Modelling Lane Changing Behaviour of Heavy Commercial Vehicles

Transcription

1 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Sara Moridpour 1, Majid Sarvi 2, Geoff Rose 3 1 Post Graduate Studet, Moash Uiversity, Melboure, VIC, Australia 2 Lecturer, Moash Uiversity, Melboure, VIC, Australia 3 Associate Professor, Moash Uiversity, Melboure, VIC, Australia 1 Itroductio Lae chagig maoeuvre ad specially lae chagig maoeuvre of heavy vehicles has a high level of iteractio amog all vehicle movemets. Lae chagig maoeuvre has a sigificat effect o macroscopic ad microscopic characteristics of traffic flow due to its iterferig ature. Traffic cogestio has a sigificat effect o drivig patters ad the lae chagig behaviours of drivers. It is believed that, drivers have differet lae chagig patters i free flow coditios ad cogested traffic coditios. Traffic volume i motorways icreases rapidly ad this cosiderable growth itesifies the importace of comprehedig drivers behaviour (Wright 2006). Uderstadig the drivers behaviour i lae chagig maoeuvre is importat due to its implicatio i variety of traffic ad trasport modellig such as: Trasportatio plaig ad traffic maagemet strategies, Safety studies ad capacity aalysis, Speed oscillatio ad its effect o road capacity ad safety, The effects of lae chagig o traffic flow patters, This paper provides a review o existig lae chagig models ad their suitability to model lae chagig behaviour of heavy vehicles. I additio, this paper explais the limitatios of the curret lae chagig models i estimatig the lae chagig behaviour of heavy vehicles. Furthermore, it will preset a framework to capture the lae chagig behaviour of heavy vehicles. Fially, some isights to future work are preseted. 2 Literature review May studies have bee udertake o the lae chagig behaviour of drivers based o differet approaches. These studies have bee coducted to cosider the lae chagig behaviour, for differet purposes. The differet approaches i lae chagig behaviour studies ad their classificatios are summarized i Figure 1. Lae chagig behaviour studies are udertake for some importat purposes. 2.1 Drivig Assistace The first sigificat purpose of lae chagig behaviour studies is its applicatio i capacity aalysis ad road safety studies (Hetrick 1997; Zwaeveld ad Arem 1997; Godbole et al. 1998; Lygeros et al. 1998; Nagel et al. 1998; Hoogedoor ad Bovy 2001; Kospe et al. 2002; Hatipoglu et al. 2003; Dijck ad Heijde va der 2005). To improve the capacity ad safety aspects of the road, drivig assistace models has received attetio i recet years. Therefore, several lae chagig models for collisio prevetio ad automatio purposes have bee developed to improve the road capacity ad road safety which are out of the scope of this study. 30 th Australasia Trasport Research Forum Page 1

2 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles 2.2 Drivig Performace The secod sigificat purpose of lae chagig behaviour studies is to fid out the drivers lae chagig patters i differet traffic coditios ad differet situatioal ad evirometal characteristics. Fid out drivers lae chagig patters i differet traffic coditios is useful to develop drivig performace models. Lae chagig performace models are applied to simulate the drivers lae chagig behaviour through microscopic traffic simulators. Lae chagig performace models ca be categorized ito tactical lae chagig models ad operatioal lae chagig models as it is show i Figure 1. Drivers behaviour ca be categorized ito three broad categories based o drivers respose to their eviromet. These three categories are: strategic, tactical ad operatioal (Sukthakar et al. 1997). At the highest level, which is the strategic level, the route is chose ad the goals of the trip are determied. At the itermediate level which is the tactical level, maoeuvres are selected to achieve the short term objectives such as decisio to pass a slow movig vehicle. At the lowest level which is the operatioal level, the maoeuvres are coverted to cotrol operatios. Therefore, i the followig sectios, the previous studies o tactical ad operatioal lae chagig behaviour will be explaied with more details. Lae Chagig Drivig Performace Drivig Assistace Tactical Performace Collisio Prevetio Automatio Operatioal Performace Artificial Itelligece (AI) Rigid Mechaistic Neural Networks Fuzzy Logic Stimulus Respose Discrete Choice Psychological Game Theoretic Probabilistic Figure 1: Classificatio of available approaches i lae chagig behaviour studies 30 th Australasia Trasport Research Forum Page 2

