ANALYSIS AND MODELING TIME HEADWAY DISTRIBUTIONS UNDER HEAVY TRAFFIC FLOW CONDITIONS IN THE URBAN HIGHWAYS: CASE OF ISFAHAN

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1 TRANSPORT ISSN prit / ISSN olie 2 Volume 26(4): doi:.3846/ ANALYSIS AND MODELING TIME HEADWAY DISTRIBUTIONS UNDER HEAVY TRAFFIC FLOW CONDITIONS IN THE URBAN HIGHWAYS: CASE OF ISFAHAN Sayyed Mahdi Abtahi, Mohammad Tamaaei 2, Hosei Haghsheash 3, 2 Dept of Civil Egieerig, Isfaha Uiversity of Techology, Isfaha, Ira 3 Dept of Civil Egieerig, Sharif Uiversity of Techology, Tehra, Ira s: 2 (correspodig author); 3 Submitted 7 December 2; accepted 25 Jauary 2 Abstract: The time headway of vehicles is a importat microscopic traffic flow parameter which affects the safety ad capacity of highway facilities such as freeways ad multi-lae highways. The preset paper iteds to provide a report o the results of a study aimed at ivestigatig the effect of the lae positio o time headway distributios withi the high levels of traffic flow. The mai issue of this study is to assess the driver s behavior at differet highway laes based o a headway distributio aalysis. The study was coducted i the city of Isfaha, Ira. Shahid Kharrazi six-lae highway was selected for collectig the field headway data. The uder-study laes cosisted of passig ad middle laes. The appropriate models of headway distributios were selected usig a methodology based o Chi-Square test for each lae. Usig the selected models, the headway distributio diagrams were predicted for high levels of traffic flow i both the passig ad middle laes ad the relatioship betwee statistical criteria of the models ad the driver s behaviors were aalyzed. The results certify that the appropriate model for the passig lae is differet tha the oe for the middle lae. This is because of a differet behavioral operatio of drivers which is affected by specific coditios of each lae. Through car-followig coditios i the passig lae, a large umber of drivers adopt usafe headways. This shows high risk-ability of driver populatio which led to cosiderably differeces i capacities ad statistical distributio models of two laes. Keywords: headway, distributio, model, car-followig, driver behavior, traffic flow, passig ad middle laes.. Itroductio The time headway or headway is the time, i secods, betwee two successive vehicles as they pass a poit o the roadway, measured from the same commo feature of both vehicles (Highway Capacity Maual 2). This parameter is oe of the fudametal microscopic traffic flow characteristics. These characteristics are of great importace for plaig, aalyzig, desigig ad operatig roadway systems (Jakimavičius, Buriskieė 29; Mesarec, Lep 29). Therefore, it must be aalyzed as accurate as possible based o real behavior of drivers (Kerer, 29). Traffic egieers ad plaers should be well aware of real behaviors of drivers i choosig the desired headways. I fact they should be able to predict the driver s behaviors while facig the headways i order to have better plaig ad traffic maagig through differet coditios. This is because of the fact that time headways ad their distributios would affect differet flow parameters icludig capacity, level of service ad safety (Thamizh Arasa, Koshy 23). Precise modelig ad aalysis of vehicle headway distributio helps traffic egieers to maximize roadway capacity ad miimize vehicle delays (Zhag et al. 27). Headway distributios are also eeded to ru digital simulatios through modelig multilae traffic i drivig simulators (Zwahle et al. 27). Moreover, with headway aalysis it is possible to get cogitio from the reasos of accidets ad the ways for icreasig the road safety. It should be poited out that i most capacity modelig; the safety headway requiremet is ot take ito accout durig the model calibratio ad parameter estimatio. This may partly explai why some problems are ofte experieced o roadways carryig less traffic tha the perceived capacity (Yi et al. 24). There are differet factors affectig the time headway distributio of vehicles ad their suitable models such as traffic volume, ratio of large sized or heavy vehicles mixed i, lae positio, road structure, daytime or Copyright 2 Vilius Gedimias Techical Uiversity (VGTU) Press Techika

