile and interpret available data Collect data and observe system Conceptualisation History matching Prepare data for Prepare data for model using model using estimated estimated parameters parameters Interpret results Compare results with observed data Improve Conceptual model Good Poor comparison comparison Sensitivity runs Yes More data needed? No Predictive simulation runs Fig 2.1: Model usage flow chart Source: Agbede (1996) 19 Table 2.1: Overview of traffic flow models AR: area of application (cross-section, single lane stretches, multilane stretches, aggregate lane stretches, discontinuities, motorway network, urban network, and other). Source: (Hoogendoorn and Bovy, 2001) 20 2.3.3 Traffic Simulation Simulation is a particular type of modelling approach. It is quantitative and usable in place of the real system in order to represent the behaviour of that system (Eisner, 1988). Simulation is more of an art; it does not have specific theory that can be applied to solve problems. It is mastered more by practice, by actually modelling and simulating small systems (Hira, 2001). Simulation modelling is usually associated with complex processes which cannot be readily described in analytical terms. It is increasingly being used in traffic flow studies to satisfy a wide range of requirements such as: • Highway capacity estimation (Dey et al., 2008) • Intelligent transportation and intelligent vehicle simulations (Yin et al. 2009) • Evaluation of alternative treatments in traffic management • Design and testing of new transportation facilities (e.g., geometric designs) • Operational flow models serving as a sub-module in other tools (e.g. model- based traffic control and optimisation, and dynamic traffic assignment) • Training of traffic managers • Safety Analysis (Lieberman & Rathi, 1997; Hoogendoorn & Bovy, 1998). 2.3.4 Traffic Simulation Models Traffic simulation models are designed to emulate the behaviour of traffic in a transportation system over time and space to predict system performance. Simulation model runs can be viewed as experiments performed in the laboratory rather than in the field. The models include algorithms and logic to: • generate vehicles into the system to be simulated. • move vehicles into the system. • model vehicle interactions. Simulation models are becoming increasingly popular and effective tools for managing traffic flows (Gibson and Ross, 1977). Traffic flows are dynamic in nature and involve complex processes, which are difficult to characterise numerically (Radilat and Tiller, 1981). Traffic simulation models have unique characteristics because of the interactions among the drivers, vehicles, and roadway. Simulation modelling has evolved as a tool with the advent of the computer. Simulation models are mathematical/logical representations (or abstractions) of real-world systems, which take the form of software executed on a digital computer in an 21 experimental fashion (Lieberman and Rathi, 1997). Traffic flow simulations can be used to optimise traffic flows and capacity. Modelling gives the engineer the ability to inexpensively choose the best of alternatives before actually committing financial resources to the implementation of the improvement on the field (Kubel et.al., 1978; Li et al. 2008). During its more than forty years long history computer simulation in traffic analysis has developed from a research tool of limited group of experts to a widely used technology in the research, planning, demonstration and development of traffic systems (Pursula, 1999). In general, simulation is defined as dynamic representation of some part of the real world achieved by building a computer model and moving it through time (Drew 1968). The use of computer simulation started when D.L. Gerlough published his dissertation: "Simulation of freeway traffic on a general-purpose discrete variable computer" at the University of California, Los Angeles, in 1955 (Kallberg 1971). From those times, computer simulation has become a widely used tool in transportation engineering with a variety of applications from scientific research to planning, training and demonstration. Several researchers have applied traffic flow theory to develop models to simulate traffic flows in many areas. Bandyopadhyay (2001) developed a computer simulation model for traffic flow on a city road in Calcutta having mixed traffic conditions by considering five types of vehicles: tram, double-decker bus, single-decker bus, minibus and car. A realistic and operational macroscopic traffic flow simulation model which requires relatively less data collection efforts was developed, calibrated and applied to simulate a section of the 1-64-40 corridor in the St. Louis metropolitan area by Haefner and Li (1998). Putcha et al. (2006) developed a new traffic flow model to predict the speed of the traffic in terms of the mean free flow speed and the density. Adebisi and Chiejina (1983) evaluated and calibrated some appropriate mathematical traffic flow models to demonstrate that a workable theoretical and empirical basis exists for characterising bus travel times which provided local bus transit planners in Kaduna an analytical framework. 2.3.5 Classifications of traffic simulation models The availability of adequate mathematical models is a prerequisite to describe and solve traffic flow problems. Generally speaking, mathematical modelling of traffic flow results in a nonlinear dynamic system. The nonlinear and complicated characteristics of flow dynamics makes it difficult to have a universal traffic flow model that applies to all traffic situations at all times. 22 Generally, simulation models are classified into two as highlighted in the Federal Highway Administration (FHWA) Report on microsimulation process. 