3 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Tactical performace models Webster et al. (2007) developed ad evaluated a tactical lae chagig model, usig a forward search algorithm to represet driver s aticipatio ad maoeuvre plaig behaviour. The forward search algorithm geerates a brachig tree of sequetial actios for each modelled vehicle at each time iterval i the simulatio. This algorithm, takes ito accout the chages i the state of the subject vehicle ad surroudig vehicles to geerate a brachig tree of sequetial actios. Each brach represets a particular actio which is chose by the driver ad also the evets which would be probably occurred as a reaso of this set of choices. The sequece of actios leadig to the best outcome is the selected ad the subject vehicle applies the first actio of that sequece. Although the model Webster et al. developed, has better performace tha the basic lae chagig models, they used several simplifyig assumptios. First, i the forward search tree, the surroudig vehicles do ot chage their car followig situatio ad they ca ot perform lae chagig maoeuvre. This assumptio is i cotrast to real traffic behaviour i which the behaviour of the subject vehicle affects the behaviour of the surroudig vehicles ad the surroudig vehicles decide o their drivig behaviours cosiderig the behaviour of the subject vehicle. Secod, i the forward search tree, the subject vehicle s lae chagig decisios were restricted to situatios that a acceptable gap i the adjacet lae was available. This assumptio is oly acceptable i free flow coditios ad i cogested traffic coditios the acceptable gaps are prepared by either the lag vehicle s courtesy or the subject vehicle s forcig. Fially, the developed model is oly for Discretioary Lae Chages (DLC) which ormally takes place with the aim of speed advatages. Discretioary lae chages perform whe the driver is ot satisfied with the drivig situatio i the curret lae ad wats to gai some speed advatages. Schleoff et al. (2006) developed a hierarchical multi resolutio framework for movig object predictio which icorporates multi predictio algorithms ito a sigle framework. They tried to develop a framework i which the results from a short term predictio algorithm ca be used for stregthe or weake a situatio based log term predictio algorithm s results. I log term predictio algorithm, for each vehicle o the road the curret positio ad speed of the vehicle is give to the algorithm ad for each possible future actio, the algorithm creates a set of ext possible positios ad assigs a cost to each actio. The cost is based o the traffic characteristics of the surroudig vehicles ad the distace of the vehicle from the obstacle. The total cost is the sum of the ecoutered costs by performig each actio. Based o the cost of each actio, the algorithm computes the probability for that actio. The algorithm also builds the predicted vehicle trajectories for each vehicle, based o the possible path each vehicle will have i a predetermied time iterval. The algorithm recalculates the vehicle s positio set ad their probabilities ad fially, the future positio of each vehicle is determied based o the highest probability of the possible locatios. To combie the results of two algorithms, Schleoff et al. developed a ew methodology. For each vehicle, set of positios ad probabilities is gaied ad the distace betwee the positios obtaied from the short term ad log term algorithms is computed. If the distace was less tha a threshold, there was o eed for adjustmet ad the most probable positio from the log term algorithm was the aswer, else the distace betwee results of the short term algorithm ad the other positios obtaied from the log term algorithm were calculated ad the positio with the least distace which was less tha the threshold was accepted as the ext positio ad all other probabilities should be adjusted ad scaled accordigly Operatioal performace models Operatioal performace behaviours are the lowest level of drivers behaviour to cotrol operatios. To perform a operatioal behaviour, the driver cosiders oly the ear future. 30 th Australasia Trasport Research Forum Page 3

4 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Cosequetly, i a operatioal lae chagig maoeuvre, the driver oly cosiders the traffic situatio i the ear future to perform lae chagig. These models are useful i simulatig the lae chagig patters of drivers. Differet operatioal performace models are exploded i details, below Rigid mechaistic models The rigid mechaistic models are those which make a relatioship betwee explaatory variables ad depedat variable. I these models the magitude of the result depeds o the amouts of the idepedet variables. Mechaistic lae chagig approaches do ot usually icorporate the ucertaities of drivers perceptio ad decisio. Stimulus respose models Wiedema ad Reiter (Wiedema ad Reiter 1978), developed a theoretical lae chagig model to explai the huma decisio process durig the lae chagig. This lae chagig model is iflueced by the driver s perceptio of the surroudig vehicles. They assumed that huma drivig behaviour is aturally distributed ad differet drivers have differet characteristics. These differet drivig characteristics ca be observed i drivig capabilities, abilities i perceptio ad estimatio, eeds of safety, desired speed ad maximum acceptace of acceleratio ad deceleratio which characterises drivers aggressiveess. Wiedema ad Reiter assumed that the drivers lae choice is iflueced by their ow wishes about drivig ad based o this assumptio they distiguished betwee the lae chages from the slower to the faster laes ad from the faster to the slower laes. I their model, the desire to perform a lae chage to the faster lae ca be a result of a obstructio caused by a slow movig vehicle i the curret lae ad the level of obstructio ca be a fuctio of the differeces betwee the speed of the frot vehicle ad the desired speed of the subject vehicle. I their model, the decisio to chage ito the slower lae ca be the reaso of a obligatio to be i the right lae or to allow a faster vehicle to pass. A chage to a slower lae is accepted oly whe the subject vehicle will ot be obstructed by a slow movig vehicle for a specific time iterval. Fially, chages to both faster ad slower laes are possible if the maoeuvre is safe. This safety ca be evaluated by the distace ad speed differeces of the subject vehicle ad the frot ad rear vehicles i the curret lae ad the lead ad lag vehicles i the target lae. Assumig that all drivers decisios are based o huma perceptios, they classified the surroudig iflueces as actual iflueces ad potetial iflueces. Actual iflueces are the real surroudig vehicles characteristics which ifluece the driver s perceptios ad decisios such as distaces ad relative speeds. Potetial iflueces are the driver s estimatio of the surroudig vehicles situatios i the ear future. Gipps (1986), proposed a framework for the structure of lae chagig decisios ad the executio of lae chagig. This framework ca be used to explai the lae chagig behaviour i freeways ad urba streets where traffic sigals, obstructios ad heavy vehicles ifluece the decisio procedure. I Gipps s model, the driver s decisio to chage lae is the result of cosiderig three factors icludig: whether it is physically possible ad safe to chage laes, whether it is ecessary to chage laes ad whether it is desirable to chage laes. Gipps defied three zoes to characterize the drivers behaviour durig the lae chagig maoeuvre. These three zoes are based o driver s distace to his iteded tur. Whe the tur is i far distace, it has o effect o driver s lae chagig decisio ad the driver tries to maitai the desired speed. Whe the tur is i middle distace, the driver igores the opportuities which have speed advatage but require havig a lae chage i a wrog 30 th Australasia Trasport Research Forum Page 4

