Modeling Speed Disturbance Absorption Following State-Control Action- Expected Chains: Integrated Car-Following and Lane-Changing Scenarios

Transcription

1 Paper No.: Modelig peed Disurbace Absorpio Followig ae-corol Acio- Epeced Chais: Iegraed Car-Followig ad Lae-Chagig cearios A Paper ubmied o The Trasporaio Research Board for Review for Preseaio Publicaio a he TRB 84h Aual Meeig i Washigo, D.C. Jauary 9-3, 5 By Ruihua Tao, Ph.D. Marylad Deparme of Trasporaio Office of Traffic afey, 749 Coelley Drive Haover, MD 76 Phoe: ; Fa: rao@sha.sae.md.us Heg Wei, Ph.D., P.E. Deparme of Civil Eviromeal Egieerig Uiversiy of Ciciai Baldwi Hall, PO Bo 7 Ciciai, OH 45-7 Fa: hegwei99@yahoo.com Yihai Wag, Ph.D. Deparme of Civil Eviromeal Egieerig Uiversiy of Washigo More Hall, Bo 357 eale, WA Tel: ; Fa: yihai@u.washigo.edu ad Virgiia P. isiopiku, Ph.D. Uiversiy of Alabama a Birmigham Hoeh 3, 53 3rd Ave. ouh Birmigham, AL Tel: ; Fa: vsisiopi@uab.edu 5455 words plus ables ad 6 figures Toally 7455 words < 75 words

2 Modelig peed Disurbace Absorpio Followig ae-corol Acio-Epeced Chais: Iegraed Car-Followig ad Lae-Chagig cearios Ruihua Tao, Heg Wei, Yihai Wag, ad Virgiia P. isiopiku ABTRACT This paper eplores driver behaviors i a paired car-followig mode i respose o a speed disurbace from he fro vehicle. A Curre ae-corol Acio-Epeced ae A Chais is developed o provide a framework for modelig hierarchy of epeced acios icurred i he eed of speed disurbace absorpio. Three car-followig scearios ad oe lae-chagig sceario are ideified wih defied percepual iformaive variables o describe he process of speed disurbace absorpio. Those variables iclude dyamic spacig vs. he follower s speed, disurbace-effecig/edig spacig, headway, acceleraio/deceleraio, speed recovery period, speed advaage, ad lae-chagig duraio. A sigifica advace i car-followig modelig ha is refleced i he paper is he iegraio of carfollowig ad lae-chagig behaviors i he A chais, ad criical values of percepual iformaive variables are saisically developed as a fucio of he follower s speed, usig observed vehicle rajecory daa. Moreover, models for he probabiliy of a lae-chagig respose o a speed disurbace ideified by he speed advaage variable, ad models for accepable lae-chagig decisio-makig codiios a he adjace laes, are developed based o he aalysis of observed vehicle rajecory daa. The work preseed i his paper provides well udersadig of speed disurbace ad speed absorpio pheomeo ad car-followig ad lae-chagig behaviors a he microscopic level. This esablishes he foudaio for furher research o he muliple speed disurbace absorpio ad is impac o raffic sabiliies a he macroscopic aalysis level. Key Words: peed Disurbace Absorpio, Car-followig, Lae-Chagig, Percepual Iformaive Variables, Acio Chais, Microscopic imulaio, Modelig.

