Twaddle and Grigoropoulos 1 MODELING THE SPEED, ACCELERATION AND DECELERATION OF BICYCLISTS FOR MICROSCOPIC TRAFFIC SIMULATION

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1 Twaddle and Grgoropoulo MODELING THE SPEED, ACCELERATION AND DECELERATION OF BICYCLISTS FOR MICROSCOPIC TRAFFIC SIMULATION Heather Twaddle (Correpondng Author) Char of Traffc Engneerng and Control Technche Unvertät München Arctrae, 0 Munch, Germany Phone: + Fax: + Emal: heather.twaddle@tum.de Georgo Grgoropoulo Char of Traffc Engneerng and Control Technche Unvertät München Arctrae, 0 Munch, Germany Phone: + Fax: + Emal: george.grgoropoulo@tum.de Word Count:,0 word + fgure and table (,0 word) =, word Submtted Augut t, 0 Submtted for preentaton and publcaton to the Tranportaton Reearch Board th Annual Meetng, January 0-, 0

2 Twaddle and Grgoropoulo 0 ABSTRACT In th paper model are developed, calbrated and evaluated to decrbe the acceleraton and deceleraton procee of bcyclt n three tate; whle acceleratng from a top, deceleratng to a top and whle fluctuatng around the dered travelng peed. Such model are neceary to relably mulate the peed profle of bcyclt n mcrocopc traffc mulaton. To accomplh th am, a ample of 00 proceed trajectore from bcyclt at four nterecton n Munch, Germany ued to analyze the dynamc charactertc of bcyclt. The average crong peed, the fluctuaton n crong peed a well a the mnmum and the maxmum peed of unnfluenced bcyclt who cro at a green lght are analyzed and correlaton between thee varable are nvetgated. The acceleraton and deceleraton profle of bcyclt who top at a red lght, but are unnfluenced by other bcyclt, are ued to evaluate four acceleraton/deceleraton model; the contant model, lnear decreang model, two term nuodal model and polynomal model. Two adapton of the model are developed and evaluated, one to derve acceleraton and deceleraton a a functon of peed rather than tme and the other to account for the oberved fluctuaton n bcyclt travelng peed. The polynomal model found to be the mot flexble and produce the overall bet etmate of the acceleraton profle. The contant model wa found to bet etmate deceleraton a well a acceleraton and deceleraton whle fluctuaton around the dered peed. Keyword: Mcrocopc Traffc Smulaton, Bcycle Modelng, Bcycle Dynamc

3 Twaddle and Grgoropoulo INTRODUCTION Mcrocopc mulaton of road traffc frequently ued to analyze the effcency of road traffc and to forecat the effect of future tranportaton meaure before mplementaton. More recently, traffc mulaton tool have been ued to analyze traffc afety. Th done by calculatng urrogate traffc afety ndcator uch a Tme to Collon (TTC), Pot Encroachment Tme (PET) and Deceleraton Rate enung from nteracton between mulated road uer (). In both type of aement, the oundne of the analy depend on the valdty of the mathematcal model ued to recreate the movement of road uer (). However, the calculaton of urrogate afety ndcator much more entve to the fnte accuracy of the road uer trajectore than are effcency analye. Even eemly mall dvergence between the trajectore followed by road uer n realty and thoe of the mulated vehcle, pedetran and bcyclt can caue gnfcant error n the reultng urrogate afety meaure. The dered peed of a motorzed road uer typcally modeled n a mcrocopc traffc mulaton by takng the peed lmt of the road egment. The dered peed of a bcyclt n contrat doe not depend on the peed lmt of the roadway, but rather on the peronal preference, phycal capablte and tactcal maneuver of the bcyclt, a well a the type and qualty of the nfratructure, the traffc control and the gven traffc tuaton (). In the mcrocopc mulaton, the peed of all road uer controlled n each tme tep by an acceleraton nput that calculated from an acceleraton model. The ablty of acceleraton model to delver accurate peed dependng on the tuaton and the current tate of the bcyclt are eental n creatng realtc trajectore of bcyclt n mcrocopc traffc mulaton, partcularly for afety analye. A number of tude have been carred out to meaure the peed of bcyclt a they cro gnalzed nterecton, wth mean peed etmate rangng between. m/ and. m/ ( 0). In mot cae where acceleraton examned, contant acceleraton aumed and the mean acceleraton etmated from vdeo data. Etmate of mean acceleraton range between 0. m/ and.0 m/ (,,, ). Although a number of model have been propoed n the lterature to decrbe the acceleraton proce of motorzed vehcle, very few examnaton of acceleraton and deceleraton profle of bcyclt were found n the lterature. The mot common and mpltc approach for modelng acceleraton the contant acceleraton model a ( t) = a, where the acceleraton at any pont durng the acceleraton proce a ( t) equal to the mean acceleraton. In many applcaton, uch a n the etmaton of crong tme for calculatng nter-green tme at gnalzed nterecton, the contant model provde uffcent level of detal. However, f the am to model dynamc behavor wth enough accuracy to evaluate traffc afety, th approach lack crucal detal of the acceleraton profle (, ). Another approach commonly ued for modelng acceleraton wth more detal than the contant model the lnear decreang acceleraton model. In th model, the maxmum acceleraton exerted when the acceleraton maneuver begun and decreae lnearly untl the dered peed reached. Such an approach ued n the Neceary Deceleraton Model for the modelng of bcyclt dynamc by (), a decrbed n equaton. a( ) = t o a where: a ( ) = acceleraton at peed () o = dered peed t = total acceleraton tme Hafeng et al. () propoed a non-lnear decreang model of acceleraton a a functon of tme to model acceleraton and deceleraton of bcyclt. The maxmum acceleraton thu occur at t = 0 and rapdly decreae durng the acceleraton proce. Lnear and non-lnear decreang acceleraton model are expected to produce more realtc reult than contant acceleraton approache but do not reflect S- haped acceleraton curve that have been oberved for motorzed road uer (). Such curve are a