5 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles directio. Whe the driver comes close to turig movemet, he should be i the correct lae or the adjacet lae ad gaiig speed advatage is ot importat. Gipps lae chagig model has bee developed o the basis of his car followig model which makes some limits o the driver s brakig rate to have a safe speed respect to the precedig vehicle ad also this safe speed is limited by the driver s desired speed i order to prevet the ifluece of the vehicles or obstructios far from the vehicle o the driver s decisio. His lae chagig model is a simple model ad the revised versio of this model is applied i several microscopic traffic simulators. Despite, the popularity of Gipps lae chagig framework, his model has some assumptio problems. He assumes that the lae chagig occurs whe a gap of sufficiet legth is available ad it is safe to chage lae which causes some limitatios i cogested traffic coditios. Moreover i Gipps s model, the zoes are defied determiistically ad he did ot cosider the differeces betwee drivers ad eve withi drivers over time. Although the lae chagig models which are based o stimulus resposes are simple models ad the whole decisio process is cosidered i oe model, but it is difficult to calibrate the model parameters. Also, the applied explaatory variables are some primary variables ad a simple framework has bee applied to model the lae chage decisio. The geeral procedure of developig a stimulus respose model, the cosidered stages i a lae chagig model which is based o stimulus resposes, the cosidered explaatory variables ad the stregths ad the weakesses of this model type are summarized i Table 1. Discrete choice models Discrete choice models ca be applied i developig probabilistic lae chagig models. Ahmed (Ahmed 1999) developed a probabilistic model to describe the lae chagig behaviour, based o discrete choice framework. He modelled the lae chagig behaviour as a sequece of three stages: decisio to cosider a lae chage, choice of the target lae ad acceptace of a gap of sufficiet size i the desired lae to execute the lae chagig decisio. Ahmed categorized the lae chagig movemets ito three classes, Madatory Lae Chages (MLC) ad Discretioary Lae Chages (DLC) ad forced mergig. Madatory lae chages happe whe a driver is forced to leave the curret lae because of takig a exit off ramp, a obstructio or lae blockage i the curret lae or lae use regulatio. Discretioary lae chages perform whe the driver is ot satisfied with the drivig situatio i the curret lae ad wats to gai some speed advatages. For istace whe the average speed of a lae is less tha the desired speed of the driver or whe the driver is obstructed by a slow movig heavy vehicle. Forced mergig takes place i heavily cogested traffic coditios, whe the gap of the sufficiet size is created through courtesy or forcig. I his model, i the first stage, if the driver is ot satisfied with drivig coditios i the curret lae, eighbourig laes are compared to the curret lae ad the driver selects a target lae. Lae utilities are determied by defied explaatory variables i the target lae choice model. I the secod stage, a gap acceptace model is used for lae chagig performace. The mathematical formulatio of the discrete choice framework for the lae chagig procedure i his model icluded three differet utility fuctios for decisio to cosider a lae chage, choice of the target lae ad choice of the acceptable gap. These utility fuctios are applied to fid out the probability of havig a lae chage maoeuvre. The lae chagig models developed by Ahmed, did ot capture the trade off betwee madatory ad discretioary lae chagig decisio process. Also, his model, as Gipps s model, assumed that the existece of the MLC situatio is determied based o the distace to the exit off ramp. Moreover, he cosidered the lae chagig behaviour of heavy vehicles oly i the DLC models as a dummy variable. Defiitio of a dummy variable to cosider the 30 th Australasia Trasport Research Forum Page 5

6 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles effect of heavy vehicles as the subject vehicle just captures the differece i the size of the acceptable gaps betwee passeger cars ad heavy vehicles ad did ot cosider the vast differeces i the operatioal characteristics of the passeger cars heavy vehicles. The effect of heavy vehicles as the subject vehicle oly cosidered i DLC models because the umber of observatios was ot adequate i the MLC ad forced mergig ad the defied dummy variable as the subject vehicle was ot meaigful. Toledo (Toledo 2003), developed a itegrated probabilistic lae chagig model which allows drivers to cosider both madatory ad discretioary lae chages at the same time. He used a discrete choice framework to model the lae chagig decisio process. I his model, the decisio process for the lae chagig maoeuvre was cosidered as two steps: choice of the target lae ad the gap acceptace decisio. He classified the efficiet explaatory variables i lae chagig behaviour ito four categories: eighbourhood variables, path pla variables, etwork kowledge ad experiece, ad drivig style ad capabilities. He defied a target gap choice set for the gap acceptace of the subject vehicle. I his target gap choice set, the subject vehicle ca select the gap ext to the subject vehicle i the target lae, or the forward gap or the backward gap i the target lae. Also he developed a acceleratio/deceleratio model to capture the acceleratio/deceleratio behaviour of the subject vehicle i choosig the target gap. A typical formulatio of the lae chagig behaviour which is based o Toledo s work is show i Equatios 1, 2 ad 3. Equatio 1 is to model the target lae choice ad the Equatio 2 is for modellig the gap acceptace behaviour. laei laei laei laei laei U ( t) = X ( t) β + α v + ε ( t) laei = CL, RL, LL (1) Where, U laei (t) = the utility of lae i to driver at time t, X laei (t) = the radom term associated with the lae driver/vehicle, laei β = the correspodig vector of parameters, laei ε (t) = the radom term associated with the lae utility, v = the driver specific radom term. To model the gap acceptace behaviour, he defied a critical gap ad assumed that if the size of the observed gap is larger tha the critical gap, the gap will be accepted ad if the size of the gap is less tha the critical gap, the gap will be rejected. The formulatio of the critical gap is show i Equatio 2. gap g TL, cr gap g TL gapg gapg gapg l( G ( t)) = X ( t) β + α v + ε ( t) gapg = lead, lag (2) Where, gapg TL, cr G ( t) = the critical gap g i the target lae measured i meters, gap g TL X (t) = the vector of explaatory variables affectig the critical gap g, gapg β ε gapg =the correspodig vector of parameters, 2 ( t) ~ N(0, σ ) =the radom term, gapg gapg α =the parameter of the driver specific radom term v. Also, it should be metioed that to accept a gap, both the lead ad the lag gaps should be larger tha the critical lead ad critical lag gaps which is cosidered i Equatio 3. P Chage to target lae TL, v ) = (3) ( P Accept lead gap TL v ) P ( Accept lag gap TL, v ) = ( t t, leadtl leadtl, cr lagtl P ( G ( t) > G ( t) TL, v ) P ( G ( t) > G t t lagtl, cr ( t) TL, v t ) 30 th Australasia Trasport Research Forum Page 6