3 Tao, Wei ad Wag. INTRODUCTION igle-lae car-followig models basically address speed-spacig relaioships as oe vehicle follows aoher o a sraigh roadway where here is o passig eglecig all oher subsidiary asks such as seerig, rouig, ec. []. i ypes of car-followig models have bee developed or discussed i he pas more ha a half of he ceury. These si ypes are: safey-disace car-followig models, simulusrespose car-followig models, 3 acio-poi car-followig models, 4 fuzzy logic-based car-followig models, 5 huma eleme-based car-followig models, ad recely emerged 6 percepual-saisficig approach a framework of a car-followig model. The firs four ypes of car-followig models were hisorically reviewed by Bracksoe ad McDoald []. There has bee he lack of iformaio as o whe ad where he models would be successful [3]. Mehmood e al. [4] ideify ad discuss he assumpios ivolved i may eisig car-followig models ha resric he models abiliy o eplai ad predic driver behaviors i acual raffic siuaios. Boer s sudy [5] raises some impora issues ha have bee igored i egieerig car-followig models, icludig he followig: car followig is oly oe of he may asks ha drivers perform simulaeously ad receives herefore oly iermie aeio ad corol; drivers are saisfied wih a rage of codiios ha eed beyod he boudaries imposed by percepual ad corol limiaio, ad 3 i each drivig ask drivers use a se of highly iformaive percepual variables o guide decisio makig ad corol. O he basis of hese hree issues, Boer proposes a percepual-saisficig heory based framework ha seeks o depar from deermiism ad preses wo approaches o furher develop he area, amely saisfyig behavior ad ask schedulig, which are apparely cojucive o raffic psychology progresses. The problem wih his approach, as Bracksoe ad McDoald pois ou [,3], is he difficuly i obaiig daa for calibraig he model. Va Wisum [6] esablishes a huma eleme-based model ha describes he relaios of psychological facors ime headway, disace headway, ad deceleraio used by he driver i car followig. His model is based upo hree assumpios: a drivers uses ime headway as a safey margi; if disace o he lead vehicle is larger ha he preferred disace headway ha he/she ries o maiai, here is o safey-relaed reaso for he driver o decelerae uil he preferred disace headway is reached; ad 3 he deceleraio iiiaed by he driver is a fucio of he Time-o-Collisio TTC parameer, which is esimaed by he driver. imilar o Boer s model, Va Wisum s model has o bee esed wih daa. Above sudies ad issues ispired he auhors o coduc furher research usig video appig observaios, eraced vehicle rajecory daa from he videoapes, ad simulaio daa from ruig CORIM as well. The auhors observaios imply he cogruecy ad cosisecy of Boer s aoomy of drivig asks from high level o low level sraegic, acical, ad operaioal [7]. raegic level of drivig ask icludes he moives ad he goals for ravelig deermiig origi ad desiaio O-D ad plaig lik-based roue. Tacical level is cocered wih seekig appropriae liks ha are coecios of he plaed roue ad laes ha access o he dowsream e-roue lik. As a resul, laebased aleraive roues are ideified durig e roue drivig. Operaioal level is viewed as he low level ask hadlers ad skilled-based corollers [7]. A his level he driver eecues corol commads wih deeriy, smoohess, ad coordiaio, cosaly relyig o feedback from his ow resposes o he dyamics of he sysem s couerpars lead vehicle ad roadway raffic. I is oiceable ha local ad asympoic sabiliies occur a his level of drivig asks. Based o Boer ad Hoedemaeker s percepual-saisficig heory-based framework [5], he auhors propose he modified framework of a driver s drivig asks a he above hree levels, as show i Figure. This paper summarizes he auhors work [8, 9] i eplorig driver behaviors i a paired car followig mode i respose o a speed disurbace from he fro vehicle, ad develops a cocep of he A