2 376 S. M. Abtahi et al. Aalysis ad modelig time headway distributios uder heavy traffic flow coditios... ight time ad weather (Daisuke et al. 999). Some studies have ivestigated the headway distributios i freeways ad highways. Mei ad Bulle (993) ivestigated differet statistical distributios for headways measured o two southboud laes of a four-lae highway durig the morig peak period. It was cocluded that at both selected laes, the logormal distributio with a shift of.3 or.4 secods was the best model for the time headways i high traffic flows. I a study coducted i iterstate highways of Illiois, U.S. by Sadeghhosseii (22), the headways were collected at the flow rates varyig from 4 to 74 vehicles per hour per lae. The study recommeded usig the logormal model with a shift of.36 secods to geerate the time headway distributio for ay traffic volume for both left ad right laes. I aother study, Thamizh Arasa (23) ivestigated the headway data collected from a four-lae divided urba arterial i Cheai City i Idia. The egative expoetial statistical distributio was foud to be suitable for modelig headways over the etire rage of traffic flow ad differet laes. Bham ad Acha (26), surveyed time headways of drivers i steady state car-followig for differet types of freeway sectios. The data sites cotaied a basic freeway sectio, a ramp merge, a lae drop ad a ramp weave sectio. It was foud that the shifted logormal distributio provided a better fit for all the metioed sites compared to the shifted gamma distributio. Al-Ghamdi (2) carried out a aalysis o time headways observatios o urba roads i Riyadh, Saudi Arabia. The flow rage of the vehicles observed was divided ito three classificatios of low (<4 vph), medium (4 2 vph), ad high (>2 vph) levels of traffic flow. Followig his data aalysis, he foud that the best models for headways i low, medium ad high levels of flow were egative-expoetial, shifted-expoetial ad Erlag distributios, respectively. Meawhile, he added that most of the researches coducted so far o headway distributios have focused o low traffic coditios. The headway distributio modelig is, however, still vague i high levels of traffic flow. Luttie (996) performed a thorough aalysis of vehicle headways collected from rural highways i Filad. He cocluded that the gamma distributio ca be used for low-to-moderate traffic volumes which have low probability for short headways. He also suggested that despite the fact that logormal distributio is either simple or realistic eough, it ca be cosidered as a model for the follower headway distributio (Luttie 994). Zwahle et al. (27) ivestigated the portability of the cumulative headway distributios for differet traffic volumes ad traffic laes i Ohio freeways. The results of the research showed that the headway distributios for differet laes are early the same for similar hourly traffic volumes. Daisuke et al. (999) collected headway data from differet sites i Japa ad used Sythetic erlag distributio model to ivestigate the effects of some factors o time headway distributio. They also attempt to fid a law i relatio with the model parameters. It was leart through results that each lae has a specific backgroud that may affect time headway distributio. The majority of past studies were performed based o etire headway data collected from a highway without separatig data of each lae. Also, most of those studies were udertake uder low or medium flow rate coditios. The preset paper iteds to provide a report o the results of a study aimed at ivestigatig the effect of lae positio o time headway distributios withi high levels of traffic flow. The mai issue of this study is to assess the driver behaviors at two highway laes based o headway distributio aalysis. Shahid Kharrazi six-lae highway was selected for collectig the field headway data. The uder-study laes cosisted of the passig ad middle laes. The appropriate models of headway distributios were selected i a Chi-Square test based methodology for each lae ad the relatioship betwee statistical criteria of the selected models ad the driver behaviors i the laes were aalyzed. 