7 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Where, TL { RL, LL} = the target lae which is left lae or right lae, leadtl lagtl G ( t), G ( t) = the available lead ad lag gaps i the target lae. Choudhury et al. (Choudhury et al. 2007) developed a mergig behaviour framework which itegrated ormal, cooperative ad forced mergig compoets of a lae chagig behaviour at the same time. I cogested traffic coditios, usually, acceptable gaps are ot available ad the mergig maoeuvre is a more complicated behaviour. For istace, drivers may merge ito the target lae through the courtesy of the lag driver i the target lae or they may force i ad compel the lag vehicle i the target lae to slow dow ad prepare the gap of sufficiet size. The probabilistic model that they developed to model the lae chagig process durig the cogested traffic coditios cosists of three steps. I the first step, i the ormal mergig process each driver compares the available lead ad lag gaps i the through lae with the critical lead ad lag gaps which are the miimum acceptable ad safe gaps to merge i ad if the available gaps are greater tha the critical gaps, the driver merge ito the through lae. I the secod step, if the gaps are ot acceptable, the mergig vehicle evaluates the speed, acceleratio ad positio of the through vehicles ad aticipates whether the lag vehicle i the through lae, prepares courtesy for the driver. If the lag vehicle i the through lae decides to prepare courtesy to the mergig vehicle, starts to decelerate ad therefore the gap starts to icrease. The size of the aticipated gap depeds o the legth of the time which is cosidered to estimate the legth of the gap ad also the driver s perceptio ad plaig abilities to estimate the legth of the gap. I the third step, if the aticipated gap is ot acceptable, the driver cosiders whether to remai i the mergig lae or compels the lag driver i the target lae to slow dow ad prepare the adequate gap for him to merge i. This decisio depeds o the urgecy of the merge ad driver s level of aggressiveess ad also traffic coditio. The geeral procedure to develop a probabilistic model, the cosidered stages i a probabilistic lae chagig model, the explaatory variables which ormally used to develop this type of lae chagig model ad the stregths ad the weakesses of this model type are summarized i Table 1. Discrete choice models ca be applied i developig game theoretic models. Game theory is a mathematical model to study the decisio makig activities of the people, based o their level of iformatio (Kita 1999). Pei ad Xu (Pei ad Xu 2006) developed a lae chagig structure which costitutes two types of lae chagig behaviour i cogested traffic coditios, based o game theory. They established a model for lae chagig maoeuvre, based o traffic iformatio ad the drivers experieces ad developed a model for drivers cooperatio based o time ad load security. Pei ad Xu modelled the forced lae chagig i cogested traffic coditios through a game amog the subject vehicle ad the target lag vehicles. The driver who wats to merge ito the target lae may choose the waitig tactic to improve the safety ad prevet crashes, but as the time elapses, the ecessity of lae chagig will be more importat ad the subject vehicle performs a forced lae chagig while the follower i the target lae reduces the speed to prevet ay crash. They metioed that the vehicle i the target lae will icrease his beefits by reducig the speed ad preparig a sufficiet sized gap for the subject vehicle to perform a lae chagig maoeuvre ad also will icrease the subject vehicle s beefits. They developed their game theoretic lae chage model based o two assumptios. First, the subject vehicles lae chagig tactics was relevat to their waitig time ad safety. I this model, they defied safety as the distace of the subject vehicle to the covergece poit. While the waitig time was loger or the distace was shorter, the probability to chage lae was stroger. Meawhile, the lag vehicle s cooperatio tactics was based o the safety ad optimum travel time. 30 th Australasia Trasport Research Forum Page 7

8 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles The geeral procedure to develop a game theoretic model, the stages of developig a game theoretic model, the explaatory variables ad the stregths ad the weakesses of this model type are preseted i Table 1. Psychological models The Frech Natioal Istitute for Research i Trasportatio ad Safety, INRETS, developed a drivig behaviour model which ca ru either as a ordiary traffic simulatio model or host a drivig simulator which called is ARCHISIM (Espié et al. 1994; Champio et al. 2001; El Hadouaj et al. 2000). This psychological model has bee developed based o the cocept of decisio makig durig drivig. I ARCHISIM, the behaviour of the subject vehicle is based o a few fudametal priciples. Each driver tries to miimize the iteractio with his eviromet, icludig other drivers ad road characteristics. Withi ARCHISIM, drivers are simulated i virtual vehicles ad each driver has a model of his eviromet ad iteracts with the other vehicles (passeger cars, trucks, trams, etc), the ifrastructure (traffic lights cotrollers) ad the road. Withi ARCHISIM, each driver has specific skills, aims ad characteristics ad also drivers are autoomous ad ca potetially react to ay situatios. Drivig aggressiveess has ifluece o some characteristics of the traffic such as traffic flow ad also ifluece o the probability of vehicle accidets (Moussa 2004). Accordig to Moussa, traffic desity ad drivig aggressiveess are the most importat parameters, ifluecig the traffic characteristics. Therefore, uderstadig the drivig aggressiveess is a importat issue i drivig behaviour studies such as lae chagig. Tasca (2000) reviewed the literature o aggressive drivig behaviour ad the causes of them. He metioed that there are three mai categories of characteristics which cotribute the aggressive drivig: Situatioal ad/or evirometal coditios, Persoality or dispositioal factors ad Demographic variables. Reviewig the literature, Tasca categorized the followig factors as the mai determiat characteristics i aggressive drivig behaviours: - Age (e.g. youger drivers are more likely to show aggressiveess), - The traffic situatio which cause aoymity (e.g. darkess), - Obstructig by uexpected traffic cogestio, - The driver s believe i his or her drivig skills, - Geerally beig aggressive i all social activities. Accordig to his studies, some of the specific behaviours which costitute aggressive drivig ca be classified as follows: - Tailgatig, - Drivig at high speeds which is more tha the orm ad results i frequet tailgatig ad frequet ad abrupt lae chagig, - Weavig i ad out of traffic, - Improper passig (e.g. cuttig i too close i frot of vehicles beig overtake), - Improper lae chagig, - Failure i givig the right of way to aother drivers or road users, - Uwilligess to cooperate to other drivers uable to merge or chage laes due to traffic coditios, - Passig o the road shoulder or passig o the right, - Prevetig other drivers from passig. Laaglad (2005) selected three microscopic traffic simulators to model the level of aggressio of drivers i his studies. These three microscopic traffic simulators were: AIMSUN, MITSIM) ad PARAMICS. Accordig to his studies, oe of the most importat issues i modellig the drivers level of aggressiveess is to fid out the itesity of the 30 th Australasia Trasport Research Forum Page 8