4 Tao, Wei ad Wag Chais. Four scearios of car-followig ad lae-chagig behaviors are ideified i respose o a speed decrease of he fro vehicle. The impac of he followig vehicle driver s respodig behavior o dyamic spacig bewee he paired vehicles is aalyzed ad miimum dyamic spacig for each sceario are obaied from he observed rajecory daa. As oe of he epeced resposes, decisiomakig for a lae chage is iegraed wih he car-followig acio chais. Observed vehicle rajecory daa are applied o ideify he percepual iformaive variables for lae-chagig decisios ad are aalyzed o coclude applicable miimum safey spacig i car-followig ad lae-chagig eecuios. Probabiliy models of usig lae-chagig respose as a soluio o absorb speed disurbaces from he fro vehicle ad accepable codiios a he adjace lae for lae chagig decisio-makig are developed. The work preseed i his paper advaces he udersadig of speed disurbace ad speed absorpio pheomeo ad modelig a car-followig mode a he microscopic level.. HIERARCHY OF TATE-CONTROL ACTION CHAIN TO PEED DITURBANCE Drivers geerally egage i muliple asks o roads. Whe followig aoher vehicle o a sigle lae, he driver is mosly ivolved i moiorig-assessig/decisio makig-corollig processes. Oce a moiorig process is iiiaed by aeio i is decomposed io four sages: pay aeio o he percepual variables ha characerize a paricular ask i he form of he prese sae; use hose variables o evaluae curre ad epeced fuure saes, 3 assess wheher he prese performace will mos likely remai accepable for a cerai amou of ime, ad if so 4 deermie whe aeio should be give o he ask agai. If he prese performace is o saisfacory, he he driver iiiaes a appropriae corol process ha employs a suiable skill o brig he vehicle wihi a limied ime io a accepable sae ha is epeced o remai accepable for some ime [6]. The logic of he driver s respose o a speed disurbace is illusraed i Figure. Whe a speed disurbace occurs, his disurbace could eiher be recovered or o. A recovered speed disurbace ormally ehibis wo phases: speed reducio ad recovery as show i Figure 3. The followig vehicle may respod o i immediaely or someime laer, or jus keep is origial speed uil he speed disurbace is recovered. Whe he drive respods o a speed disurbace i fro, he/she may choose o respod o i by corollig he vehicle speed or he vehicle pah lae chagig. Assumig a speed disurbace is iiiaed a ad recovered a T, i.e., he lead vehicles speed decreases a ad ges back o is origial speed afer a period of ime T recovery period, he followig vehicle could respod i differe ways, amely, hree car-followig scearios ad lae-chagig sceario, which cosiue he basic ae-corol Acio-Epeced ae chais see Figure 3. If he iiial spacig ad lead vehicle s speed are accepable o he follower a, ad he reduced spacig remais accepable over T, o acio is acually i eed for he follower. I his case, T is viewed as olerable recovery period. This case is caegorized io car-followig sceario a, as illusraed i Figure 3. If durig T he sae of he spacig percepual variable becomes uaccepable due o decreased spacig caused by he reducio of he lead vehicle s speed, he followig driver iiiaes a corol acio of deceleraio or lae-chagig. If i is allowed o brig he uaccepable sae of he spacig percepual variable back o a accepable level durig T, he follower remais i he same lae while reducig he speed o corol he spacig ad he reisae followig he lead vehicle. This case is caegorized io car-followig sceario b, as illusraed i Figure 3 3. I should be oed ha he percepio of accepable or uaccepable percepual spacig varies from driver o driver. The drivers who would like o use corolled deceleraio may adop a larger spacig as a accepable hreshold ha drivers who choose o hi he brake pedals harder.