1. Classification based on the detail of the system a. Microscopic Models: These models simulate the characteristics and interactions of individual vehicles. They essentially produce trajectories of vehicles as they move through the network. The processing logic includes algorithms and rules describing how vehicles move and interact, including acceleration, deceleration, lane changing, and passing manoeuvres. Microscopic models are potentially more accurate than macroscopic simulation models. However, they employ many more parameters that require calibration. b. Mesoscopic Models: These models simulate individual vehicles, but describe their activities and interactions based on aggregate (macroscopic) relationships. Typical applications of mesoscopic models are evaluations of traveller information systems. For example, they can simulate the routing of individual vehicles equipped with in- vehicle, real-time travel information systems. The travel times are determined from the simulated average speeds on the network links. The average speeds are, in turn, calculated from a speed-flow relationship. Most of the parameters of the microscopic models cannot be observed directly in the field (e.g., minimum distances between vehicles in car-following situations). Chen et al. (2010) combined the mesoscopic headway distribution model and the microscopic vehicle interaction model to simulate different driving scenarios, including traffic on highways and at intersections. A mesoscopic approach with groups of vehicles is used in CONTRAM (Leonard et al. 1978), a tool for analysis of street networks with signalised and non-signalised intersections. c. Macroscopic Models: These models simulate traffic flow, taking into consideration aggregate traffic stream characteristics (speed, flow, and density) and their relationships. Typically, macroscopic models employ equations on the conservation of flow and on how traffic disturbances (shockwaves) propagate in the system. They can be used to predict the spatial and temporal extent of congestion caused by traffic demand or incidents in a network; however, they cannot model the interactions of vehicles on alternative design configurations (Chakroborty, 2006). Macroscopic traffic flow simulation models are easier and less costly to maintain. They are appropriate if the model development time and resources are limited, 23 although, they carry a risk that their representation of the real-world may be less accurate, less valid or inadequate (Lieberman and Rathi, 1997). Also, the parameters of the macroscopic models (e.g., capacity) are observable in the field. Most of the well known macroscopic applications in traffic flow analysis area originate from the late 1960's or the early 1970's. The British TRANSYT-program (Byrne et al. 1982) is an example of macroscopic simulation of urban arterial signal control coordination and the American FREQ- and FREFLO-programs (Byrne et al. 1982) plus the corresponding German analysis tool (Cremer,1979) are related to roadway applications. 2. Classification based on randomness in traffic flow a. Deterministic Models: These models have no random variables; all entity interactions are defined by exact relationships (mathematical, statistical or logical). For example, it is assumed that all drivers have a critical gap of 5 s in which to merge into a traffic stream, or all passenger cars have a vehicle length of 4.9 m. b. Stochastic Models: These models have processes which include probability functions. Stochastic simulation models have routines that generate random numbers. The sequence of random numbers generated depends on the particular method and the initial value of the random number (random number seed). Changing the random number seed produces a different sequence of random numbers, which, in turn, produces different values of driver-vehicle characteristics. Stochastic models require additional parameters to be specified (e.g., the form and parameters of the statistical distributions that represent the particular vehicle characteristic). More importantly, the analysis of the simulation output should consider that the results from each model run vary with the input random number seed for otherwise identical input data. Deterministic models, in contrast, will always produce the same results with identical input data. 2.3.6 Traffic simulation model building Lieberman & Rathi (1997) highlighted the basic steps in traffic simulation model development process as the following: • Define the problem and model objectives • Define the system • Develop the model 24 • Calibrate the model - calibration is the process of quantifying model parameters using real-world data. It is often a difficult and costly undertaking. • Model verification - verification is a structured regimen to provide assurance that the model performs as intended. • Model validation - validation establishes that the model behaviour accurately and reliably represents real world system being simulated, over a range of conditions anticipated. Model validation involves the following activities. – Acquiring real world data which, to the extent possible, extends over the model’s domain. – Reducing and structuring these empirical data so that they are in the same format as the data generated by the model. – Establishing validation criteria, stating the underlying hypotheses and selecting the statistical tests to be applied. – Developing the experimental design of the validation study, including a variety of scenarios to be examined. – Performing the validation study. – Identifying the causes for any failure to satisfy the validation tests and repairing the model accordingly. The validation activity is iterative. As differences between the model results and real world data emerge, the developer must “repair” the model, then revalidate. Considerable skill and persistence are needed to successfully validate a traffic simulation model. • Documentation - traffic simulation models, as is the case for virtually all transportation models, are data intensive. To make good use of these models, users must invest effort in data acquisition. 2.3.7 Vehicle generation algorithm Jia ( 2008) generated uniform random variables to simulate poisson arrival of cars on a freeway during a period of heavy flow. The probability density function of X is   0.15.. for x ≥ 0.5 (2.2) Let X = the time headway for two randomly chosen consecutive cars. (0.5 s is regarded as the minimum average time headway between the two cars). 