9 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles stimulus. This meas to comprehed the level of ifluece each mai determiat characteristic have i aggressive drivig behaviours of the driver (weight of a certai stimulus). For istace, what level of cogestio will cause a driver to drive more aggressively ad how log does this factor ifluece the driver s aggressiveess. He assumed that the mood of a driver while he is drivig ca represet drivig level of aggressiveess. The variable factors which ifluece the level of aggressio cause a temporarily emotioal reactio. This affects the driver s mood for a period of time. Laaglad used a simplified algorithm of Velasques, which is a emotioal algorithm, to model the level of aggressio of drivers. He defied the level of emotio at each time iterval ad determied the itesity of that emotio Artificial itelligece models (AI) Rigid mechaistic models do ot icorporate the icosistecies ad ucertaities of driver perceptio ad decisios (McDoald et al. 1997). These models quatify variables ito crisp magitudes (Das et al. 1999). I recet years, several approaches have become popular to solve the problems of rigid mechaistic models. Some of these approaches are the approaches which are based o Artificial Itelligece (AI). AI approach primarily focuses o the developmet of systems which ca lear rules automatically from repeated exposure to data, so called eural etworks. Although these models are useful, but if ay additioal iput adds to this type of models, they should be recostructed agai. Oe of the other types of AI, which is Fuzzy logic, allows defiig a quatifiable degree of ucertaity i the model ad i this way reflects the atural or subjective perceptio of real variables. I Fuzzy logic models, the parameter space which ca be observed i real world, are divided ito a umber of overlappig sets ad each oe is associated with a particular cocept (McDoald et al. 1997). Das et al. (1999) proposed a ew microscopic simulatio methodology based of Fuzzy IF_THEN rules ad they called their software package as AASIM (Autoomous Aget Simulatio Package). The major motivatio of usig a fuzzy kowledge based approach to model the driver behaviour is because fuzzy modellig provides a effective meas to chage ay highly oliear system ito IF-THEN rules. I additio, fuzzy logic is well equipped to hadle ucertaities that are preset i real world traffic situatios. I their microscopic simulatio methodology, lae chages are classified as madatory ad discretioary lae chages ad the madatory lae chage occurs either due to approachig exits or whe the vehicles curret lae merges ito aother oe. I AASIM, to decide whe a madatory lae chage happes, the madatory lae chage fuzzy rules cosider ot oly the distace to the approachig exit or merge poit, but also the umber of lae chages that are required. Whe multiple lae chages are required, the probability of makig a decisio to chage lae icreases. I their framework, the decisio output is a biary (yes or o) aswer. The discretioary lae chage rules of AASIM provide a biary decisio which is based upo two parameters, the driver s speed satisfactio level ad the cogestio levels of the laes i the adjacet left or right laes. The driver speed satisfactio is based o the history of the speed that the driver has bee drivig. I AASIM, after the driver decides to perform a lae chagig maoeuvre, the gap fidig is the ext stage. The fuzzy rules try to fid all the required data for car followig ad also speeds ad gaps of the vehicle i the destiatio lae, ad calculate a acceleratio value which is differet from that geerated by the ormal car followig rules. If there is a acceptable size of gap i the destiatio lae, the gap fidig rules eable the vehicle to speed up or slow dow to make itself closer to the gap, but at the same time cosider the safe space with the lead vehicle i the preset lae. The variables which are cosidered i AASIM s gap fidig model iclude; speed, forward gap, forward speed, forward gap i the 30 th Australasia Trasport Research Forum Page 9

10 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles destiatio lae, back gap i the destiatio lae, forward speed i the destiatio lae, back speed i the destiatio lae. The last stage i AASIM lae chage model is settig the gap acceptace rules. These rules look for the gaps ad speeds of the vehicle ahead ad behid the vehicle i the destiatio lae, the distace to the ext exit or lae merger (ifiite for discretioary lae chages). The variables which are cosidered i AASIM s gap acceptace rule are forward gap i the destiatio lae, back gap i the destiatio lae, forward speed i the destiatio lae, back speed i the destiatio lae, ad exit/merger distace. A typical formulatio of the lae chagig behaviour which is based o Das et al. s work is show i Equatios 4 ad 5. The discretioary lae chage model is based o traffic cogestio i the target lae ad the driver s satisfactio level. Equatio 4 models the driver s satisfactio level ad the traffic cogestio i the target lae is modelled through Equatio 5. ( ew) ( old ) v σ = (1 ε ) σ + ε ( ) (4) vmi Where, σ = driver s satisfactio, which is the history of how fast the driver has bee drivig, v = the speed of the vehicle durig the curret iteratio, v lim = the speed limit of the freeway, ε = costat quatity called the satisfactio learig rate. di v Δ i e (1 ) i vlim c = (5) Where, c = the local lae cogestio, d i = the distace of the i th vehicle, Δ = a costat. i e di Δ McDoald et al. (1997) ad Wu et al. (2000) described the developmet of a fuzzy logic motorway Simulatio model (FLOWSIM) ad also tried to establish fuzzy sets ad systems for motorway drivig behaviour models. To model the lae chagig behaviour, they classified the lae chagig maoeuvres ito two differet categories icludig; lae chagig to the ear side which is maily to prevet disturbig the fast movig vehicles which approach from behid ad the lae chagig to the off side lae with the aim of gettig speed advatage. To establish the offside lae chagig model they defied two variables; overtakig beefit ad opportuity. The overtakig beefit is defied by the speed gai whe a offside lae chage is performed, ad the opportuity is about the safety ad comfort of the lae chagig maoeuvre, which is measured by the time headway to the earest approachig rear vehicle i the offside lae. The ear side lae chagig model uses two variables, pressure from rear ad gap satisfactio i the earside lae. The variable pressure from rear is the time headway of the followig vehicle, while gap satisfactio is defied as the period of time for which it would be possible for the subject vehicle to stay i the gap i the earside lae, without reducig speed. The geeral procedure ad the stages to develop a lae chagig fuzzy model, the explaatory variables ad the stregths ad the weakesses of fuzzy models are summarized i Table th Australasia Trasport Research Forum Page 10