2. Data Collectio ad Primary Aalysis The field data were collected i Isfaha, Ira. Isfaha is a metropolita area with a populatio of over 6. The data collectio was doe by videotapig a ietymeter log basic sectio, picked from Shahid Kharrazi six-lae highway o December, 29 (Fig. ). The highway is a part of Isfaha third traffic rig, which is uder uiterrupted flow coditios. A video camera was mouted o the top of a high buildig adjacet to the highway, to capture cotiuously the movig traffic i differet hours of the day. After reviewig the films, a 9 miutes time-study of morig peak hours was selected for data extractio. The time-study was selected so that the traffic flows were at the high levels. The extracted data were from two laes: the passig lae adjacet to the highway media (amed as left lae or lae 3) ad middle lae (lae 2). For each lae, the time-study was divided ito eightee cosecutive 5-miute time itervals. Usig Ulead Video Studio software, the momets i which each vehicle passed from the marker istalled ext to the road (referece poit), were recorded. The accuracy of the operatio was :3 secods. Totally, about 54 time headways were recorded from both laes Fig.. A view of the selected basic sectio

3 Trasport, 2, 26(4): (3 ad 2). It is worth metioig here that the domiat part of traffic compositio at both laes was related to passegers cars. At the metioed time-study, the percetage of passegers cars i the passig lae ad the middle lae were 97.2 ad 9.6, respectively. I order to obtai the flow rate of each time-iterval, vehicle flows were coverted ito passeger-car flows usig passeger-car equivalets suggested by Highway Capacity Maual (2). The traffic flow rate raged from about 8 passeger s car per hour per lae (pc/h/l) to over 25 pc/h/l for passig lae. That was about 4 to 2 pc/h/l for the middle lae. Also, the space, mea speed was determied for each 5-miute time iterval. Therefore, a sample size of 3 vehicles was selected radomly from each lae for this purpose, ad the passig time of each vehicle through the basic sectio was calculated. The mai statistical characteristics of data collected from two laes are show i Table. Table. Statistical characteristics of the collected data Characteristics of Traffic Observed Passig Lae (Lae 3) Middle Lae (Lae 2) Sample Size Mea Flow Rate (pc/h/l) Max Flow Rate (pc/h/l) Mi Flow Rate (pc/h/l) Passeger Car (%) Space Mea Speed (km/h) Mea of Headways (sec) Media of Headways (sec).3.78 Max Headways (sec) Mi Headways (sec).3.2 Accordig to the Table, the mea flow rate i the passig lae is higher tha the mea flow rate i the middle lae. This shows that the lae utilizatio by vehicles is ot homogeous for both laes at the peak hours of traffic. Several driver traiig programs state that 2 secods is the miimum headway for safe followig (Michael et al. 2). The Table also shows that high flow coditios, a high percet of drivers i the passig lae ad more tha half of drivers i the middle lae choose the headways less tha safe headway. This is because of the fact that the mea value ad media value of headways i the passig lae ad media value i the middle lae are less tha safe headway. Whe the rear vehicle closes to less tha a two secod headway, the car-followig is commoly cosidered to commece (Brackstoe et al. 29). I order to classify the collected headway data, the flow scopes with the legth of pc/h/l were defied for each lae ad the headways belogig to each 5-miute time iterval were put ito the correspodig flow scope. For istace, headways belogig to the iterval with flow rate of 967 pc/h/l were put ito the flow scope of 9 to 2 pc/h/l. Five ad three flow scopes were defied for the passig ad middle laes, respectively. Table 2 shows some of the characteristics of the time headways put ito each flow scope. Accordig to the Table 2, the icrease i the flow rate, resulted i a decrease i the mea ad stadard deviatio of headways. With compariso of mea ad media values for each flow scope, it is show that the media value was less tha mea value for differet high levels of traffic flow. This idicates the large cocetratio i short headways so that 5% of the drivers choose the headway which are less tha the mea of the headways. Table 2. Characteristics of headways with separatio of flow rate Positio Flow Rate Scope (pc/h/l) Average Flow Rate (pc/h/l) Average Speed (km/h) Sample Size Mea of Headways (sec) Media of Headways (sec) Stadard Deviatio of Headways (sec) Passig Lae (Lae 3) Middle Lae (Lae 2)