25 After generating uniform random variables Ui ∈ (0,1) U = 0.15..i (2.3)   ln . /0.15+0.5 (2.4) Depending on a random number between (0.1) with uniform distribution, the vehicles generated were assigned into different routes. Vehicle generation algorithm can also be developed by considering the mean headway (H) of vehicles (as given in equation 2.4) to generate vehicles at the beginning of the simulation run.   3600/" (2.5) If the model uses the shifted negative exponential distribution to simulate the arrival of vehicles at the network entry node instead of the uniform distribution, then vehicles will be generated as time intervals: h=(H-h1)[ln(1-Rn)]+H-h1 (2.6) where: h = headway (in seconds) separating each generated vehicle h1 = specified minimum headway (e.g., 1.0 s) Rn = random number (0 to 1.0) 2.4 Headway Distribution Models Headway is the time interval between two consecutive vehicles passing an observation point (Luttinen, 2004). It has been described as the fundamental building blocks of traffic flow, because the inverse of the mean headway is the rate of flow (Dawson and Chimini, 1968; Salter and Hounsell, 1996). The traffic flow reaches its maximum value at the minimum value of headway. At any period of time, the individual values of headway vary greatly. The extent of these variations depends largely on the highway and the traffic conditions. At low flow regimes, headway values vary from zero between overtaking Hagring (1996) listed three requirements that headway distributions need to fulfil: they must fit the observed data well, describe driver behaviour adequately, and be useful for prediction. Most headway distribution models are probability distribution models (Abdul-Magd, 2007; Chakroborty, 2006; Salter, 1990). These 26 models are generally categorised into two classes: free traffic models and constrained traffic flow models (Helbing, 2001; and Nagatani, 2002). Free traffic models assume random arrival of vehicles, examples are negative exponential distribution, displaced negative exponential distribution (or shift negative exponential distribution), log- normal distribution, Pearson Type III distribution and Erlang distribution. The second is probability distribution models developed for both free traffic flow and constrained traffic flow. Although these models are more practical in urban transportation system, the parameters of the models are complicated (Zhang et al., 2007). Examples are bunched exponential distribution and double displaced negative exponential distribution (Cowan, 1975). 2.4.1 Headway Distribution Models for Free Flow Negative exponential distribution model (M1): This is the basic model for free flow distribution models. It assumes poisson arrivals of vehicles and it is valid when traffic flows are light. Detail descriptions of negative exponential distribution are given by many researchers: Kinzer (1933), Tolle (1971), Cowan (1975), Leuzbach (1988), Arasan and Koshy (2002). M1: f (x) =0 (x < 0) (2.7) f (x) = 1− −λx e (x ≥ 0) (2.8) λ is the flow rate (vehicles per time unit). M2: f (x) =0 (x <τ ) (2.9) ( ) = 1− −γ (x−τ ) f x e (x ≥τ ) (2.10) M3 (Erlang Distribution): f (x) =0 (x < 0) (2.11) (kλ) kx = k −1 −kλx f (x) ∫ x e dx 0 (k −1)! (x ≥ 0) (2.12) M4 (Pearson Type III Distribution - Gamma Distribution): f (x) =0 (x < 0) (2.13) λkx = k −1 −λx f (x) ∫ x e dx (x ≥ 0) (2.14) 0 Γ(k) M5 (Log-normal Distribution): 27 f (x) = 0 (x < 0) (2.15) x 1 f (x) = exp[ (ln −µ )2− x σ 2∫ 2 ]dx (x ≥ 0) (2.16) 0 2πσ n n ∑ ln 2xi ∑ (ln xi − µ ) where µ = 1 ;σ 2 = 1 n n −1 (2.17) 2.4.2 Headway Distribution Models for Constrained Flow M6 (Bunched Negative Exponential Distribution): It was first proposed by Cowan (1975). This model overcomes the shortcomings of negative exponential distribution and the displaced negative exponential distribution in predicting headway probabilities for small headways and for high arrival flow rates. The model assumes that a proportion of vehicles, θ, are tracking behind preceding vehicles at headway of τ. These vehicles are bunched. The rest are travelling at headways greater than τ and are described as free vehicles. The formula is as follows: f (x) =0 (x < τ) (2.18) ( ) = 1 − (1 − θ ) −γ (x−τ )f x e (x ≥ τ) (2.19) Akcelik and Chung (1994) gave a detail description of the model in detail and gave the results of its calibration using real-life data for single-lane traffic streams and simulation data for multilane traffic streams. The traffic streams of the study sites are all unqueued. M7 (General Bunched Exponential Distribution): This model is also developed by Cowan (1975). It is a further generalisation of the bunched exponential model and gives the tracking headway a general distribution as well. This model is certainly more realistic but more complex. f (x) = 0 (x < 0) (2.20) x −γuf (x) = θΒ(x) + (1 −θ )∫ Β(x − u)γe du (x ≥ 0) (2.21) 0 M8 (Double Displaced Negative Exponential Distribution (DDNED)): This model is developed by Griffiths and Hunt (1991). f (x) = 0 (x < τ) (2.22) = φλ λ1 ( x−τ )f (x) e + (1− φ)λ λe 2 ( x−τ ) (x ≥ τ) (2.23) 1 2 Where 0.5 ≥ φ > 0 . 28 The parameter Φ is weighting factor, τ is the displacement parameter, and λ1, λ2 are constants associated with the traffic flow. Sulliavan (1994) observed that DDNED can model smaller headways more accurately than the Bunched Negative Exponential model. M9 (Composite Distribution): f (x) = 0 (x < 0) (2.24) f (x) = (1−θ )F1 (x) + θF2 (x) (x ≥ 0) (2.25) where θ is the proportion of the followers F1(x) is the distribution for leaders, usually a negative exponential distribution F2(x) is the distribution for followers. Although the models above can fit the real traffic situation well, the derivation of unknown parameters is complicated. In Table 2.2, a comparison of headway distribution models is presented. 