4 Twaddle and Grgoropoulo charactered by low acceleraton at the begnnng of the acceleraton maneuver, maxmum acceleraton at ome md-pont durng the maneuver and decreang acceleraton untl the dered peed reached. Akçelk & Bgg () propoed and teted three model that all reflect the oberved S-haped peed curve meaured by the reearcher a well a the contrant of zero acceleraton and jerk at the begnnng and end of the acceleraton proce; the polynomal model, the two-term nuodal model and the three-term nuodal model. For motorzed vehcle, the polynomal model of acceleraton wa found to outperform the other model. The equaton propoed by Akçelk & Bgg () are gven n equaton -. Luo (0) ued GPS trackng data wth a frequency of one obervaton per econd from bcyclt to ft an adapted polynomal acceleraton model. The model preformance wa deemed atfactory for acceleraton but not deceleraton. n m a( t) = ra ( ) Polynomal Model () m a( t) =Ca m (n Bn ) Two-Term Snuodal Model () a( t) = Ram (0. Pco 0.co Pco ) Three-Term Snuodal Model () where: a (t) = acceleraton at tme t a m = maxmum acceleraton t a = total acceleraton tme r, n, m, C, B, R, P = model parameter t = = tme rato t a In th paper, trajectory data from a ample of 00 bcyclt who are unnfluenced by other bcyclt are ued to calbrate and evaluate four of the acceleraton model found n the lterature. A new method for modellng acceleraton a a functon of peed, whch undertood n th paper a the momentary peed, or the peed of a gven road uer at a pecfc pont n tme, rather than tme defned baed on the rato propoed by Akçelk & Bgg (). Th method ha two advantage; frt the trajectory data can be analyed wthout pror determnaton of the tart tme of a gven acceleraton maneuver and, econd, the reultng acceleraton profle can be ued wthn a mcrocopc mulaton to drectly derve an acceleraton value baed on the gven peed and maneuver of a bcyclt. In addton, an approach for ncludng the fluctuaton n the rdng peed of bcyclt drectly n the acceleraton model developed and evaluated. The reearch methodology dcued n detal n the followng ecton. The reult of the model fttng are preented and dcued ubequently. Concluon and outlook for future work are ncluded at the end of the paper. METHODOLOGY Data analy Vdeo data analy allow for the automated extracton of trajectore (poton and velocty n each vdeo frame) at a hgh temporal reoluton for a large ample of road uer. Dynamc tuatonal varable, ncludng the poton and velocty of other road uer and the phae of the traffc gnal, can be ealy extracted or appended. Vdeo data wa collected at four nterecton n Munch, Germany, for two to four day per nterecton durng the ummer month. The tudy nterecton were elected to enure a wde varety n the type of bcycle nfratructure and traffc volume at the nterecton. However, all nterecton are located wthn the cty center of Munch, le than. km from Marenplatz, the central quare of