11 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles 2.3 Limitatios of existig lae chagig models Reviewig the literature, major limitatios of previous studies are revealed i the existig lae chagig behavioural models. They are summarized below: A specific lae chagig behaviour model for heavy vehicles, There have bee may passeger car lae chagig models described i the literature. However, oe of the previous studies dealt with the lae chagig behaviour of heavy vehicles. Table 1: The efficiet operatioal performace models 1 i lae chage modellig ad their characteristics Model Types Stimulus Respose Probabilistic Game Theoretic Fuzzy Logic Decide o depedat variables, Calibrate the models. Geeral Procedure to Develop the Model Decide o: 1- Idepedet optios, 2- Depedat variables, Calibrate the probabilistic fuctios. Decide o: 1- Number of players, 2- Players beefit fuctio, 3- Type of the game, 4- All relevat huma resposes, Calculate the pay off matrices. Decide o: 1- Depedat variables, 2- Liguistic terms (sets) ad membership fuctio, 3- Rule sets for iferece system, Calibrate the fuzzy models. Cosidered Stages i Lae Chagig Model Developmets ad Explaatory Variables (EV) 1. Decide o a MLC or DLC. EV: Maximum subject s safe speed ad brake, frot vehicle s locatio ad the effective legth, subject s estimatio of frot s brake. 2. Decide o a lae chage to the faster lae or the slower lae. EV: Duratio ad legth of the lae chage maoeuvre, time ad distace headway to surroudig vehicles. Simplicity i modellig the lae chagig maoeuvre, Cosiderig the whole decisio process i oe model, Small umber of applied variables. Difficulties i calibratig the model parameters, Usig primary variables ad simple framework to model the lae chage decisio. Decide to have a lae chage, EV: MLC-Exit/merger distace, umber of lae chages, DLC-Speed differece, deceleratio of lead vehicle, presece of heavy vehicle, Choose the target lae, EV: Subject speed, relative distace ad speed to surroudig vehicles, presece of heavy vehicle, tailgatig, avoid the right most lae, exit distace, Accept a gap of sufficiet size i the desired lae. EV: Subject's relative speed respect to lead ad lag vehicle, relative lead ad lag gaps. Decisio o the basis of maximum gaied utility, At each stage, gettig probabilistic results istead of biary aswers (yes or o). Obligatio to calculate all the probability fuctios to fid the utility of each choice. Stregths Weakesses Choose players as the most iteractig vehicles, Choose the game type, Defie players beefit fuctio, Defie all available games of players, Calculate the pay off matrices. EV: The subject s speed, the maximum safe speed for lae chage, waitig time, maximum tolerated waitig time, traffic desity i target lae ad jam desity. Mathematical modellig of the drivers decisio makig, Cosiderig the microscopic iteractios betwee the iterferig vehicles, Complexity i modellig the iteractios betwee multiple players, Difficulties i calculatig the pay off matrices, Simplicity i modellig the lae chage as two- player game. 1. Decide o MLC or DLC, MLC or DLC, EV: MLC-Exit/merge distace, umber of lae chages, DLC-Left ad right lae cogestio, driver satisfactio. Fid a gap i target lae, EV: Speed, frot gap, ad speed, lead ad lag gap, lead ad lag speed. Acceptace of a gap. EV: Lead ad lag gap, lead ad lag speed, exit/merger distace. 2. Decide to have a lae chage to left or right. EV: Left chage-motivatio, opportuity, Right chagepressure, Gap satisfactio. Cosiderig huma's imprecise perceptio ad decisio base, Icorporatig more variables tha the mathematical models, Calibratig the model with a optimizatio algorithms, Fidig the fuzzy rules from umerical data. Validatio process of the membership fuctios, Difficulties ad complexity i abstractig fuzzy rules, Needig specific data collectio to defie the fuzzy set thresholds. 1 Psychological models ad eural etworks are ot applicable to model the lae chagig behaviour 30 th Australasia Trasport Research Forum Page 11