5 Tao, Wei ad Wag 3 I order o avoid a possible collisio, he brakig acio of he driver of he followig vehicle ca sar as early as whe he driver perceives he speed drop of he lead vehicle o as lae as whe he/she has reached he miimum brakig disace o avoid he arge risk. Moreover, he adopio of deceleraio raes would differ amog drivers. ome may jus release he gas pedal o reduce he vehicular speed i respose o he speed drop of he lead vehicle whe a large eough spacig is available. Oher drivers may apply corolled brakig o corol heir speed ad he spacig bewee he wo vehicles, whereas some drivers may choose o brake a he las miue wih maimum brakig force. Figure 3 3 shows a area embraced by blue lie where a corol acio may be ake. If a he iiial sae of he percepual variables of he followig vehicle is uaccepable ad a arge risk level, a appropriae corol acio is immediaely ake o brig hem away from he arge risk. I his case he ieracive speeds of he wo vehicles are show i car-followig sceario c of Figure 3 4. If a adjace lae allows higher speed, a lae chage may be eecued. This case is caegorized io lae-chagig sceario, as show i Figure 3 7. A percepual variable, speed advaage ha will be discussed laer, is employed o ideify he codiio of gaiig speed from he adjace lae. If he iiial spacig ad lead vehicle s speed are accepable o he follower a ad he recovery period is iolerable o he follower, a lae chage may be eecued whe a adjace lae allows higher speed. If o adjace lae is perceived advaageous i speed, he follower acs wih car-followig sceario b. Models for hree car-followig scearios ad he lae-chagig sceario are discussed i deails he followig secios. 3. CENARIO OF PEED DITURBANCE ABORPTION 3. Car-followig cearios If he driver decides o reduce he vehicle speed i respose o he speed disurbace, he speeds of he wo vehicles ierac ad he dyamic spacig bewee he wo vehicles ca vary grealy bu will follow he followig law: = d d Where, = fro vehicle = he firs followig vehicle = begiig ime poi of he sceario, = ime variable, = speed of vehicle lead vehicle a ime, = speed of vehicle followig vehicle a ime, = disace headway bewee vehicles, ad a ime. I each ime ierval, he spacig chages dyamically. Figure illusraes he basic sae-corol acioepeced chais ha are preseed wih hree car-followig scearios ad lae-chagig sceario. Table preses a summary of variables i miimum spacig models for all sudy scearios ad cases. Table gives observed maimum acceleraio or deceleraio values for each -mph icreme for deermiig

6 Tao, Wei ad Wag 4 hresholds of acceleraio as simulaig a car-followig sceario. Two corol variables are used i he followig secios: The spacig whe he follower begis respose o speed disurbace is called Disurbace-Effecig pacig Ef; ad The spacig whe he follower begis speed recovery from speed disurbace is called Disurbace-Edig pacig E. The values of hese wo variables are deermied by equaios ha are derived from saisic aalysis of observed vehicle rajecory daa, as show i Table. 3.. Car-Followig ceario a I his sceario as show i Figure 3, he followig vehicle does o respod o he speed disurbace from he lead vehicle ad acceps a reduced spacig bewee hem. Durig he ime ierval, ] vehicle reduces is speed ad a speed disurbace is developed. Accordig o Rohery s [ coclusio [] from reeamiig he daa obaied i he sudies by Todosiev [] ad Rohery [], he deceleraio rae of a idividual vehicle ca be assumed as almos cosa. Thus, Equaio becomes: = where, <, [, ], ad Mi = =, a = Where, = deceleraio rae of vehicle, I he ime ierval, T ] he dyamic spacig bewee he wo vehicles becomes: =, ad Mi = T = [ ], a = T 3 I he case of sceario a durig he eire period of [ ], has a miimum value of, T Mi = T = [ ], a = T 4 Where, = acceleraio rae of vehicle. 3.. Car-Followig ceario b Uder his sceario, a corol acio ca be ake a ime as lae as reachig he miimum Ef, whe a driver of he followig vehicle mees he miimum brakig disace requireme for reducig is speed o avoid a collisio. The deceleraio rae ca vary ad as a resul he corol acio may ed earlier or lae. Thus, here eis hree possible cases deermied by he begiig ime ad g force applied by a corol acio: < ad > ; < ad < ; ad 3 > ad >, show i ceario b of Figure 3. Case : < ad >