5 Twaddle and Grgoropoulo Munch, n mxed ue area. The layout of the four nterecton are hown n Fgure (frame extracted from the vdeo data). Vdeo were recorded ung a GoPro Hero Black Edton wth a full HD reoluton (frame ze: 0x00 pxel) at frame per econd. A wde angle len wa ued to collect trajectory and tuaton data from a larger area. Th, however, ntroduced dtorton ue n the automated vdeo analy that were later rectfed. Two hour of vdeo data from each nterecton were elected from the total vdeo footage for trajectory extracton. For all of the nterecton, two hour contnuou vdeo egment were elected durng the mornng peak hour (from about :0 am to :0 am), wth favorable lghtng condton (few hadow) and a lttle dturbance from wnd a poble. a) b) c) d) 0 0 FIGURE Camera vew of the nterecton a) Arctrae-Thereentrae b) Arnulftrae- Sedltrae c) Karltrae-Luentrae d) Martrae-Sedltrae. The open ource oftware Traffc Intellgence () wa ued to extract trajectory data from the elected vdeo egment. The oftware baed on a two-tep proce n whch all movng feature n the vdeo are tracked n the frt tep and grouped nto road uer hypothee baed on proxmty and mlarty n the econd tep. Both tep are regulated by a number of parameter that are calbrated dependng on the mage qualty and the ze and peed of the road uer. A dual calbraton method wa developed and mplemented that categorze the feature baed on ther locaton n the vdeo frame a probable car or pedetran/bcyclt n the frt tep (). The groupng parameter were ndependently adjuted to the repectve peed and ze of the pecfc road uer for the econd tep. Thu the road uer were clafed a car, bcyclt or pedetran baed on ther peed and locaton. The calbraton parameter were ntentonally et to be over entve and to over-egment rather than over-group road uer. Th enured that trajectory data wa extracted for a maxmzed porton of bcyclt. However, th made t neceary to nvet a conderable amount of work n manually potproceng the trajectory databae. Erroneou or uperfluou trajectore were removed, djonted trajectore belongng to the ame road uer were combned and fally clafed object were corrected. The dtorton that wa ntroduced through the wde angle len wa corrected by pot-proceng the SQLte trajectory databae produced by Traffc Intellgence (the current veron of Traffc Intellgence

6 Twaddle and Grgoropoulo nclude a method for rectfyng vdeo data before proceng). OpenCV (opencv.org) wa ued to determne the ntrnc camera parameter and the dtorton coeffcent of the GoPro Hero camera wth the waterproof houng. The poton pont of the trajectore were remapped baed on the reultng matrce and the velocte were recalculated n each frame. The hgh reoluton of the vdeo mage a well a the heght and angle of the camera durng recordng allowed for the extracton of hgh qualty trajectory data. The relatve accuracy of the poton recorded n each tme tep etmated to be between -0 cm. However, poton value are calculated by Traffc Intellgence for a ngle road uer by fndng the mean of the poton of all feature that are grouped nto that road uer n each frame. A a reult, the poton data can jump lghtly from frame to frame a new feature are detected and other are lot. The reultng noe n the data become more pronounced a the poton value are dfferentated once to get velocte and twce to obtan acceleraton. In order to reduce th effect, the data wa aggregated from a frequency of obervaton per econd to obervaton per econd for the velocty value and. obervaton per econd for the acceleraton value. At both dfferentaton tep, the data wa fltered ung the Savtzky-Golay method () wth the wndow ze of and an order of two. Th aggregaton and flterng method proved to produce vald dtance-tme, peed-dtance and acceleraton-dtance plot of the road uer trajectore when compared to manually calculated value. The Cty of Munch provded data from the traffc gnal at three of the four reearch nterecton for the data collecton perod. Each of thee gnal traffc actuated and nformaton regardng the tme of each phae change automatcally catalouged ( econd precon). Interecton controlled by a fxed-tme gnal control and therefore the phae change tme data not recorded. Th nformaton wa extracted manually from the vdeo data wth lghtly le precon. The reultng trajectory data wa fltered to nclude only unnfluenced bcyclt. The behavor of a bcyclt can be hndered at urban nterecton by two man factor; the preence and acton of other road uer and the traffc gnal control. In order to olate the unnfluenced (or dered) behavor of the bcyclt a well a the non-confounded repone to both the gnal control and the acton of other road uer, the bcyclt were dvded nto four group, a hown n Table. Bcyclt n Group A arrve at the top lne of the nterecton whle the traffc gnal green and have more than a two econd tme gap to any leadng bcyclt (unnfluenced). Group B bcyclt arrve whle the traffc gnal red and there are no other bcyclt topped at the nterecton (traffc gnal nfluence). TABLE Clafcaton of Bcyclt Group Interference from gnal control (red gnal upon approach) Interference from other bcyclt (followng t gap < ) No Ye No Group A (N=0) Not analyzed Ye Group B (N=) Not analyzed The qualtatvely verfed trajectory data from the 00 bcyclt n Group A and Group B are ued to nvetgate the crong peed, acceleraton and deceleraton of bcyclt at gnalzed nterecton. The average crong peed, the varaton n crong peed a well a the mnmum and the maxmum peed of bcyclt n Group A are analyzed and correlaton between the analy varable are nvetgated. The acceleraton, deceleraton and peed obervaton from the trajectore of bcyclt n Group B are ued to examne the acceleraton model preented n the ntroducton. Modelng acceleraton and deceleraton Acceleraton typcally modeled a a functon of tme. However, n realty, a bcyclt doe not accelerate dependng upon tme, but rather dependng upon h or her gven peed, dered peed and the tuatonal retrant. Whle proceng the data, the acceleraton and peed can be drectly extracted from