12 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Drivers level of aggressiveess, Drivers aggressio has a udeiable ifluece o drivig ad lae chagig behaviour of drivers. Despite the importace of drivers aggressiveess ad its effect o drivig behaviour, i most of the curret lae chagig models, the drivers' level of aggressiveess have ot bee cosidered. Tactical lae chagig behaviour, To perform a lae chagig maoeuvre, the driver cosiders the curret state of the surroudig vehicles ad the ear future behaviour of surroudig vehicles at the same time. However, i most of the curret lae chagig models oly the operatioal lae chagig behaviour is cosidered ad the tactical lae chagig decisio of drivers has bee eglected. The available tactical lae chagig models developed for passeger cars are very simple i their structure ad may simplifyig assumptio has bee applied to develop them. Therefore, these tactical lae chagig models are ot suitable for modellig lae chagig behaviour of heavy vehicles. 3 A framework for lae chagig behaviour of heavy vehicles This sectio highlights the mai cotributio of this study, explais the aims of the study ad proposes the work that will be carried out to achieve these aims. Cotributio of this study is based o the limitatios of the previous studies which are highlighted i the previous sectio. This study will develop a specific lae chagig model for heavy vehicles durig cogested traffic coditios. Figure 2 shows the coceptual framework of this research. 3.1 Ivestigatio of Lae Chagig Characteristics Heavy vehicles impose some physical ad psychological effects o surroudig traffic. These effects are the result of two mai factors: the physical characteristics of heavy vehicles (e.g. legth ad size) ad their operatioal characteristics (e.g. acceleratio, deceleratio ad maoeuvrability) (Al-Kaisy ad Jug 2005). For better uderstadig of the differeces betwee the behaviour of heavy vehicle drivers ad passeger car drivers durig the lae chagig maoeuvre, their behaviour ca be compared from a few secods before the lae chagig performace to a few secods after the completio of lae chagig. This compariso makes it possible to realize the differece betwee the explaatory variables i lae chagig decisio of heavy vehicles ad passeger cars. Furthermore, for similar variables, it will be possible to compare the magitudes of each variable ad the thresholds of each variable for heavy vehicles ad passeger cars (Figure 3). 3.2 Developmet of a operatioal ad tactical lae chagig model There have bee several studies i modellig the lae chagig behaviour i the literature. However, i all of these studies the lae chagig models have bee developed for passeger cars. Some of the recet lae chagig models idirectly tried to cosider the lae chagig behaviour of heavy vehicles through defiitio of a dummy variable (Ahmed 1999). I these models a dummy variable is defied which captures the vehicle type. If the lae chagig vehicle is a heavy vehicle, the dummy variable s magitude will be oe ad otherwise it is zero. They defied differet sizes as the acceptable gaps for passeger cars ad heavy vehicles. Moreover, they defied differet speed limits for passeger cars ad heavy vehicles. Therefore, their lae chagig models oly captures the differece betwee the size of the acceptable gap for the passeger cars ad heavy vehicles ad the differeces i maximum speed. I real traffic, there is a iteractio betwee the heavy vehicle which 30 th Australasia Trasport Research Forum Page 12

13 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles decides to have a lae chagig maoeuvre ad the surroudig traffic. The adjacet vehicles have differet drivig patters (e.g. speed, acceleratio ad headway) whe the heavy vehicle wats to perform a lae chagig maoeuvre. Moreover, most of curret lae chagig models are based o short term goals or short term plas. This meas that, i curret lae chagig models, oly the operatioal behaviour of vehicles is cosidered ad o sigificat attetio has bee paid to tactical lae chagig behaviours ad ear term plas. Although there are some tactical lae chage models i the literature, they are very simple i their structure ad may simplifyig assumptio has bee applied to develop them. The tactical lae chagig behaviour is more importat for heavy vehicle drivers, as most of them are professioal drivers ad are pretty familiar with the characteristics of the road. Moreover, because of the heavy vehicle s height, the drivers have a good view to see the surroudig traffic better tha the passeger car drivers. Stage 1 Literature Review 1. Study effects of lae chagig o macroscopic traffic characteristics 2. Idetify ad classify the existig lae chagig models 3. Uderstad heavy vehicles physical ad operatioal characteristics 4. Study the structure of acceleratio/deceleratio models Stage 2 Compilig Data for Model Developmet 1. Prelimiary aalysis of the available data ad determie the available trajectory data 2. Determie the supplemetary trajectory data Stage 3 Ivestigatio of Lae Chagig Characteristics 1. Ivestigate the effects of heavy vehicle lae chagig o surroudig traffic 2. Determie variables for characterizig lae chagig behaviour of heavy vehicles 3. Determie the differeces i lae chagig behaviour of heavy vehicles ad passeger cars Stage 4 Model Developmet Stage 4-1 Develop a Model for Operatioal Lae Chagig Behaviour 1. Develop a heavy vehicle lae chagig model 2. Develop the acceleratio/deceleratio model for heavy vehicles durig the lae chagig process 3. Formulate a aggressive behaviour model for heavy vehicle drivers Stage 4-2 Develop a Model for Tactical Lae Chagig Behaviour 1. Develop a tactical lae chagig model for heavy vehicles 2. Cosider courtesy ad deceleratio behaviour of the followig vehicle i the target lae Stage 5 Calibratio ad Validatio 1. Calibrate the developed models through microscopic traffic simulatios 2. Validate ad compare the obtaied results of the developed model with the observed trajectory data 3. Compare the performace of the developed model with the curret models used i microscopic traffic simulatio tools 3 Figure 2: The predicted stages ad cosidered milestoes i this study. 30 th Australasia Trasport Research Forum Page 13

14 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Drivers aggressiveess is aother importat issue i drivig behaviour. The drivers level of aggressiveess affects their drivig patters ad behaviours ad therefore, their lae chagig behaviour. Based o the level of aggressiveess, the drivers have differet sizes of acceptable gap, differet levels of acceleratio ad deceleratio ad differet speeds ad headways. Also, differet lae chagig patters are selected by drivers respect to their level of aggressiveess. These are some psychological models i the literature, which estimates the drivers level of aggressiveess. However, i most of the curret lae chagig models, the drivers aggressiveess have ot bee cosidered or it has bee modelled as a radom parameter which assigs to each driver without payig attetio to the real drivig characteristics of that driver. Left Lag Gap Left Lead Gap Target Left Lae Left Lag Vehicle Total Left Gap Left Lead Vehicle Follow Gap Frot Gap Curret Lae Follow Vehicle Subject Vehicle Frot Vehicle Right Lag Gap Right Lead Gap Target Right Lae Right Lag Vehicle Total Right Gap Right Lead Vehicle Figure 3: Some importat parameters i lae chagig maoeuvre. 4 Coclusio Some of the importat previous studies o lae chagig behaviour were summarized i this paper. Reviewig the literature, there are may limitatios i the existig lae chagig behavioural models. Therefore, it is importat to propose a ew framework for lae chagig behaviour of heavy vehicles based o the limitatios of the previous studies. The proposed framework cosiders the followig steps: Ivestigate the lae chagig characteristics of heavy vehicles, Lae chagig characteristics of heavy vehicles iclude: the effects of heavy vehicle lae chagig o surroudig traffic, fudametal variables i lae chagig behaviour of heavy vehicles ad the differeces i lae chagig behaviour of heavy vehicles ad passeger cars. Develop a model for lae chagig behaviour of heavy vehicles, The lae chagig model will cosider operatioal ad tactical lae chagig patters of heavy vehicles. Calibrate ad validate the developed models. This work preseted a framework for modellig lae chagig behaviour of heavy vehicles. It is believed that the preset framework would overcome the limitatios of existig lae chagig models by developig a specific lae chagig model for heavy vehicles. 5 Refereces Ahmed, K. I. (1999). Modelig Drivers' Acceleratio ad Lae Chagig Behavior. Departmet of Civil ad Evirometal Egieerig, Massachusetts Istitute of Techology. Doctor of Sciece. Al-Kaisy, A., Jug, Y. ad Rakha, H. (2005). Developig Passeger Car Equivalecy Factors for Heavy Vehicles durig Cogestio Joural of Trasportatio Egieerig Vol. 131(7): pp th Australasia Trasport Research Forum Page 14