2.4.3 Parameter estimation and calibration of headway models The process of headway model development consisted of testing the field data by using a number of existing simple models and progressing with increasing degrees of complexity until an acceptable match between the field data and the model output is obtained (Khasnabis & Heimbach, 1980). Several researchers have employed simple mathematical models based on Poisson and Erlang distributions to estimate headway parameters for flows at low levels. Complex mathematical headway distribution models such as Log-normal, Pearson Type III and Hyperlang are however employed in parameter estimation of high flows. Parameters of headway distribution models must be properly estimated before the models can be applied. Their goodness of fit is significantly affected by the quality of the estimated parameters (Zhang et al., 2007). Hagring (2000) highlighted three methods usually employed in headway parameters estimation: the method of moments, the maximum-likelihood method and the least-squares method. Zwahlen et.al, (2007) employed the least-squares method to generate hyperbolic fit distributions to approximate headway distributions of free-flowing traffic on Ohio Freeways. 29 Table 2.2: Comparison of headway distribution models Distribution Research Addition Equations Model Objective or Character of Study Site M1: Negative f ( x ) = 0 Random arrival - Exponential f ( x ) = 1 − e − λ x under light Distribution traffic volume. M2: f (x) = 0 (x<τ ) Random arrival - Displaced under light Negative f (x) = 1 − −γ ( x−τ ) e (x ≥τ ) traffic volume. Exponential Distribution M3: Erlang f (x) = 0 (x < 0) Random arrival - Distribution under light x (kλ) k = k −1 −kλx traffic volume. f (x) ∫ x e dx 0 (k −1)! (x ≥ 0) M4: Pearson f (x) = 0 (x < 0) Random arrival - Type III under light λk traffic volume. x k −1 −λx f (x) = ∫ x e dx Data collected 0 Γ(k) from highway of U.S.A. were (x ≥ 0) tested. Volumes from 551 to 1369 vph. Not fit well. f (x) = 0 (x < 0) - x 1 2 f (x) = 2 ∫ exp[− (ln x−µ ) 2 σ ]dx Random arrival 0 2πσ under light traffic volume. (x ≥ 0) Data collected where from highway of U.S.A. were n n M5: Log- ∑ ln x ∑ 2(ln x − µ) tested. Volumes normal i i from 551 to 1 2 1 Distribution µ = ;σ = 1369 vph. Fit n n −1 better than M4. M6: Bunched f (x) = 0 (x < τ) Tested in single Different Negative lane and multi- sites with Exponential = − − θ −γ (x−τ )f (x) 1 (1 )e (x ≥ τ) lane road in different Distribution Australia. location of Widely used for lane. estimating capacity and performance of roundabouts and other unsignalised junctions. 30 M7: General Constrained No Bunched f (x) = 0 (x< 0) Traffic Flow application Exponential presented in x Distribution f (x) = θΒ(x) + (1 −θ )∫ Β − γ −γu (x u) e du the 0 literature. (x ≥ 0) M8: Double f (x) = 0 (x < τ) Study site: Using a Displaced traffic stream in hybrid Negative = φλ λ1 ( x−τ ) + − φ λ λ2 ( x−τ )f (x) e (1 ) e (x ≥ single lane in method of 1 2 Exponential busy urban area maximum Distribution τ) in U.K. Fit well likelihood with the small method and where 0.5 ≥ φ > 0 . headway as well method of as large moments to headway. derive unknown parameters M9: f (x) = 0 (x < A test was Result of Composite carried out at through + Distribution 0) single lane and left turn two-lane lane was f (x) = (1−θ)F1(x) +θF2 (x) (x ≥ signalized given. junctions, traffic 0) flow level from 500 to 2000 vph on Tokyo Expressway. 31 2.5 Highway Capacity Highway capacity can be described as the ability of a roadway to respond to drivers and vehicles. The ability of roadway is revealed as a vehicle's speed and time headway (Hwang et al, 2005). In HCM2000 (Transportation Research Board, 2000) capacity is described as maximum sustainable flow rate at which vehicles or persons reasonably can be expected to traverse a point or uniform segment of a lane or roadway during a specified time period under given roadway, geometric, traffic, environmental, and control conditions; usually expressed as vehicles per hour, passenger per hour, or persons per hour. The HCM method consists of three major steps. The first step is to find the capacity of highway facilities under ideal conditions. Second, the levels of service are selected to represent different operating qualities and to determine the maximum flow rates under these different levels of service. Finally, adjustment factors due to prevailing roadway and traffic conditions are applied to the ideal conditions to obtain the maximum flow rates at different levels of service. Capacity of a road is the major aspect for dimensioning the carriageway. The capacity corresponds to the maximum traffic volume that can be achieved by a traffic stream at a specific junction under given road and traffic conditions. For highways operating under ideal conditions, the general expression for capacity is given in equation 2.26 C = qmax (2.26) where qmax is the maximum traffic volume. However, for any segment of highways operating under non-ideal conditions, its practical capacity will normally be smaller than the basic capacity as given by equation 2.27 #$  # %∏' ' (2.27) where #$ = practical capacity C = basic capacity fj = adjustment factor for the condition j 2.5.1 Factors affecting capacity Highway capacity is affected by many factors as given by Wright (1996). The factors include: desired speed, number of lanes, separation of directions, vertical grade, composition of traffic, peak traffic factor and capacity of intersections. 32 Many of the procedures described in the HCM are based on simple tables or graphs for specified standard conditions, which must be adjusted to account for prevailing conditions different from those specified. The conditions so defined are often described in terms of ideal conditions. Ideal conditions for uninterrupted flow facilities include: • 3.65 m lane widths • 1.8 m clearance between the edge of travel lanes and the one roadside obstructions • all passenger cars in the traffic stream • a driver population comprised predominantly of regular and familiar i of the facility An ideal signalized intersection approach has • 3.65 m lane widths • level grade • no curb parking allowed on the intersection approaches • all passenger cars in the traffic stream • no turning movements at the intersection • intersection located outside the central business district • green signal available at all times Since prevailing conditions are seldom ideal, computations of capacity must be adjusted to account for departure from ideal (Oglesby and Hicks, 1982; Wright and Dixon, 2004). Prevailing conditions may be grouped into three categories: roadway, traffic or control conditions. Roadway factors include: • the type of facility and its development environment • lane widths • shoulder widths and/or lateral clearances • design speed • horizontal and vertical alignments Traffic conditions refer to the types of vehicles using the facility and how traffic flow is distributed by lane use and direction. It is well known that and heavier vehicles have an adverse effect on traffic flow in a number of ways. In addition to the distribution of vehicle types, the effects of two other 33 characteristics on capacity, service flow rates, and level of service must be considered. 