7 Twaddle and Grgoropoulo 0 0 the trajectory. The dentfcaton of a tartng tme for the maneuver, on the other hand, more challengng and n ome tuaton not poble. Smlarly, for the purpoe of traffc mulaton, modelng acceleraton a a functon of peed more practcal becaue tme, a meaured from the tart of an acceleraton proce, not readly avalable from the traffc mulaton. Speed, however, avalable n each mulaton tme tep. Indeed, mulaton oftware uch a VISSIM allow uer to et acceleratonpeed curve, whch are ued to defne the acceleraton baed on peed (0). To account for th apect of traffc mulaton, a new rato propoed n equaton baed on the concept ntroduced by (). f where: = peed rato () = peed = ntal peed = fnal peed A mlar parameter ued by Akçelk & Bgg () to evaluate the acceleraton model developed n that paper. Th parameter adapted and ued here to develop the acceleraton curve. However, gven the propoed defnton of n equaton, an acceleraton of zero at 0 would lead to a tuaton n whch a bcyclt would never accelerate from the ntal peed of 0. To reolve th ue, equaton wth an -ntercept at 0mut be altered to enure an a( ) -ntercept that greater than zero. Th done by addng a hfted functon wth an -ntercept at and an adjutable a( ) -ntercept that can be calbrated to ft the oberved data. The four acceleraton model hown n equaton - were aeed ung the oberved trajectory data. Intal tetng of the three term nuodal model proved t to be mlar to, but le accurate and more complex, than the two term nuodal. For th reaon t wa excluded from further examnaton. Smlarly, ntal tetng of a new model, the quare root model, ndcated that th approach wa not utable for modelng acceleraton or deceleraton and wa excluded from further analy. a( ) a Contant Model () a( ) a a Lnear Decreang Model () m m n m a( ) = ra m ( ) ( a ) Polynomal Model () c a( ) = Ca m (n Bn ) ( a ) Two Term Snuodal Model () c where: a( ) = acceleraton at peed rato v a = mean acceleraton a = maxmum acceleraton m = peed rato (equaton ) r, n, m, a, c, C, B = model parameter ( a ) c f