4 378 S. M. Abtahi et al. Aalysis ad modelig time headway distributios uder heavy traffic flow coditios Methodology I order to fid a appropriate model for headway distributio, the statistical models should be used to fit the data. I this study, the shifted logormal ad the shifted gamma distributios were applied to preset the headways. Logormal is a well-kow distributio model, frequetly used i may studies about headways. It is also proposed to model headways uder car-followig situatios (Greeberg 966). The gamma distributio is aother headway model widely used because of its flexibility ad compatibility (Zhag et al. 27). The mathematical equatio of the shifted logormal distributio is: f ( t tms,, ) = s( t t) 2π ( l( t t) m) 2 exp ; t >t, () 2s2 where: t is the value of the shift i secods; m ad s are two parameters of logormal distributio kow as locatio ad scale parameters, respectively. They ca be estimated by observed data as follows: ( t t) l i ˆ i= m= ; (2) 2 2 ( l( t ) ˆ i t m) ˆ i= s=. (3) The mathematical equatio of the shifted gamma distributio is: ( t t) a β β a ( t t) e f ( t taβ,, ) = ; t >t; (4) Γa Γ = x y ( x) y e dy, ( ) where: a ad β are two parameters of gamma distributio kow as shape ad scale parameters, respectively. They ca be estimated by observed data as follows: ( t t) l i l ˆ ( ) ( ˆ i= β +ψ a ) = ; (5) d( lγ( x) ) ψ ( x) = ; dx ( ti t) ˆ ˆ i= aβ =. (6) To decide which of shifted distributios is the most appropriate model for headway data i each lae, the logormal ad gamma distributio models with shifts ragig from to.75 secods (with step of.5 secods) were examied. The goodess of fit of the models was checked usig Chi-Square tests with 5% level of sigificace. The ull hypothesis for each test was as follows: The compatibility hypothesis of headway distributio with fitted model is rejected (h = ) or ot rejected (h = ). The process used for determiig the most appropriate model for headway distributio i each lae was as follows: Step : for each lae, the goodess of fit models o the distributio of total headways collected from the lae was examied. Step 2: for each lae, the goodess of fit models o distributio of the headways occurred i each pc/h/ l flow scope was examied. The flow scopes have already bee preseted i Table 2. Step 3: for each lae, the models accepted commoly i the two previous steps, were specified. Step 4: amog the models specified at the third step, the most compatible model to the data was selected as the best model for each lae. To perform that, the p- value parameter was used. I a chi2-test with 5% level of sigificace, the more the p-value ad the greater its amout tha.5, the more compatible the model is. Step 5: usig the selected model for each lae, the headway distributio diagrams were obtaied for differet levels of traffic flow. This allowed a direct coversio from traffic flow rates to correspodig headway distributios for each lae. 4. Results ad Discussio The results of modelig time headway distributios are preseted as follow: Step : for each lae, the goodess of fit models o the distributio of total headways collected from the lae was examied. I this step, 24 Chi-Square tests were doe for models with differet shifts usig MAT- LAB software ( For each test, the parameters of the model were estimated from the headway data. The results of each step are preseted i Table 3. It shows values of h for Chi-Square tests o all headways collected from each oe of two laes. The equatio of h with, represets rejectio of test ad its equatio with, represets approval of the test. As it is show i Table 3, the logormal distributio models with shifts ragig from.35 to.27 secods were well-fitted to headways i the passig lae. Nevertheless, oe of the shifted logormal models were fitted appropriately to headways i the middle lae. Thus, it ca be claimed that logormal model is ot proper for headway distributio i the middle lae. Meawhile, the results of fittig the gamma distributio models with differet shifts o headways i the passig lae shows that the gamma model is ot proper for modelig headways i it. However, gamma models with shifts ragig from.495 to.75 secods were wellfitted to headways i lae 2. The, the selected models for passig ad middle laes are shifted logormal ad shifted gamma, respectively.