7 Tao, Wei ad Wag 5 I [, ], he followig vehicle keeps is origial speed ad he dyamic spacig ad miimum spacig durig his ierval is epressed i he same way as described i Equaio. = where, <, [, ], ad Mi = = Ef mi, a = 5 I, ], he followig vehicle reduces is speed o keep a safe disace from he vehicle i fro. The dyamic spacig bewee hem ad is miimum value are: =, ad Mi = =, a = 6 Where, = deceleraio rae of vehicle. I, ], he followig vehicle keeps reducig is speed ad he lead vehicle recovers is speed. The dyamic spacig bewee hem ad is miimum value is: = -, ad Mi =, a = 7 Mi =, i.e., miimum disurbace-edig spacig. Case : < ad < I [, ], he dyamic spacig ad is miimum value are as described i Equaio 5. I, ], he speed disurbace is coiuously developed ad vehicle reduces is speed sarig a = o keep a safe disace space from he vehicle i fro uil =. A ha ime, he speed of he followig vehicle reaches he speed of vehicle. The dyamic spacig ad is miimum value are: =, ad Mi = = E mi, a = 8 I, T ], he followig vehicle keeps roughly he same speed profile as ha of he vehicle direcly i fro. The dyamic spacig bewee hem ca be regarded as cosa. Therefore, he miimum value of dyamic spacig i his case is Mi =. Case 3: > ad >

8 Tao, Wei ad Wag 6 I, he followig vehicle keeps is origial speed ad he dyamic spacig ad is miimum value are he same as i Equaio. ], [ I ], [, vehicle recovers is speed. The percepual sae of vehicle has bee kep accepable ad he followig vehicle ravels a is origial speed uil i becomes uaccepable a =. The dyamic spacig bewee he wo vehicles ad he miimum value of his spacig are: =, ad Mi = a = 9 I ],, vehicle coiuously recovers is speed ad vehicle reduces is speed o keep a safe disace headway from he vehicle i fro. The dyamic spacig ad is miimum value are: =, ad Mi = a =, I his sceario, Mi = Car-Followig ceario c I sceario c, a corol acio is ake a he ime of τ, bu he deceleraio rae may vary, from small or large, which i ur resuls i he corol acio edig earlier or laer. Thus, here eis wo possible cases, i.e. > ; ad < ; as show i ceario c of Figure 3. Case : > This case is similar o case i ceario b ecep for he begiig ime of a corol acio of he followig vehicle. Therefore: Mi = - τ, a = Case : < Case is similar o he case of ceario b wih Mi τ = =, a = I sceario a, durig he eire period of he speed disurbace of he lead vehicle he followig vehicle does o reduce is speed bu he spacig bewee he wo vehicles is reduced by

9 Tao, Wei ad Wag 7 [ ]. This spacig reducio absorbs a speed reducio i he amou of = -. For a give spacig, mus be [ safe ] 3 Oherwise, mus propagae backwards hrough he speed reducio of he followig vehicle. This propagaed speed reducio has a impac o he vehicle followig he e followig vehicle as show i Figure 4. If he spacig bewee vehicles ad is large eough o absorb he propagaed speed reducio, he mus be: [ safe ] [ safe ] 4 Oherwise, he iiial speed disurbace will be coiuously rasmied backward hrough he lie of vehicles. Therefore, Equaio 3 gives he magiude of he speed disurbace ha a sigle spacig ca absorb, ad Equaio 4 gives he magiude of he speed disurbace ha wo cosecuive spacigs ca absorb i he siuaio where he speed disurbace is propagaed. Figure 5 shows he disribuio of spacig ad headway bewee pairs of vehicles for all scearios eecued as a respose o car-followig speed disurbace. Observed miimum spacig a he corol acio imes ad hadbook-recommeded miimum safey spacig are demosraed i Figure 5, which will be discussed i deail i secio Lae-Chagig ceario for Respose o peed Disurbace Two ypes of lae-chagig behaviors, madaory ad discreioary, were radiioally defied [3, 4]. A Driver s decisio o make a lae chage is depede o his roue pla, lae saus wheher he curre lae is i he roue-lik, ad raffic codiios i he curre ad adjace laes. I has bee commoly recogized ha drivers perform madaory lae chage o coec he e lik o heir pah, bypass a dowsream lae blockage, obey lae-use regulaios, ad respod o lae-use sigs ad variable message sigs. A decisio o perform discreioary lae chage is based o wheher a driver ca olerae he leadig vehicle s speed ad he flow speed i he adjace laes. Oher reaso for discreioary lae chage also icludes obaiig queue advaage, which is very likely o occur whe a adjace lae has a shorer queue [3]. As show i Figure, oe pheomeo ha has bee previously draw lile aeio is he case whe a lae chage may be eecued i respodig o a car-followig speed disurbace from he fro vehicle. I his case he lae chage falls io he caegory of discreioary