15 Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Choudhury, C. F., Be-Akiva, M. E., Toledo, T., Lee, G. ad Rao, A. (2007). Modelig Cooperative Lae Chagig ad Forced Mergig Behavior. Trasportatio Research Board Aual Meetig. Washigto, DC. Coferece Proceedigs CD-ROM. Das, S. ad Bowles, B. A. (1999). Simulatios of Highway Chaos Usig Fuzzy Logic. 18 th Iteratioal Coferece of the North America Fuzzy Iformatio Procecsig Society - Nafips. New York, U.S.A. Dijck, T. ad Heijde va der, G. A. J. (2005). Visiosese; A Advaced Lateral Collisio Warig System. IEEE Itelliget Vehicles Symposium Coferece Proceedigs, Las Vegas, Nevada, USA. Godbole, D. N., Segupta, R. ad Hagemeyer, V. (1998). Distributed Hybrid Cotrols for Automated Vehicle Lae Chaged. Proceedigs of the 37th IEEE Coferece o Decisio ad Cotrol. Hatipoglu, C., Ozguer, U. ad Redmill, K. A. (2003). Automated Lae Chage Cotroller Desig. IEEE trasactios o itelliget trasportatio systems Vol. 4(1): pp Hetrick, S. (1997). Examiatio of Driver Lae Chage Behavior ad the Potetial Effectiveess of Warig Oset Rules for Lae Chage or SIDE Crash Avoidace Systems. Faculty of the Virgiia Polytechic Istitute & State Uiversity. Blacksburg, Virgiia. Master of Sciece. Hoogedoor, S. P. ad Bovy, P. H. L. (2001). "State-of-the-art of Vehicular Traffic Flow Modellig." Special Issue o Road Traffic Modellig ad Cotrol of the Joural of Systems ad Cotrol Egieerig, 215(4): pp Kita, H. (1999). "A Mergig-giveway Iteractio Model of Cars i a Mergig Sectio: A Game Theoretic Aalysis." Trasportatio Research Part A Vol. 33: pp Kospe, W., Sate, L., Schadscheider, A. ad Schreckeberg, M. (2002). A Realistic Twolae Traffic Model for Highway Traffic Joural of Physics A: Mathematical ad Geeral Vol. 35(15): pp Lygeros, J., Godbole, D. N. ad Sastry, S. (1998). Verified Hybrid Cotrollers for Automated Vehicles. IEEE Trasactios o Automatic Cotrol Vol. 43(4): pp McDoald, M., Wu, J. ad Brackstoe, M. (1997). Developmet of a Fuzzy Logic Based Microscopic Motorway Simulatio Mode. Proceedig of the ITSC97 Coferece, Bosto, U.S.A. Moussa, N. (2004). The Ifluece of Aggressive Drivers o the Properties of a Stochastic Traffic Model. The Europea Physical Joural B Vol. 41(3): pp Nagel, K., Wolf, D. E., Wager, P. ad Simo, P. (1998). Two-lae Traffic Rules for Cellular Automata: A Systematic Approach. Physical Review E Vol. 58(Issue 2): pp Pei, Y. ad Xu, H. (2006). The Cotrol Mechaism of Lae chagig i Jam Coditio. The 6th World Cogress o Itelliget Cotrol ad Automatio, Dalia, Chia. Sukthakar, R., Baluja, S. ad Hacock, J. (1997). Evolvig a Itelliget Vehicle for Tactical Reasoig i Traffic. Proceedigs of the Iteratioal Coferece o Robotics ad Automatio Albuquerque, New Mexico. Toledo, T. (2003). Itegrated Drivig Behavior Modelig. Departmet of Civil ad Evirometal Egieerig, Massachusetts Istitute of Techology. Doctor of Philosophy. Wiedema, R. ad Reiter, U. (1978). Microscopic Traffic Simulatio the Simulatio System Missio. Wright, S. J. (2006). Review of Urba Cogestio Treds, Impacts ad Solutios (Cosultacy Report). Traffic Maagemet Systems for Australia Urba Freeways, ARRB Cosultig-Coucil of Australia Govermets. Wu, J., Brackstoe, M. ad McDoald, M. (2000). Fuzzy Sets ad Systems for a Motorway Microscopic Simulatio Model. Fuzzy Sets ad Systems, special issue o fuzzy sets i traffic ad trasport systems Vol. 116 (Issue 1). Zwaeveld, P. J. ad Arem, B. B. v. (1997). Traffic Effects of Automated Vehicle Guidace systems. Delft, The Netherlads, Departmet of Traffic ad Trasport. 30 th Australasia Trasport Research Forum Page 15