5 Trasport, 2, 26(4): Table 3. Results of chi2- tests for distributio of totalheadways i each lae h* Lae 3 Lae 2 Shift (Sec) Gamma Logormal Logormal Gamma Step 2: for each lae, the goodess of fit of models o distributio of the headways occurred i each pc/h/l flow scope was examied. I this step, 56 Chi-Square tests were doe by MATLAB software. The logormal models with differet shifts were fitted o headway data from each flow scope of the passig lae (lae 3). For the middle lae (lae 2), the same procedure was doe usig shifted gamma models. Table 4 shows the rages of the accepted models for headway distributios. Step 3: for each lae, the models accepted ad approved commoly i the two previous steps, were specified. For each lae, the commo rage of the accepted models was cosidered. Table 4. Rages of accepted models for headway distributios Positio Passig lae (lae 3) Middle lae (lae 2) Appropriate Model Shifted Logormal Shifted Gamma Flow Rate (pc/h/l) Rage of ot rejected shifts (sec) Total data Total data O the basis of that, the logormal distributios with shifts ragig from.35 to.27 were the proper models for lae 3. For lae 2, the gamma distributios with shifts ragig from.645 to.75 secods were idetified as the proper models. Step 4: amog the models specified at the previous step, the model with the highest p-value was selected as the best oe. Table 5 shows the p-value results of Chi- Square tests for all headways. It is show that for the passig lae, the logormal model with shift of.24 secods got the higher p-value. So, it is the best model for passig lae. Similarly, the gamma model with shift of.69 secods is the most appropriate model for the middle lae. Fig. 2 exhibits the probability desity fuctios for observed data ad the selected model i each lae. Step 5: I step 2, the logormal distributio model with.24 secods shift was fitted o headways occurred i each pc/h/l flow scope. For each fittig process, two parameters of the model (locatio ad scale parameters) were estimated from the headway data. Also, for each flow scope, the average of startig ad edig flow rate was determied as the mea flow rate of the scope.

6 38 S. M. Abtahi et al. Aalysis ad modelig time headway distributios uder heavy traffic flow coditios... Probability Probability a) b) Passig Lae ( Lae 3) Observed Logormal Model Time Headway (sec) Logormal-Shift.24 Is Not Rejected FlowRate Rage (Pcu/h/l) =8 25 Time Headway Number =2835 P-Value =.65 (Critical P-Value =.5) Middle Lae ( Lae 2) Observed Gamma Model Gamma-Shift.69 Is Not Rejected FlowRate Rage (Pcu/h/l)= 5 2 Time Headway Number =2344 P-Value =.4765 (Critical P-Value =.5) Time Headway (sec) Fig. 2. Selected models fitted o the distributio of total observed headways of laes: a passig lae (lae 3); b middle lae (lae 2) The, each estimated parameter was correspoded to a mea flow rate. The, the parameters could be calculated as a fuctio of mea flow rate i the passig lae: for locatio parameter: m= F ( R 2 =.95) ; for scale parameter: s= F ( R 2 =.65), where: F is the mea flow rate i pc/h/l. Similarly for the middle lae, the parameters of the gamma distributio model with.69 secods shift could be calculated: for shape parameter: a= F ( R 2 =.95) ; for scale parameter: β= F ( R 2 =.92). By havig the parameters of each model, the headway distributios ca be obtaied for differet flow rates i each lae. Fig. 3 shows the results. At the peak hours of traffic flow, the maximum observed flow rate at which vehicles ca reasoably pass is 245 pc/h/l i the passig lae. This shows that the real capacity of the lae is somethig about this amout. While, for the middle lae, the correspodig value is about 95 pc/h/l. The specific behavioral patter of drivers i the passig lae ad their propesity to tailgate with high speeds, caused differece of capacity ad safety i the laes. Based o the results of model show i Fig. 3b for the passig lae, at the flow rates ear the capacity (245 pc/h/l), 5% of drivers choose headway less tha.5 secods (The correspodig value