10 Tao, Wei ad Wag 8 lae chage. Figure 3 7 illusraes he process whe a lae chage occurs a he ime i respose o a speed disurbace. Miimum spacig variables for lae-chagig sceario is also summarized i Table. 3.. Probabiliy of Lae-Chagig Respose Perpeuaed via peed Advaage Gipps [5] proposed he cocep of speed advaage o ideify a eed of a discreioary lae chage ad Wei e al. [6] proposed a quaiaive defiiio of speed disadvaage ad speed advaage o describe decisioal codiios for a discreioary lae chage o urba srees. I he auhors sudy of he speed absorpio pheomeo usig observed vehicle rajecory daa, speed advaage is redefied as a percepual variable for a driver o compare speed performace wih he adjace laes. peed advaage A is described i he followig mahemaical equaio. V A = V V LD LD FT 5 Where, A = speed advaage compared o a adjace lae; if V LD V FT V LD = he lead vehicles speed i a adjace lae, f/s or mph; V FT = he fro vehicles speed, f/s or mph; Usig he A variable, he probabiliy of moivaig a lae chage icurred from a speed disurbace by he fro vehicle could be esimaed by he followig equaios, which were derived from saisical aalysis of vehicle rajecory daa obaied i Kasas Ciy, Missouri [9]: For wo-way srees: 3 4 P = A = %[ ] 6 For oe-way sree: 3 4 P = A = %[ ] 7 Where P A = A = probabiliy of geeraig a moivaio o chage o he speed-advaaged lae whe = A. The correlaio coefficie R value for equaios 3 ad 4 is.9757 ad.98, respecively, a he cofidece level of 95%. For eample, if he fro vehicle speed reduces o 3 mph while he adjace lae s speed remais a 5 mph, 3.% of followers would possibly chage o he adjace lae i a wo-way sree. imilarly, 3.7% of follows do so i a oe-way sree. 3.. Accepable Codiios a he Adjace Lae o Eecue A Lae Chage Boh he gap bewee he lead i he adjace lae ad he prospecive lae chager ermed as lead gap ad he gap bewee he prospecive lae chager ad he lag vehicle ha is i he adjace lae ermed as lag gap are major facors affecig he driver s lae-chagig decisios. More sigificaly, hese accepable gaps are cohere wih he speed of he prospecive lae chager ad he lag vehicle. I is assumed ha he accepable lead gap for a lae-chagig decisio could be epressed as a fucio of he subjec vehicle s speed ad he lag gap as a fucio of he lag vehicle s speed. Figure 6 visualizes he disribuio of observed lead gaps versus lae chager s speeds ad lag gaps versus he lag vehicle s speeds. I preses he cocered gap ad speed values a he mome as he maeuver of a lae chage is sared. Comparisos bewee he observed gap values ad he