8 Twaddle and Grgoropoulo State defnton Two approache are developed and evaluated ung the oberved trajectory data; a mplfed approach that doe not nclude fluctuaton around the dered travelng peed and an ocllatng approach that nclude th fluctuaton. Whle both approache ue the rato ntroduced n equaton, the defnton of and f dffer n the two approache. Smplfed approach In the mplfed approach, bcyclt accelerate wth a gven acceleraton profle untl they reach ther dered crong peed d. They contnue at th peed wthout fluctuaton untl t become neceary to top or low down. In th approach, bcyclt are n one of three tate: State : Acceleraton: and f d State : Deceleraton: 0 and 0 State : Travelng teadly at dered peed: Ocllatng approach In realty, bcyclt are unable to mantan a contant peed whle rdng (). An approach for ncorporatng th fluctuaton nto the acceleraton model and hence nto traffc mulaton, gven ung the followng four tate. The parameter mn d and max d repreent the lower and upper peed threhold oberved n the trajectore of a bcyclt rdng normally. Thee value are ubequently ued to calculate : State : Acceleraton from a top (or a low peed): State : Deceleraton to a top (or a low peed): State : Acceleraton a part of normal peed fluctuaton: State : Deceleraton a part of normal peed fluctuaton: d f d f mn and f maxd d f and f mn d mn and f maxd d max and f mn d Model calbraton and evaluaton The acceleraton data derved from the trajectore wa plotted ung the newly defned, both ung the mplfed and ocllatng approach. To produce the obervaton pont, the acceleraton data from all bcyclt wth equal crong peed d when rounded to the nearet m/ were aggregated. The value were rounded to the nearet 0.0 and aggregated to buld large group of obervaton. The plotted pont n Fgure ndcate the medan of the oberved acceleraton for each aggregated group. The parameter were calbrated to an accuracy of 0. ung the average root mean quare error (RMSE) a a meaure of good ft. RESULTS Speed analy The trajectore of bcyclt rdng traght acro the nterecton on a bcycle lane n the ntended drecton of travel were taken a the reference group for the crong peed analy (Group A). The dynamc charactertc of th group are ummarzed n Table. The peed of the oberved cyclt found to vary a the cyclt croe the nterecton, whch upport the hypothe that bcyclt do not normally mantan a contant peed a they rde (). In order to ncorporate the peed fluctuaton nto the acceleraton model, t neceary to nvetgate the range of travelng peed oberved for bcyclt rdng unhndered though the nterecton. d

9 Twaddle and Grgoropoulo A hown n Table, an average fluctuaton of. m/ wa oberved. However, when takng the average maxmum and mnmum peed of the bcyclt n Group A nto account,.0 m/ and.0 m/ repectvely, the range of normal rdng velocte can be approxmated a 0. d v. d. It aumed that all bcyclt n Group A and Group B are part of the ame populaton of bcyclt becaue arrval at a red lght dtrbuted randomly amongt bcyclt. The reult n Table are therefore ued a a reference for the dered rdng peed of all bcyclt n the followng analye. TABLE Dynamc Charactertc of Bcyclt n Group A Group A ( t gap and Sgnal Phae: Green, N=) Mean Std. Crong peed (m/).. Crong peed range (m/).. Mnmum peed (m/).0. Maxmum peed (m/).0. Correlaton Coeffcent R (p value) Speed range (m/) -0. (p=0.00) Mn. peed (m/) Drect correlaton -0. (p=0.000) Max. peed (m/) Drect correlaton 0.0 (p=0.000) 0. (p=0.000) Acceleraton The trajectory data from Group B wa ued to tet and calbrate the acceleraton and deceleraton model for State and State, for both the mplfed and the ocllatng method. Data from the bcycle at all four reearch nterecton wa aggregated to attan a utably large dataet. In order to etmate the dered crong peed d of each bcyclt, an ext lne wa drawn between the two edge of the dewalk pavement on the oppote de of the nterectng road. The dtance between the top lne and the ext lne ranged from m to 0m, dependng on the nterecton and approach. Accordng to (), the majorty of bcyclt complete an acceleraton proce n le than m. It wa therefore aumed that the oberved bcyclt reached ther dered crong peed before crong the ext lne and d wa defned a the mean peed of the bcyclt after crong th lne. It hould be noted that the dered crong peed the dered peed whle crong an nterecton and the dered peed on egment between nterecton maybe greater or le. The calculated and correpondng acceleraton value of bcyclt acceleratng from a top are hown n Fgure. A the ocllatng approach wa found to produce better etmaton of the oberved acceleraton data, only reult from th approach are hown below. The reultng RMSE value for all the teted model are ncluded n Table. A een n Fgure, the maxmum acceleraton of the oberved trajectore ncreae wth the dered peed d. The calbrated parameter for the model for each dered peed group are ncluded n the top left corner of the chart. The mall range of the parameter r and C, whch control the ampltude of the polynomal and two term nuodal model, ndcate that the dfference between the curve of the dfferent dered peed group largely accounted for by the dfferent a m value aocated wth the dered peed group. The maxmum acceleraton reached n all cae at 0.. In theory, a( ) hould equal 0 at. However, the oberved data tend toward zero but doe not reach zero for any of the dered peed group. Th becaue d defned a the average oberved peed of a pecfc bcyclt. The peed range on the other hand defned for all bcyclt a 0. d v. d, whch reflect the average value. Per defnton, many oberved trajectore nclude maxmum peed larger than th value. The

