Modeling the Pedestrian Ability of Detecting Lanes and Lane Changing Behavior

Transcription

1 Modern Apped Scence; Vo. 1 No. 7; 216 ISSN E-ISSN Pubshed by Canadan Center of Scence and Educaton Modeng the Pedestran Abty of Detectng Lanes and Lane Changng Behavor Mohammed Mahmod Shuab 1 1 A-Imam Muhammad Ibn Saud Isamc Unversty (IMSIU) Saud Araba Correspondence: Mohammed Mahmod Shuab Coege of Shar a and Isamc Studes n A Ahsaa Department of Computer Scences A-Imam Muhammad Ibn Saud Isamc Unversty (IMSIU) A Ahsaa Saud Araba. E-ma: mh_shuab@yahoo.com Receved: February Accepted: February Onne Pubshed: March do:1.5539/mas.v1n7p1 URL: The research s fnanced by (A-Imam Muhammad Ibn Saud Isamc Unversty under the proect (Number 3587)) Abstract Incorporatng decson-makng capabty as an ntegence aspect nto crowd dynamcs modes s cruca factor for reproducng reastc pedestran fow. Crowd dynamcs modes are st sufferng from poor representaton of essenta behavors such as ane changng behavor. In ths artce we provde the smuated pedestrans n the soca force mode more ntegence as an extenson to the pedestran s nvestgaton capabty n bdrectona wakways to et the mode appear more representatve of what actuay happens n reaty. In the proposed mode the ane s structure s modeed as soca network. Thereby the smuated pedestrans wth nconvenent wakng can detect the avaabe anes nsde hs envronment nvestgate ther attractons and then make decsons to on the most attractve one. Smuatons are performed to vadate the work quatatvey by tracng the behavor of the smuated pedestrans and studyng the mpact of ths behavor on ane formaton. Fnay a quanttatve measurement s used to study the effect of our contrbuton on the pedestrans effcency of moton. Keywords: crowd dynamcs decson makng ane changng behavor soca network 1. Introducton Massve congeston s a chaengng probem whch has attracted consderabe number of researchers to devote much attenton to pedestran dynamcs studes to provde soutons. Correctng the pedestrans wakng behavors has been proven to be an essenta factor to aevate the negatve consequences of such probem. Researchers have been provoked to mprove smuatons modes to hep smuate the aspects of the mutdrectona pedestran fow and correspondngy examne the soutons for better crowd behavor and envronmenta desgn. A varety of modes has been proposed n mcroscopc studes to represent the rea aspects of the pedestrans wakng n order to examne the proposed soutons. Among whch are the Soca Force Mode (Hebng & Monar 1995; Hebng Farkas & Vcsek 2 and Shuab 214) Ceuar Automata Modes (Bue & Ader 2 and Burstedde Kauck Schadschneder & Zttartz 21) and the Dscrete Choce Modes ( Antonn Berare & Weber 26 and Robn Antonn Berare & Cruz 29). The modes are categorzed as operatona eve cass whch descrbes the nstantaneous behavors that nvove most actvtes resutng from the nteractons among pedestrans (e.g. avodng cosons devatons acceeraton and deceeraton). For the purpose of vadaton the modes are essentay requred to ntroduce rea aspects of the mutdrectona fow behavor such as the sef-organzaton phenomena and reproduce ts characterstcs accuratey as we. Lane formaton as an nterestng sef-organzaton phenomenon and ts effect on the reproducton of bdrectona fow aspects has receved much attenton from researchers such as (Bue & Ader 2; Burstedde et a. 21; Nowak et a. 213; Guo 214; Zhang 215 & Guo Wang and Zheng 215). Nowak et a. (213) proposed swappng poteness and antcpaton factors to obtan mode concde wth expermenta data. Such factors present the roe of the opposte pedestrans. Spata separaton rues as suggested by Guo (214) was provded to pedestrans extng a room to consttute anes. Guo et a. (215) dscussed two mechansms eadng to the ane formaton and they concude that avodng oncomng pedestrans s more reevant to the reproducton 1