2.5.2 Need for highway capacity analysis Generally, highway capacity analysis serves three purposes (Khisty and Lall, 2006; Kadiyali, 2007): i. To assess the adequacy or sufficiency of existing highway networks and to estimate when traffic growth is likely to exceed capacity; ii. To assist in the selection of the highway type and the dimensional needs of the network iii. To prepare estimates of operational improvements that are likely to be expected in the future from prospective changes in traffic control or highway geometry. In urban centres, capacity analysis is prerequisite to the development of appropriate highway development schemes (Osula, 2010). According to Coombe and Chua (1990), the subsequent improvements will have multiple effects on the highway system as follows: i. People may reschedule the timing of their trips to take advantage of the improved conditions at peak periods (peak contraction); ii. People may divert to use the improved part of the network (reassignment); iii. People switch from public transport to use their vehicles more (modal choice); iv. Improved road accessibility may encourage trips to be made to destinations further afield (redistribution); v. Improved levels of service on the road system may lead to increased rates of trip making for any given level of income, car ownership, population and employment (trip generation); vi. Improved road accessibility may lead to people buying more cars for any given income level; and vii. Improved roads may encourage land use to change, leading to population and employment changes in their vicinity. 34 2.5.3 Capacity analysis methods Capacity analysis is a procedure used to estimate the traffic carrying ability of a facility over a range of defined operational conditions. It also aids in providing tools for the analysis and improvement of existing facilities, and for planning and design of future facilities (Oguara, 2006). A principal objective of capacity analysis is the estimation of the maximum number of people or vehicles that can be accommodated by a given facility in reasonable safety within a specified time period. Planning, design, dimensioning and operation of highway infrastructures depend on the functions of the highway facility. Capacity analysis of a highway facility should furnish an answer to the question whether a road facility will be operational for a given or forecasted travel demand. A capacity analysis result should produce a yes/no statement indicating whether the facility will work (demand lower than capacity) or fail (demand higher than capacity). Two widely used highway capacity estimation methods are the Highway Capacity Manual (HCM) method and the statistical method. 2.5.3.1 The Highway Capacity Manual method This method is based on speed-volume-density relationship. The HCM is the authoritative guide for the performance of highway capacity analyses. The manual reflects over 40 years of comprehensive research by a number of research agencies. This document was prepared under the guidance of the Transportation Research Board's Committee on Highway Capacity and Quality of Service. The procedures described in the HCM cover a wide range of facilities, including streets and highways as well as facilities for transit, pedestrians, and bicyclists. Capacity analyses are performed for two general categories of facilities, those with uninterrupted flow and those with interrupted flow. Uninterrupted flow facilities include two-lane highways, freeways, and other multilane highways. The traffic flow conditions on such facilities result from interactions among vehicles in the traffic stream as well as between vehicles and the physical and ambient characteristics of the roadway (Wright, 1996). Hwang et.al (2005) pointed that whenever HCM is published, highway capacity is increased; 1,800pc/h/l (HCM, before 1986), 2,000pc/h/l (HCM, 1986), 2,200pc/h/l (HCM, 1994), 2,400pc/h/l (HCM, 2000). They claimed that previous results are due to two main reasons: previous research has not given much consideration to road conditions, traffic conditions, control conditions, technology 35 factors, which affect highway capacity. Second, previous research has used rough 15- min base traffic data. 2.5.3.2. The British Standard Approach This method is based upon empirical British research studies related to different discrete aspects of road operation and analysis. As a result of these studies, practical capacity design standards for use in rural and urban roads have evolved (May, 2001). In Table 2.3 below, the recommended design flows for two-way urban roads is shown. 36 Table 2.3: Recommended design flows for two-way urban roads Road Type Peak flows (veh/h) for carriageways of width (m) Single carriageways* Dual carriageways 2-lane* 4-lane+ 6-lane+ 2-lane+ 3-lane+ 6.1 6.75 7.3 9 10 12.3 13.5 14.6 18 6.75 7.3 11 A Urban motorway, no frontage access, grade-separation at intersections 3600 5700 B All-purpose road, no frontage access, no standing vehicles, negligible F F F cross-traffic 2000 3000 2550 2800 3050 2950 3200 4800 C All-purpose road frontage Development, side roads, pedestrian crossings, bus stops, waiting restrictions throughout the day, loading restrictions at peak hours 1100 1400 1700 2200 2500 1700 2100 2700 F *Total for both directions of flow; 60/40 directional split can be assumed; + for one direction of flow; includes division by line of refuges as well as central reservation; effective carriageway width excluding refuge width is used. Source: O’Flaherty (2001) 37 2.5.3.3 Statistical method The statistical method makes use of observed traffic volume distribution. The summary of the method are: • detecting peak hour 1 minute base volume and average speed • transferring 1 minute base data to 15 minute base one • finding time headway distribution using average volume • determining highway capacity when confidence intervals are 99%, 95% and 90%. With this method, Chang and Kim (2000) found that the estimated highway capacity is 2200pc/h/l at the 95% confidence interval. 