10 Twaddle and Grgoropoulo 0 acceleraton value meaured at thee hgh peed, however ranged between zero and 0. m/, whch content wth the acceleraton value oberved for bcyclt fluctuatng durng normal rdng (Fgure ). a) b) c) d) 0 FIGURE Acceleraton profle of bcycle n State : acceleraton from a top ung the ocllatng approach a,b,c) clutered accordng to the dered peed d and d) aggregated. Deceleraton The mplfed and the ocllatng approach are dentcal when conderng the deceleraton of bcyclt n Group B becaue all of the bcyclt have a d value of 0, or n other word decelerate to a complete top. The and deceleraton value of bcyclt n State for three dered peed group (a-c) and aggregated (d) are hown n Fgure. The porton of trajectore from bcyclt n Group B that ncluded the deceleraton phae wa relatvely mall compared to the acceleraton phae. Th becaue a number of the approache were not clearly vble over a uffcently long egment n the vdeo data. A a reult, the deceleraton profle are noer than the acceleraton profle. The evaluaton of the dfferent model ugget that the bet ft to the oberved data acheved by the contant model. Although a lght curve wth a maxmum deceleraton occurrng at about 0. can be oberved n three of the plotted profle, the noe n the data could have prevented an accurate fttng of the other teted model. The bet approxmaton of the

11 Twaddle and Grgoropoulo maxmum deceleraton wa attaned by the two term nuodal modal, but thee reult were ncontent between the d group. a) b) c) d) 0 FIGURE Deceleraton profle of bcycle n State : deceleraton to a top a,b,c) clutered accordng to the dered peed d and d) aggregated. Speed fluctuaton Data from bcyclt who paed unhndered through a green lght (Group A) were ued to nvetgate State and State, acceleratng and deceleratng repectvely durng normal rdng a a reult of fluctuatng travelng peed. The plotted acceleraton and deceleraton data from the oberved trajectore and the teted mathematcal model are hown n Fgure. Only the aggregated curve of all bcyclt n Group A are hown becaue no dcernable dfference baed on the dered peed d wa oberved. The reultng curve ugget that acceleraton and deceleraton value that lead to the fluctuaton n rdng peed are unform acro value and tend to be around ±0. m/.

12 Twaddle and Grgoropoulo a) b) FIGURE Acceleraton and deceleraton profle of bcycle n a) State and b) State : acceleratng and deceleratng a part of normal peed fluctuaton, repectvely. Evaluaton The average root mean quare error (RMSE) and the percentage error n the predcted maxmum acceleraton attaned ung the mplfed and the ocllatng approache are gven n Table. The RSME value gven n the table are the average RMSE value for all the clutered dered peed group (.0-.0 m/) for State : acceleraton from top and State : deceleratng to a top. For State and : acceleratng and deceleratng whle fluctuatng around the dered peed, repectvely, only the RMSE value for the aggregated cae gven a no dfference n profle of the clutered dered peed group could be dcerned. In each of the tate examned, the lowet RMSE value, or the bet model ft, a well a the lowet percentage error n the maxmum peed etmaton are bolded. The followng concluon were reached for each of the nvetgated model: The contant acceleraton model doe not produce good approxmaton of the acceleraton profle of bcyclt acceleratng from a top or a very low peed (State ). Th model, however, proved to bet match the deceleraton profle of bcyclt deceleratng to a top or very low peed (State ). Th wa alo the cae for bcyclt fluctuatng around the dered travelng peed (State and State ). Whle th model by defnton meet the requrement that a( ) 0 when 0, t doe not meet the requrement that a( ) 0 when. Th wll lead to dcontnuou jump between acceleraton and deceleraton, whch doe not reflect the mooth tranton oberved n realty. Another dadvantage of th model the nherent poor etmaton of maxmum acceleraton or deceleraton, whch can be vtal n ome cae, uch a the nvetgaton of urrogate afety ndcator. The lnear decreang model wa found to produce very poor approxmaton of the acceleraton and deceleraton profle of bcyclt n State and State. The approxmaton of the profle of bcyclt n State and State were better, but were tll outperformed by the contant model. The polynomal model found to be the mot adaptable of the model teted and wa found to delver the bet approxmaton of the oberved trajectory data n State and State. The RMSE value for the other cae were very near to the contant model. Th model, however, wa found to contently underetmate the maxmum acceleraton and deceleraton value. Another dadvantage of th model the comparatvely large number of parameter that mut be calbrated to produce prece reult. The two term nuodal model produce good etmaton of the acceleraton profle n all the examned tate. The attaned maxmum acceleraton and deceleraton were alo very content