2 of ane formaton than foowng pedestrans wakng n the same drecton. Zhang (215) nvestgated the gude press and contan effects performed by pedestrans wth same and opposte drectons on the ane changng decson. Expermentay Guo et a. (212) studed the effect of the ook-ahead behavor on the pedestran bdrectona fow. Zhang et a. (212) studed the behavor of the opposng fows n a corrdor. They concuded that pedestrans movement s more systematc and the anes are stabe and more coherent when the pedestrans exts are predetermned. Ths shows that the mportance of the subectve conscousness of the tactca eve of behavors. Researchers such as Hoogendoorn and Bovy (24); Daamen (24); and Asano Iryo and Kuwahara (21) ndcated the sgnfcance of obtanng ntegrated modes comprsed of two compementary eves: the operatona and the tactca eves. It s worth mentonng that detectng far anes and onng them as a tactca eve behavor have not been studed n the aforementoned studes. Such behavor s commony foowed by pedestrans to aevate ther nconvenent wakng and accordngy ths behavor s essenta factor for presentng a we-representatve mode that performs the decson makng capabty wth the consderaton of ane-changng capabty. In ths artce we propose a tactca mode to be ncorporated nto the Soca Force Mode. The proposed mode s based on the assumpton that the pedestran who waks nconvenenty because of the opposte fow can detect anes n order to on to reeve hs nconvenence. Ths abty s represented by the pedestran nvestgatng hs current stuaton wthn hs sghts and then makng a short-term decson. Ths paper s organzed as foows. In the next secton we ntroduce the Soca Force Mode and the decson makng capabtes ncorporated nto the mode. In the thrd secton a mode of detectng anes and onng the attractve one are ntroduced. Fnay smuatons to estabsh the resuts of our work are conducted. 2. Soca Force Mode and Decson Makng Capabty The Soca Force Mode (SFM) s a contnuous mcroscopc mode deveoped by Hebng and Monar (1995). The mode s characterzed wth ts representaton of pedestran s motvatons n terms of the surroundng pedestrans and obstaces as soca forces. The sum of these forces s mpemented n a sem-newtonan equaton resutng n the acceeraton of the pedestran's movement. Hebng et a. (2) ncorporated nto the mode physca forces whch arse n the case of physca nteractons amongst the pedestrans. The man equatons of the mode are: dx ( t) = v ( t) (1) dt where dx ( t) dt dv m = f + f + f +ε pref obect k dt k f pref (t) = γ () () () ( v t e t v t ) s the rate of change n the ocaton of pedestran at tme t; d v (t ) s the acceeraton of dt pedestran resutng from the sum of the tota forces upon hm; ε (t) s the fuctuaton of pedestran ; the functon f pref (t ) s the preferred force modeed to express the motvaton of the pedestran to adapt hs actua veocty (t) to reach another veocty v e v preferred speed ande (2) (3) at whch he prefers to wak at tme t wherev s the s the preferred drecton; and the functon f and f are the sum of a obect k forces exerted by pedestran and obect k upon pedestran. A actvtes resutng from the equatons (1-3) such as acceeraton deceeraton and avodng cosons are exampes of operatona eves based on SFM. For undrectona wakway Zanuddn and Shuab (21) and Shuab Aa and Zanuddn (213) ncorporated 2

3 decson-makng capabtes as tactca eve behavor where they proposed the ZS mode to be ncorporated nto the SFM to enabe the smuated pedestrans make decsons to avod sem-bocked stuatons such as obstaces and grouped pedestrans. The mode was represented by determnng ntermedate ponts for ther wakng accordngy changng ther routes and consequenty overtakng the encountered bocked stuatons. The (ZS) mode has been modfed n (Shuab & Zanuddn 215) to nvove aspects of bdrectona fow and ts effects on ane formaton. The mode was vadated by reproducng anes compatbe to the ane formaton n the expermenta study (Zhang et a 212). 3. Modeng Lane s Structure and Lane Jonng 3.1 Modeng Lane s Structure Wth the assumpton of unform physca appearance of pedestrans pedestran who s wakng nconvenenty can detect pedestran gatherng structures based on specfc coectve behavor of pedestrans such as coseness and veoctes. We propose the structure as a network where the nodes are the pedestrans who consttute the structures and where the connectons of these nodes are determned by coseness and veoctes. We assume frst that a pedestrans are cassfed nto two opposte-movng structures. A pedestran wth consderaby dfferent veocty from the average veocty of hs structure coud form a separate sef-organzed and dynamc structure f he s surroundng by others wakng wth smar veocty. Ths possbe structure s determned as foows: Frsty we form the obectve connecton set Ob _ set of pedestran by connectng pedestran to the mmedatey other surroundng pedestrans. Secondy we form the subectve connecton set S_ set by excudng those who are ocated at far postons and wakng at unusua veocty compared wth the surroundng pedestrans. We assgn the foowng vaue ( or 1) to each connecton: ( )* δ ( ) connect = δ (4) A B v { _. _ } A = k Ob Set v v e aσ k Ob set (5) B = k Ob_ set dst M M + bσ dst dst dst Ob _ set Ob_ set Ob _ set (6) v dst dst where σ s the standard devaton of pedestrans veoctes n Ob _ set Ob _ set ; M and Ob _ set σ are the Ob _ set mean and standard devaton of pedestrans dstances from pedestran n Ob _ set ; and a and b are constant parameters. The functon δ ( ) A v veocty of pedestran at east Ob _ set s essenta factor to excude the pedestrans whose veoctes do not match the aσ. Smary the functon δ ( ) B s essenta factor to excude pedestrans ocated far than the other mmedate adacent pedestrans. However ts roe s not cruca n extreme goba denstes n undrectona or mut-drectona wakways. The subectve connecton set for pedestran s as foows: { } S _ set = connect = 1. (7) It s worth mentonng here that the connecton of pedestran wth pedestran does not mean that 3