2.5.3.4 Dynamic highway capacity estimation method This method was developed by Hwang et al. (2005). In this method a roadway capacity is assumed to be a function of the driver and vehicle conditions, vehicle speed, and time headway, as defined by equation 2.28 #  (, * , +, , (2.28) where C = capacity of roadway i. d = driver condition vc = vehicle condition s = vehicle speed h = time headway (seconds) Unit time of highway capacity estimation is one hour, equation 2.29 can be drawn #  -./0 1,  2(, * , +3 (2.29) 2.5.3.5 Safety-based capacity analysis developed by Yi et al. (2004) for Chinese highways. The development was prompted by the claim of the researchers that none of the existing capacity analysis can be readily used on Chinese highways. Numerical approach through simulation was used to find a simplified mathematical form of free flow speed based on distance headway. 2.5.4 Level of Service (LOS) The Level of Service (LOS) is a qualitative concept that has been developed to characterise acceptable degrees of congestion as perceived by motorists (O’Flaherty, 2001). It is commonly accepted as a measure of the restrictive effects of increased volume (Oglesby and Hicks, 1982). In metropolitan areas, the capacity of the road networks affects the level of service, ranging from flow conditions to congested 38 conditions on roads, and high to low frequency of services on public transport (Oluwoye, 2009). Six levels of service (Levels A through F) define the full range of operating conditions with LOS A representing the best or ideal to LOS F being the worst or forced flow condition as shown in Table 2.4. The appropriate degree of congestion to be used in planning and designing highway improvements is determined by considering a variety of factors. These factors include the desires of the motorists, adjacent land use type and development intensity, environmental factors, and aesthetic and historic values. The factors must be weighed against the financial resources available to satisfy the motorists’ desires. The service flow rate for a designated LOS is the maximum hourly rate at which vehicles reasonably can be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions. Table 2.4: Level-of-Service Characteristics Level of Service Description A Free flow with low volumes and high speeds. B Reasonably free flow, but speeds beginning to be restricted traffic conditions. C In stable flow zone, but most drivers are restricted in the freedom to select their own speeds. D Approaching unstable flow; drivers have little freedom to select their own speeds. E Unstable flow; may be short stoppages F Unacceptable congestion; stop-and-go; forced flow. 1 Source: Adapted from the AASHTO Green Book. 1995 Highway Capacity Manual (Special Report 209), Transportation Research Board, Washington, DC, Third Edition, updated 1994 39 Table 2.5 presents the relationship between highway type and location and the level of service appropriate for design as suggested by the AASHTO Green Book. Taking into consideration specific traffic and environmental conditions, the responsible highway agency should attempt to provide a reasonable and cost-effective level of service. It has been claimed that the LOS is more of an engineering tool useful for assessing and planning operational analyses. This is because it is difficult to calculate as the defined standards at which the different levels are set always depend on the specific type of traffic situation that is studied (Maerivoet and De Boor, 2005). However, Polus and Cohen (2009) have proposed a new level-of-service variable that can be easily estimated from the field data to measure the quality of the flow both inside and between platoons. 2.5.5 Acceptable Degrees of Congestion AASHTO (2001) suggests some principles to aid in deciding on the acceptable degree of congestion. • Traffic demand should not exceed the capacity of the highway even during short intervals of time. • The design traffic volumes per lane should not exceed the rate at which traffic can dissipate from a standing queue. • Motorists should be given some latitude in the choice of speeds (speeds could be related to the length of the trip). • Operating conditions should provide a degree of freedom from driver tension that is consistent with trip length and duration. • There are practical limitations to having an ideal roadway. • The attitude of motorists toward adverse operating conditions is influenced by their awareness of the construction and right-of-way costs necessary to improve service. 40 Table 2.5: Guide for Selection of Design Levels of Service Type of Area and Appropriate Level of Service Highway Rural Rural Rural Urban and Type Level Rolling Mountainous Suburban Freeway B B C C Arterial B B C C Collector C C D D Local D D D D 1 Source: Adapted from the AASHTO Green Book. 1995 Highway Capacity Manual (Special Report 209), Transportation Research Board, Washington, DC, Third Edition, updated 1994 2.5.6 Design hourly volume The design hourly volume is one-hour vehicular volume in both directions of travel in the design year selected for travel. The capacity analysis is based on the idea that for economic reasons a transport facility will never be designed to accommodate the highest possible traffic volume. In fact a certain congestion frequency is accepted. For this reason, the design hourly volume is defined as the traffic volume which occurs during the 30th largest peak hour within a year. The 30th peak hour is determined by sorting, in a descending order, the hourly traffic volumes of all 8760 hours of a year. From this list the value number 30 is Capacity selected as hourly traffic volume. It is accepted that during these 30 hours the level of service of the facility will be low. However for the rest of the time period the facility will accommodate the traffic at a required level. 