13 Twaddle and Grgoropoulo when compared to the other model. Becaue th model ha one le parameter than the polynomal model, t lghtly eaer to calbrate. TABLE Root Square Mean Error (RMSE) and the Percent Error n the Maxmum Acceleraton/Deceleraton of the Teted Model State Contant Lnear Decreang Polynomal Two Term Snuodal RMSE % e a m RMSE RMSE % e a m RMSE % e a m Smplfed approach 0.0 -% % 0.00 % 0.0 -% % 0.0 -% Ocllatng approach 0.0 -% % % 0.0 -% % 0.0 -% % % % % % % The lghtly lower RMSE value derved ung the ocllatng approach ugget that the oberved acceleraton data can be better ft f the peed fluctuaton around the average rdng peed are taken nto account. The method ntroduced n th paper provde a vald poblty for ncludng th fluctuaton n the acceleraton and deceleraton model. There are however other method that could be ued to defne, uch a the uage of the maxmum oberved peed for d ntead of the average peed. CONCLUSIONS AND OUTLOOK In th paper the acceleraton-peed profle from a ample of 00 bcyclt who were unnfluenced by other bcyclt are ued to evaluate four acceleraton and deceleraton model; contant, lnear decreang, two term nuodal and polynomal. The bcyclt are eparated nto two group, one group that rode unhndered through an nterecton at a green lght, and another that topped at a red lght, A new rato defned and mplemented baed on the a a tme rato concept ntroduced by Akçelk & Bgg (). The new concept ue the acceleraton tate a well a the peed rather than the tart tme and duraton of a proce a a ba for dervng acceleraton. Th allow for the drect analy of the trajectory data wthout frt needng to extract the tart and end tme of an acceleraton or deceleraton proce. A further beneft of th defnton that the peed readly avalable n mcrocopc mulaton, makng drect mplementaton of the the adapted model poble. The evaluaton of the four model ndcate that the polynomal model provde the mot flexblty and obtan the mot contently low RMSE value for all the acceleraton tate. The maxmum acceleraton and deceleraton value were, however, underetmated by th model. The contant model lghtly outperform the polynomal model n State : deceleraton to a top and n State and, acceleratng and deceleratng a part of normal peed fluctuaton, repectvely. The two term nuodal model produce good etmaton of the acceleraton and deceleraton profle whle alo provdng accurate etmate of the maxmum acceleraton and deceleraton. The electon between thee three acceleraton model therefore depend on the applcaton and whether an overall good ft, the