4 S _ set = S _ set. We ntroduce Structure noton to denote the set of a pedestrans connected to pedestran wth a path (st of connectons). Fnay usng equvaence casses created by connecton reaton we ntroduce the Struc _ Set noton as the set of a structures ocated n the physca envronment by gob mposng the foowng: Structure = Structure f there s a path between pedestran and and Structure Structure = φ f no path between them. For pedestran Struc _ Set noton s ntroduced to denotes the set of a structures ocated wthn hs sght. In ths artce we focus on ntroducng anes and accordngy we compose the subectve set of the anes Lanes _ Set for pedestran wth the consderaton of a structures n Struc _ Set that have sgnfcant szes coud be ftted by a near curve wth acceptabe error and are drected toward the destnaton of pedestran wth acceptabe devaton. 3.2 Modeng the Attractons of Lanes The goa of modeng the attracton (repuson) of anes under nvestgaton s to et each excted pedestran on the ane that has the greatest attracton (the east repuson). We assume that the attracton (repuson) of a ane s nfuenced by the specfc attrbutes of two factors: the gap between the pedestran and the ane and the ane tsef. The effect of the gap s assocated wth ts ength and the antcpated pedestrans cosons whe penetratng the gap to on the consdered ane. The effect of the ane s assocated wth ts average veocty. Thus we suggest the tme whch mpcty ncudes both veocty and dstance to express the repuson determned by each factor. Correspondng to each ane k ocated wthn the nvestgaton area of pedestran we attach for pedestran a route k dvded nto two parts (e.g. see Fgure 2): The gap s part represented by a ne that connects pedestran to the nearest pedestran who beongs to ane k and the ane part represented by the fttng ne that starts from the pont of ntersecton wth the gap s part and ends at the boarder of the nvestgaton area. Besdes we attach for each pedestran an orgna route drected to hs destnaton. The ast route s consdered as the ane part and the gap part has ength equas zero. Fgure 1. Three routes are attached to pedestran : two of them are assocated wth the consttuted anes movng towards hs drecton and the thrd s the route towards hs destnaton The ane and gap parts nhert the characterstcs of the ane and the assocated gap respectvey. The mode of routek the repuson of route k denoted bytme s a near combnaton of the repusve effects of ts parts gap Tme k ane and k Tme as foows: 4

5 where the varabe () () () routek gapk anek Tme t = Tme t + Tme t (8) Tme gapk Tme anek Exper gapk ength = (9) v ength = v gapk ( σ ) anek anek (1) gapk σ s the average oca densty of the pedestrans n contact wth the gap ne; v ( gap k Exper σ ) s the expermenta veocty obtaned from expermenta data of mutdrectona wakway. As can be seen the greater the ane s veocty the esser the repuson effect and accordngy the more key the excted pedestran w choose ane to foow. On the other hand hgher vaue of gap densty resuts n ower vaue of gap veocty and accordngy greater repuson effect. The ndex of the best route assessed by pedestran s determned as foows: { mn( ) _ } route () k () BestRoute t = ndex Tme t Lane ane set. (11) k k Fnay we assgn to each pedestran a varabe DS by whch hs decson shoud be governed. Ths decson varabe DS s modeed as a functon of the varabes resutng from the nvestgaton process (the repusons of the aternatve routes): DS BestRoute () () CurrRoute 1 Tme t Tme t U = (12) otherwse wheretme BestRoute s the repuson of the new route chosen by pedestran ; CurrRoute Tme s the repuson of the th current choce at the tme of decson; U s the threshod of utty for whch the pedestran may change hs th current choce to the new one. The crteron for modeng U s the varyng effect of the soca attrbute among the ndvduas n the popuaton. Hgh soca attrbute of a pedestran renders hm more respectfu of the others. The member ntends to devate from hs current route; t may cause more nteractons wth other pedestrans or the transgresson of communty rues such as voatng the terrtora areas of the others. If he has a ow vaue of th hs soca attrbute the vaue of U woud decrease such that the pedestran makes ths decson faster than one who has a hgher vaue of hs soca attrbute. Fnay Equaton (3) and the desred drecton are repaced by f pref (t) = γ () () () CurrRoute ( v t e t v t ) (13) e CurrRoute BestRoute e DSchange = 1 = CurrRoute e DSchange =. (14) 4. Smuaton Resuts and Dscusson 4.1 Smuaton Specfcaton To perform smuatons we used MATLAB verson 1 on a 2.5 GHz Inte (R) Core 7 workstaton. Equatons (1) and (2) are soved expcty by numerca ntegraton (Euer s method). The smuatons n the frst scenaro 5