for observed data is.8). While the media of headways ear the middle lae capacity (95 pc/h/l) is.63 secods as show i Fig. 3d, (The correspodig value for observed data is.56). Differet behavioral variables such as uexpected brakig of vehicles ad lae chagig lead to time headway reductio (Kerer 29). To evaluate the reaso of differet selected models for the laes ad its relatio with the car-followig behavior more precisely, we ca remove the effect of flow rate. Thus, for the same flow scopes, the statistical criteria such as mea, media ad stadard deviatio values were calculated based o the selected models ad were compared with observed data. The results are preseted i Table 5. Accordig to the Table 5, at the same flow scopes, the mea value of headways i the passig lae is a little higher tha the oe i the middle lae. While, the media value of headways i the passig lae is less tha oe i the middle lae. This issue is satisfied for both the model ad the observed data ad is the reaso for the differet obtaied distributios i the laes. This shows that the car-followig behaviors are differet, eve at the same flows i differet laes. Also, at the same flows, the speed of vehicles i the passig lae ad dispersal of headways are more ad this is because at the same flow coditios, the drivers i the middle lae move closer to the lae capacity level compared to drivers i passig lae. Therefore, their headways are close to each other. Table 5. Compariso of characteristics of headways for laes at the same flow Flow Rate scope (pc/h/l) M.*: Model; O.*: Observed Lae Mea (sec) Media (sec) Std. (sec) M. * O. * M. O. M. O

7 Trasport, 2, 26(4): a) b). Percetage pc/h/l 65 pc/h/l 75 pc/h/l 85 pc/h/l 95 pc/h/l 25 pc/h/l 25 pc/h/l 225 pc/h/l 235 pc/h/l 245 pc/h/l Cumulative Percetage pc/h/l 65 pc/h/l 75 pc/h/l 85 pc/h/l 95 pc/h/l 25 pc/h/l 25 pc/h/l 225 pc/h/l 235 pc/h/l 245 pc/h/l.6 c) Headway (sec)..9 d) Headway (sec).5.8 Percetage pc/h/l 55 pc/h/l 65 pc/h/l 75 pc/h/l 85 pc/h/l 95 pc/h/l Cumulative Percetage pc/h/l 55 pc/h/l 65 pc/h/l 75 pc/h/l 85 pc/h/l 95 pc/h/l Headway (sec) Fig. 3. Predicted headway distributios: a probable desity fuctio of headways i lae 3; b cumulative desity fuctio of headways i lae 3; c probable desity fuctio of headways i lae 2; d cumulative desity fuctio of headways i lae Headway (sec) Coclusios The preset study was performed to ivestigate the time headway distributios at urba multi-lae highways. The Iraia drivers behaviors i choosig the headway were aalyzed withi high levels of traffic flow. Some of the results are listed below:. I the car-followig coditios, a large umber of drivers adopt headways which are less tha safe headway. A compariso of mea ad media values idicates that at all flow scopes, the media is less tha mea. It reveals the cocetratio of short headways; i a way that 5% of drivers choose headways less tha mea. This is because of a high risk-ability of driver populatio which results i safety reductio. 2. The results of modelig shows that the appropriate models for headway distributio are differet i the passig ad middle laes uder heavy traffic coditios. The logormal model with.24 secods shift was selected as the appropriate model for headway distributio of the passig lae. For the middle lae, the gamma model with.69 secods shift was selected as the most appropriate model. This is because of differet behavioral operatio of drivers which is affected by specific coditios of each lae. 3. Because of the specific patter of drivers for car-followig i the passig lae ad their propesity to tailgate with high speed at peak hours of traffic flow, the capacity of the passig lae is higher tha oe for the middle lae ad thus, the distributios ad statistical criteria are cosiderably differet for the laes. 4. The car-followig behaviors are differet, eve at the same flows i differet laes. Ackowledgemet The authors would like to express their sicere thaks ad appreciatios to Isfaha Muicipality for their praiseworthy cooperatio with us i implemetig this research.