14 Twaddle and Grgoropoulo maxmum acceleraton or deceleraton or the eae of mplementaton are prorty. The lnear decreang model wa found to produce the pooret etmaton of the acceleraton profle. Fnally, a method for ncludng the fluctuaton n rdng peed drectly n the acceleraton model developed. A comparon between the RMSE value derved ung the mplfed approach, whch doe not nclude peed fluctuaton, and the ocllatng approach, whch doe nclude peed fluctuaton ndcate that ocllatng approach better ft the oberved acceleraton data. The mplfed approach, however, le complcated to mplement n mcrocopc mulaton and tll adequately matche the oberved acceleraton and deceleraton profle. The reult of th paper can be ued by traffc engneer and reearcher to more accuratly model the acceleraton and deceleraton profle of bcyclt a they cro gnalzed nterecton. Th wll enable a more realtc mulaton of bcycle traffc, whch wll n turn ncreae the accuracy and relablty of effcency and afety analye carred out ung mulated or modelled traffc cenaro. In future work, the developed acceleraton and deceleraton curve n combnaton wth the regreon model for etmatng the dered peed baed on the drvng maneuver, drecton of travel and type of nfratructure can be mplemented n mcrocopc traffc mulaton oftware to model the dynamc charactertc of bcyclt wth ncreaed detal. Subequent analye of traffc effcency and afety n urban area that nclude gnfcant level of bcycle traffc wll produce more relable reult. ACKNOWLEDGEMENTS Th reearch upported by the Federal Mntry of Economc and Technology on the ba of a decon by the German Bundetag. Reearch wa carred out wthn the framework of the project UR:BAN. REFERENCES. Gettman, D., and L. Head. Surrogate Safety Meaure from Traffc Smulaton Model. Tranp. Re. Rec. J. Traportaton Re. Board, 00, pp. 0. Avalable at: Archer, J., and I. Koonen. The potental of mcro-mulaton modellng n relaton to traffc afety aement. ESS Conf. Proc., Twaddle, H., T. Schendzelorz, and O. Fakler. Bcycle n Urban Area: Revew of Extng Method for Modelng Behavor. Tranp. Re. Rec. J. Tranp. Re. Board, 0, pp. 0.. Lng, H., and J. Wu. A tudy on cyclt behavor at gnalzed nterecton. IEEE Tran. Intell. Tranp. Syt., Vol., No., 00, pp... Opela, K. S., S. Khanab, and T. K. Datta. Determnaton of Charactertc of Bke Traffc at Urban Interecton. Tranp. Re. Rec. J. Tranp. Re. Board, Vol., 0, pp. 0.. Parkn, J., and J. Rotheram. Degn peed and acceleraton charactertc of bcycle traffc for ue n plannng, degn and appraal. Tranp. Polcy, Vol., No., 00, pp... Rubn, D., and S. Handy. Tme of Bcycle Crong: Cae Study of Dav, Calforna. Tranp. Re. Rec., Vol., No., 00, pp.. Avalable at: Khan, S., and W. Rakuntorn. Charactertc of Pang and Meetng Maneuver on Excluve Bcycle Path. Tranp. Re. Rec., Vol., No., 00, pp. 0.. Taylor, D. B. Analy of Traffc Sgnal Clearance Interal Requrement for Bcycle-Automoble Mxed Traffc. Tranp. Re. Rec. J. Traportaton Re. Board, Vol. 0,, pp Wachtel, A., J. Foreter, and D. Pelz. Sgnal Clearance Tmng for Bcyclt. ITE J., Vol., No.,, pp... Fglozz, M., N. Wheeler, and C. Monere. A Methodology to Etmate Bcyclt Acceleraton and Speed Dtrbuton at Sgnalzed Interecton. Tranp. Re. Rec., Vol., 0, pp... Pen, W. Bcyclt Performance on a Multue Tral. Tranp. Re. Rec., Vol., No.,, pp..

15 Twaddle and Grgoropoulo 0. Akcelk, R., and D. C. Bgg. Acceleraton Profle Model for Vehcle n Road Traffc. Tranp. Sc., Vol., No.,, pp... Andreen, E., M. Chrab, and A. Seyfred. Bac drvng dynamc of cyclt. Smul. Urban Mobl., 0, pp... Hafeng, J., W. Tao, J. Pengpeng, and H. Hun. Reearch on cyclt mcrocopc behavor model at gnalzed nterecton. th Road Saf. Four Cont. Conf., 0.. Luo, D. Modelng of Cyclt Acceleraton Behavor Ung Naturaltc Data. KTH Royal Inttute of Technology, 0.. Jackon, S., L. Mranda-Moreno, P. St-Aubn, and N. Sauner. A Flexble, Moble Vdeo Camera Sytem and Open Source Vdeo Analy Software for Road Safety and Behavoural Analy. Tranp. Re. Rec., Vol., No. January, 0, pp. 0.. Twaddle, H. et al. Ue of automated vdeo analy for the evaluaton of bcycle movement and nteracton. Proc. SPIE 0, Vdeo Survell. Tranp. Imagng Appl. 0, 0.. Savtzky, A., and M. J. Golay. Smoothng and dfferentaton of data by mplfed leat quare procedure. Anal. Chem., Vol.,, pp.. 0. PTV PLanung Tranport Verkehr AG. VISSIM 0 Uer Manual. Karlruhe, 00.