2.5.7 Capacity of two-lane highways A two-lane highway is an undivided highway having one lane for use by traffic in each direction, and over-taking of slower vehicles requires the use of the opposing lane when sight distance and gaps in the opposing traffic stream permit (Salter, 1990). The principal function of two-lane highways is efficient mobility (Khisty and Lall, 2006). With a low traffic volume, the vehicle operator has wide latitude in selecting the speed at which he wishes to travel. As traffic volume 41 increases, the speed of each vehicle is influenced in a large measure by the speed of the slower vehicles. As traffic density increases, a point is finally reached where all vehicles are travelling at the speed of the slower vehicles. This condition indicates that the ultimate capacity has been reached. Capacity expansion is one way of reducing traffic congestion, although some studies indicate that this approach provide only slight reductions in urban traffic congestion (TTI, 2009). Capacity expansion is one of the approaches suggested by Aworemi et al. (2009) in addressing the consistent traffic congestion experienced by motorists on Lagos roads. 2.5.8 Capacity analysis of two-lane highways Two-lane highways can be analysed either as two-way segments obtaining traffic performance measures for both direction of travel combined or as directional segements, with each direction of travel considered separately. The following presents the simplified procedure for conducting a capacity analysis for the highway mainline: 1. Select the design year. 2. Determine the DHV. 3. Select the target level of service. 4. Identify and document the proposed highway geometric design (e.g. lane width, clearance to obstructions, number and width of approach lanes at intersections). 5. Using the HCM, analyse the capacity of the highway element for the proposed design: (a) Determine the maximum flow rate under ideal conditions (MSF); (b) Identify the adjustments for prevailing roadway, traffic and control conditions; and (d) Calculate the service flow rate (SF) for the selected level of service. The service flow rate for two-lane highways (Wright, 1996; and Oguara, 2006) is given by equation 2.30. The maximum service volume under ideal conditions is given in Table 2.6. 45  2800 % \9 % : % ; % <= (2.30) where (v/c)i = maximum volume-to- capacity ratio associated with level of service i 42 : = adjustment factor for directional distribution of traffic ; = adjustment factor for lane width and/or lateral clearance restrictions <= = adjustment factor for the presence of heavy vehicle in the traffic stream Table 2.6: Maximum service volumes under ideal conditions Level Passenger cars per hour per lane in one direction of Design speed = 113 km/h Design speed = 97 km/h Service Freeway Multi-lane Freeway Multi-lane Two-lane* A 700 700 - 650 420 B 1100 1100 1000 1000 756 C 1550 1400 1400 1300 1204 D 1850 1750 1700 1600 1792 E 2000 2000 2000 2000 2800 F ** ** ** ** ** * For both directions: level terrain segment with ideal geometries ** Unstable, highly variable Source: Adapted from Oguara (2006) 43 CHAPTER 3 METHODOLOGY 3.1 Traffic Survey In line with the objectives of this study, Traffic survey was conducted on three purposively selected heavily-trafficked two-lane highways (Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona-Apata) in the Ibadan metropolis. The selection was based on the regular traffic congestion usually experienced on some segments of these roads during morning peak period (7.00 am and 8.30 am) and evening peak period (4.00 pm and 6.00 pm). Traffic survey was conducted on the roads between February 2008 and April 2009 to capture the stream characteristics and road features. These include traffic composition, average speed of travel, location of bus-stops and notable features along the routes of study. 3.2 Traffic Data Collection Video camera technology was employed to capture headway data for this study. Early studies used pneumatic tubes for traffic data collection. This method is easily capable of providing volume counts and therefore flow rates directly, and with care can also provide time headways (Garner and Uren, 1973; Hall, 1997). More recent systems have used paired presence detectors, such as inductive loops spaced about five to six meters to provide direct measurement of volume and of time headways, as well as of speed when pairs of them are used. Owolabi and Adebisi (1993) employed these methods to collect headway data along Zaria-Samaru Road using a pen recorder instrument connected to an automatic traffic counter and simultaneously monitored flows with the same device. Video camera technology is a more recent method of traffic data collection (Hall, 1997). In its earliest application, video cameras were used to acquire data in the field, which was then subsequently played back in the laboratory for analysis. In these early implementations lines were literally drawn on the video monitor screen for data reduction. This procedure has been automated and the data reduction can now be conducted simultaneously with data acquisition. The video camera used for this study is SONY HDR-HC3 camcorder. The detail operation of the camera is given in Appendix A1. 44 3.2.1 Headway data capturing and extraction At various times within the period of traffic survey, some sections of the roads were focused in the field of a Sony HDR-HC3 Camcorder (Plate 3.1). Headway data were captured during morning peak period (7.00 am and 8.30 am) and evening peak period (4.00 pm and 6.00 pm) from Monday to Friday of each week. The video data recorded in Digital 8 camera tapes was transferred to compact discs in mpeg format. The compact discs were played on a computer using Media Player software, which allowed for variable play speed settings at normal, slower or faster speed. The media player also had enhancement option to move the video forward or backward one frame at a time. This made it a little easy to record times successive vehicles pass the selected reference line on the screen for the exercise. The headway data was partitioned into 15-minute time intervals. The vehicle counts for each 15-minute time period were multiplied by 4 to obtain the hourly traffic volume (HCM 2000). 