6 were conducted to exhbt the abty of smuated pedestrans to detect the exstence of anes and onng them for convenent wakng. The wakway of the current smuatons s straght wth eptca functonaty as n a racetrack (Zanuddn and Shuab 21). The specfcaton of the smuated pedestrans s as foows: The smuated pedestrans are dvded nto two groups. The postons of the frst group were ntazed randomy n the smuated area (wakway) smutaneousy (see Fg. 2) and ther moton nstantaneousy were drected towards the rght (the destnaton). The second group of pedestrans was drected to the opposte sde. Sum pedestrans of the second group were ntazed n the upper rght part of the wakway. A pedestrans have preferred veoctes wth the mean equa to 1.34 m/s and standard devaton of.26 m/s. Tabe 1. Pedestran parameters Varabe Parameter Smuaton vaue m Range of pedestrans' mass [ 77 83] kg r Range of pedestrans' radus [.25.27] m ε Range of fuctuaton source of the pedestran s [ (.1 )* v ] acceeraton whch s randomy assgned to each ndvdua. 4.2 Detectng Lanes and Lane Changng Behavor The crteron to vadate the above work s the appearance of changng routes that s the smuated pedestrans from the second group and who are wakng n nconvenent routes woud change routes to more approprate ones. In vew of ths crteron the smuated pedestrans who are traced are some pedestrans ntazed uneveny who change ther drecton toward the formed anes to conserve ther veocty and wak comfortaby. Wth ong range dmenson of the nvestgaton area the nconvenenty wakng smuated pedestrans ntazed n the rght upper part were abe to detect the far ane and make a decson to on ths ane. Whe crossng the counter fow sma anes were consttuted. The moderate dense crowd s a reason heped rase the formaton of sma anes whe n hgh dense crowd the pedestrans are forced to be dspersed because of the ntense of the head-of confcts (Guo et a. 215) Fgure 2. onng ane behavor by group of pedestrans n bdrectona pedestran fow 4.3 The Effcency of Moton Three groups of smuatons are conducted to study the nfuence of dverse ntersectng anges chosen by the 6

7 pedestrans onng a ane. We defne the ntersectng ange between two pedestran fows to be equa to zero f both fows are drected oppostey and toπ f both fows n the same drecton. For each group of smuatons dfferent ntersectng anges are consdered that s π / 6 and π /4 respectvey and for each ange fve smuatons are conducted to determne the means and the devatons of the effcency of pedestrans moton. The effcency of moton s a quanttatve measurement used by Hebng and Monar (21) on the bass of the Soca Force Mode. Ths measurement heps optmze the pedestran factes whether the pedestrans are wakng convenenty n the consdered facty or not. In Fg. 3 the foowng resuts are produced. The resutng mean of the effcency of moton shown n Fg. 3 sghty decreases wth the decrease of the ange of changng the route of moton. The reason for ths s that the pedestrans wth sma ntersectng ange are causng ess head on confct than the arger ntersectng ange and accordngy passng each other wth ess coson. On the contrary wth hgh ange of ntersecton the crossng behavor s the domnant and hgh contact occurs whch deay the moton of the pedestrans. Fnay accountng for the devaton of effcency of moton for each ange of ntersecton t s observed that the devaton when hgh ange of changng route s hgher than the others wth ower anges. Ths s due to the varabty of coson occurrence n the hgh anges smuatons. The resut ndcates that head-on confcts of dfferent ntersectng anges have dfferent nfuences on the effcency of moton n the ntersectng area. Ths resut urges the necessty of correctng the crossng behavor of the pedestrans by gudng them to the rght ange of ntersectng wth the east effort. Fgure 3. the error bars show the means and devatons of the effcency of moton wth respect to the ntersectng ange 5. Concuson In ths work an ntegence aspect of pedestran behavor has been ntegrated nto the Soca Force Mode as a decson-makng capabty. The pedestrans nvestgate the area under ther sghts to ook for more comfortabe fow to wak n or anes to on. The smuatons have shown the pedestran s abty of makng decsons to on anes enabes the excted pedestrans to reduce the ntense of the head-of confcts resutng from the counter fow and reduce the potenta emergence of bocked stuatons. Our work resuts n more effcent moton than the orgna mode. We suggest an extenson of ths work to nvove modeng and detectng varous pedestrans structures such as groups. Moreover we encourage nvestgatng ther effects on fow by consderng dfferent orderng of drectona fow and ncorporatng some aspects such as a sem-bocked stuaton or physca characterstcs such as obstaces and was. Acknowedgments We thank the A-Imam Muhammad Ibn Saud Isamc Unversty for supportng ths work under the proect (Number 3587). References Antonn G. Berare M. & Weber M. (26). Dscrete choce modes of pedestran wakng behavor. 7