8 382 S. M. Abtahi et al. Aalysis ad modelig time headway distributios uder heavy traffic flow coditios... Refereces Al-Ghamdi, A. S. 2. Aalysis of time headways o urba roads: case study from Riyadh, Joural of Trasportatio Egieerig 27(4): doi:.6/(asce) x(2)27:4(289) Bham, G. H.; Acha, S. R. P. 26. Statistical models for preferred time headway ad time headway of drivers i steady state car followig, i Applicatios of Advaced Techology i Trasportatio: Proceedigs of the Nith Iteratioal Coferece. 3 6 August 26, Chicago, Illiois, USA, doi:.6/4799(23)54 Brackstoe, M.; Waterso, B.; McDoald, M. 29. Determiats of followig headway i cogested traffic, Trasportatio Research Part F: Traffic Psychology ad Behaviour 2(2): doi:.6/j.trf Daisuke, S.; Izumi, O.; Fumihiko, N O estimatio of vehicular time headway distributio parameters, Traffic Egieerig 34(6): Greeberg, I The log-ormal distributio of headways, Australia Road Research 2(7): 4 8. Highway Capacity Maual. 2. Trasportatio Research Board, Natioal Research Coucil. Washigto, U.S.A. 34 p. Jakimavicius, M.; Buriskiee, M. 29. A GIS ad multi-criteria-based aalysis ad rakig of trasportatio zoes of Vilius city, Techological ad Ecoomic Developmet of Ecoomy 5(): doi:.3846/ Kerer, B. S. 29. Itroductio to Moder Traffic Flow Theory ad Cotrol: the Log Road to Three-Phase Traffic Theory. st editio. Spriger. 278 p. Luttie, R. T Idetificatio ad estimatio of headway distributios, i Procedigs of the 2d Iteratioal Symposium o Highway Capacity, Luttie, R. T Statistical Aalysis of Vehicle Time Headways. Doctoral Dissertatio. Helsiki Uiversity of Techology, Filad. 93 p. Available from Iteret: < tkk.fi/diss/99x/isb x/isb x.pdf>. Mei, M.; Bulle, A. G. R Logormal distributio for high traffic flows, Trasportatio Research Record 398: Mesarec, B.; Lep, M. 29. Combiig the grid-based spatial plaig ad etwork-based trasport plaig, Techological ad Ecoomic Developmet of Ecoomy 5(): doi:.3846/ Michael, P. G.; Leemig, F. C.; Dwyer, W. O. 2. Headway o urba streets: observatioal data ad a itervetio to decrease tailgatig, Trasportatio Research Part F: Traffic Psychology ad Behaviour 3(2): doi:.6/s ()5-2 Sadeghhosseii, S. 22. Time Headway Ad Platooig Characteristics of Vehicles o Iterstate Highways. PhD. Dissertatio.Uiversity of Illiois, USA. 36 p. Thamizh Arasa, V.; Koshy, R. Z. 23. Headway distributio of heterogeeous traffic o urba arterials, Joural of the Istitutio of Egieers 84: Yi, P.; Zhag, Y.; Lu, J.; Lu, H. 24. Safety-based capacity aalysis for Chiese highways a prelimiary study, IATSS Research 28(): Zhag, G.; Wag, Y.; Wei, H.; Che, Y. 27. Examiig headway distributio models with urba freeway loop evet data, Trasportatio Research Record 999: doi:.34/999-5 Zwahle, H. T.; Oer, E.; Suravaram, K. 27. Approximated headway distributios of free-flowig traffic o Ohio freeways for work zoe traffic simulatios, Trasportatio Research Record 999: 3 4. doi:.34/999-4

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