3.3 Headway Modelling Process 3.3.1 Theoretical Headway Generation Algorithm The following steps were employed to generate theoretical headways of traffic streams based on the composition of observed headways. 1. Define headway group Gi. (i) hi∈Gi (3.1) (ii) di≤ hi∏   .? 1  *@ (3.14) where C = Practical capacity V = flow rate kc = congestion factor fi = adjustment for factor i 3.5.1 Determination of Adjustment Factors 1. Adjustment factor for highway conditions (f1) A   BCA: (3.15) We = effective lane width This was the average width of each lane actually available for use by the motorists. Wd = designed lane width The designed lane width for all the roads was 3.65 m 2. Adjustment factor for traffic stream characteristics (f2)   1  E F G D C100 (3.16) M = percentage of motor-cycles in the traffic stream T = percentage of tankers (3-axle or more) in the traffic stream 4. Adjustment factor for adequacy of traffic control devices (f3) A maximum value of 1 is assigned when effective and efficient traffic control devices are provided on the road.   H 1 I J(KLM . 0 N  N 1 I OPL(KLM/5QR (3.17) . 52 5. Adjustment factor for roadside activities including on-street parking (f4) A maximum value of 1 is assigned when there are no roadside activities such as mobile shops and on-street parking on the roadway.   H 1 I TUP S 0 N  N 1 I L9MVVMV+ R (3.18) S 3.7 Statistical Analysis Non-parametric tests for differences between hyperbolic fit distributions of the observed and simulated headways were carried out using Kolmogorov-Smirnov goodness-of-fit test. The Kolmogorov-Smirnov test (KS-test) tries to determine if two data sets differ significantly (Oyawale, 2005). The KS-test has the advantage of making no assumption about the distribution of data. It is non-parametric and distribution free. Kolmogorov-Smirnov test is preferred because it is more efficient than the Chi-square test for small samples (Metcalfe, 1997; Johnson, 2001). Analysis of Variance (ANOVA) of the simulation results versus the field data were carried out with suitable statistical packages. The validation error was computed with equation 3.19.   ∑XYZ[Y\]^_X ∑Y \]^_ (3.19) sim field where C and C are simulated and field capacities respectively. Brockfeld et al. (2004) and proposed that the absolute error a model produces is related to difference in simulated and observed traffic flow variable. 53 Plate 3.1. Sony HDR-HC3 Camcorder Plate 3.2. Traffic Flow Simulator Screen 54 CHAPTER 4 RESULTS AND DISCUSSIONS 4.1 Traffic Survey Results 4.1.1 General Summary The summary of preliminary traffic survey has been categorised into three: roadway conditions; traffic stream compositions; and control devices as shown in Table 4.1. The visual assessment of the horizontal and vertical alignments of the roads under study showed no technical defects. The correctness of this assessment was demonstrated in the improvement scheme carried out on J Allen-Oke Bola after the conduct of the traffic survey: the horizontal alignment was maintained and; the new profile was kept close to the existing profile. Road side activities such as on-road marketing, vulcanising and mobile shops for small businesses were visible on the shoulders of all the roads. On-street parking were also noticed on the three roads. Traffic streams consisted mainly of passenger cars although the proportion of motor cycles (11 %) is considered appreciable on J Allen-Oke Bola road. Traffic control was done mainly by the traffic wardens. Many of the road users disregarded the information conveyed by other traffic regulatory devices (markings and signs) on the roads. 55 Table 4.1: Summary of preliminary traffic survey Road Name: Total Garden- J Allen-Oke Bola Odo Ona-Apata Agodi Gate Roadway Conditions: Number of Lanes 2 2 2 Lane width (m) 3.55 3.65 3.65 Effective lane width (m) 3.30 3.65 3.65 Shoulder width (m) 1.5 1.5 1.5 Lateral clearance 1.5 1.5 1.5 Design speed (km/h) 80 80 80 Horizontal alignment OK OK OK Vertical alignment OK OK OK Traffic stream composition (%): Motor-cycles 5 33 6 Cars 70 50 55 Commercial Buses 23 15 35 Tankers 2 2 4 Control Devices: Traffic light None None None Traffic signs Few Few Few Traffic markings Few Few Few Traffic regulations Traffic Warden Traffic Warden Traffic Warden Roadside activities: On-street business Few Few Few On-street parking Few Few Few 56 4.1.2 Average traffic flow The average vehicular flow was 715 ± 3, 970 ± 5 and 1118 ± 9 vph per lane as shown in Table 4.2 for Total Garden-Agodi Gate, J Allen-Oke Bola and Odo Ona- Apata roads respectively. Table 4.2: Average traffic flow on selected roads in vph Total Garden- J Allen- Odo Ona- Period Agodi Gate Oke Bola Apata October 2008 712 970 1127 Nov. 2008 718 965 1105 Jan. 2009 716 977 1110 Feb. 2009 713 972 1123 March 2009 718 963 1125 April 2009 711 974 1120 Average Flow 715 970 1118 Standard Deviation 3 5 9 Generally, vehicular movements approached unstable state for traffic flows above 650 vph per lane for the three roads. In this state, drivers had little freedom to select their own speeds and there were frequent short stoppages. The unstable flows could be said to be fluctuating between LOS D and E as described in previous Table 2.4 in Chapter 2. 57 4.1.3 Field Headways The minimum headway of field data ranged between 0.31 s and 0.40 s for approximated traffic flows between 700 and 1200 vph respectively. Average headway of 5.16 s was recorded at 700 vph and the lowest value of 2.98 s at 1200 vph as shown in Table 4.3. (See Appendix A2 for a typical set of extracted field headway data). Table 4.3: Minimum and maximum values of field headway Approximated Minimum Maximum Average Traffic flow headway headway headway (vph) (s) (s) (s) 700 0.40 44.02 5.16 800 0.37 39.27 4.48 900 0.35 36.22 4.02 1000 0.34 35.17 3.61 1100 0.33 30.42 3.28 1200 0.31 22.11 2.98 The percentage compositions of the field headways are shown in Table 4.4. Five headway composition groups identified are: a. Group 1 - (0.3≤h<1) b. Group 2 - (1≤h<2) c. Group 3 - (2≤h<4) d. Group 4 - (4≤h<10) e. Group 5 - (10≤h< 45) The percentage composition of each headway group per flow regime is as shown in Table 4.4. High percentage compositions of short headways were observed for all the flow regimes: 31.6 %, 31.7 % and 32.0 % for 700, 1000 and 1200 vph respectively for G2 (1