8 Transportaton Research Part B Asano M. Iryo T. & Kuwahara M. (21). Mcroscopc pedestran smuaton mode combned wth a tactca mode for route choce behavor. Transportaton Research Part C Bue V. & Ader J. (2). Ceuar automata mcrosmuaton of b-drectona pedestran fows. Journa of the Transportaton Research Board Burstedde C. Kauck K. Schadschneder A. & Zttartz J. (21). Smuaton of pedestran dynamcs usng a two-dmensona ceuar automaton. Physca A Daamen W. (24). Modeng Passenger Fows n Pubc Transport Factes. Ph. D. Thess Deft Unversty of Technoogy Netherands. Guo R.Y. Wong S. C. Xa Y. H. Huang H. J. Lam W. H. K. & Cho K. (212). Emprca evdence for the ook-ahead behavor of pedestrans n b-drectona fows. Chn. Phys. Lett. 29(6) Guo R. Y. (214). Smuaton of spata and tempora separaton of pedestran counter fow through a botteneck Physca A Guo W. Wang X. & Zheng X. (215). Lane formaton n pedestran counter fows drven by a potenta fed consderng foowng and avodance behavors Physca A Hebng D. & Monár P. (1995). Soca Force Mode for pedestran dynamcs. Physca Revew E Hebng D. Farkas I. & Vcsek T. (2). Smuatng dynamca features of escape panc. Nature Hebng D. Buzna L. Johansson A. & Werner T. (25). Sef-Organzed Pedestran Crowd Dynamcs: Experments Smuatons and Desgn Soutons Transp. Sc Hebng D. Farkas I. J. & Vcsek T. (21). Freezng by heatng n a drven mesoscopc system Phys. Rev. Lett Hoogendoorn S. P. & Bovy PHL. (24) Pedestran route-choce and actvty schedung theory and modes. Transportaton Research Part B: Methodoogca 38(2) Lan L. Ma X. Song W. Rchard Y. We X. & Ma J. (215). J. Stat. Mech. P Nowak S. & Schadschneder A. (213). A Ceuar Automaton Approach for Lane Formaton n Pedestran Counter fow Traffc and Granuar Fow Robn T. Antonn G. Berare M. & Cruz J. (29). Specfcaton estmaton and vadaton of a pedestran wakng behavor mode. Transportaton Research Part B: Methodoogca 43(1) Shuab M. M. Aa O. M. & Zarta Z. (213). Incorporatng predcton factor nto the nvestgaton capabty n the soca force mode: appcaton on avodng grouped pedestrans App. Math. Inf. Sc Shuab M. M. (214). Preservng Socay Expected Crowd Densty n front of the Ext for the Reproducton of Expermenta Data by Modeng the Pedestrans behnd Percepton. J. Stat. Mech. P Shuab M. M. & Zanuddn Z. (215) An nvestgaton capabty mode for bdrectona pedestran fow modern Apped Scence Zanuddn Z. & Shuab M. (21). Incorporatng Decson Makng Capabty nto the Soca Force Mode n Undrectona Fow. Research Journa of Apped Scences 5(6) Zhang J. Kngsch W. Schadschneder A. & Seyfred A. (212). Orderng n bdrectona pedestran fows and ts nfuence on the fundamenta dagram J. Stat. Mech

9 Zhang Q. (215). Smuaton mode of b-drectona pedestran consderng potenta effect ahead and behnd. Physca A Copyrghts Copyrght for ths artce s retaned by the author(s) wth frst pubcaton rghts granted to the ourna. Ths s an open-access artce dstrbuted under the terms and condtons of the Creatve Commons Attrbuton cense ( 9