11 Tao, Wei ad Wag 9 recommeded miimum safe gaps miimum safey brakig disaces plus reacig disaces a varied speeds recommeded i Kasas Drivig Hadbook are also preseed i Figures 6. I is obviously see from Figures 6 ha a porio of he samplig drivers, as perform discreioary lae chages, acually acceps smaller gaps ha he hadbook-recommeded values. Those drivers accepig o less ha he hadbook-recommeded values are viewed as coservaive drivers, oherwise as regular drivers. The criical accepable gaps are modeled usig a curve represeig he lower boudary of he observed daa, as show by he lowes curve i Figure 6. Accepable gap codiios o eecue a discreioary lae chage ca be described by he followig equaio v sub coservaive drivers Lead/Lag Gap >.556Vsub e ad <.3336V sub regular drivers Disurbace-Effecig pacig Variable The auhor s fidigs from vehicle rajecory daa [9] idicae ha 9% of observed discreioary lae chages happe before he lae-chagers speeds are acually affeced by he speed disurbace from he fro vehicles. I oher words, as boh a adjace lae is oe of roue-lae ad provides accepable gap codiio, a driver who is poeially rapped i he car-followig speed disurbace eds o swich oo a adjace lae before reducig is speed. uch a probabiliy is 9% o he observaio basis. I summary, a driver eds o cosider a discreioary lae chage oly whe he followig wo codiios eis: The driver perceives ha he speed of he head vehicle is less ha his or her desired speed; The driver perceives ha he could remai or icrease speed by chagig o aoher lae. Refereeig o Figure ad Figure 3 7, he driver will commece a lae chage a before reachig he miimum safey spacig. The spacig a his mome is called he disurbace-effecig spacig, or Ef. Figure 5 shows he disribuio of spacig ad headway bewee pairs of vehicles whe a lae chage is eecued as a respose o car-followig speed disurbace. Equaios for esimaig miimum spacig ad headway are derived from he saisical aalysis as show i Figure 5. They are described as follows. Those miimum spacig ad headway models are also recommeded as hresholds corol for car-followig scearios, as summarized i Table. Miimum disurbace-effecig spacig vs. speed V: mi 6.484e =.3336V.97V.6398V Regular Driver Coservaive Driver Miimum headway H mi vs. speed V regular Driver:.6V -.49V.83 V 3 f/s H mi =.49V 3.668e V < 3 f/s 3..4 Acceleraio, peed ad Lae-Chagig Duraio A lae chager may accelerae or decelerae whe maipulaig a lae-chagig maeuver so as o keep a safe headway o he lead vehicle or o he lag. Acceleraio varies wih he idividual speeds of he lae chager ad he lead vehicle, as well as he differeces bewee hem. Table gives observed maimum acceleraio or deceleraio values for each -mph icreme for deermiig hresholds of acceleraio as simulaig a lae-chagig maeuver.

12 Tao, Wei ad Wag The auhors observaios also idicae ha lae-chagig duraio has lile cohere relaioship wih speeds of over f/sec 3 m/s. For discreioary lae chage, he average duraio of lae chagig rages from.33 secods o.5 secods wih sadard deviaios from.56 o.93 secods. Therefore,.3 ~.5 secods may be recommeded as a geeral descripio of he lae-chagig duraio. 4. CONCLUION The coribuios ha have bee made hrough he sudies preseed i his paper iclude he followig. New fidigs from observaios ad vehicle rajecory daa are isilled io he curre kowledge of udersadig he car-followig behaviors i respose o a speed disurbace ad he process of a speed disurbace absorpio ad/or propagaio. Heurisic models for ae-corol Acio-Epeced Chais are developed o iegrae carfollowig ad lae-chagig behaviors i respose o speed disurbace i a car-followig mode Threshold values of major percepual variables are derived from vehicle rajecory daa, amely, miimum disurbace-effecig/edig spacig i.e., Ef ad E, maimum acceleraio/deceleraio a a corol acio ime, ad lae-chagig duraio. Models for probabiliy of lae-chagig respose o speed disurbace via speed advaage variable, ad models for accepable lae-chagig decisio-makig codiios a he adjace laes, are developed based aalysis of observed vehicle rajecory daa. As a resul of above fidigs, a ew heurisic drivig modelig framework is proposed based o Boer s Percepual-aisficig Theory-Based framework. I provides a simplified, easily udersadable archiecure for modelig ravel ad drivig behaviors. The work preseed here sheds some ligh o he effec ha a sigle speed disurbace of a fro vehicle has o he spacig ad speed of he followig vehicle i a car-followig mode a he microscopic level. This esablishes he foudaio for furher research o muliple speed disurbace absorpio ad is impac o raffic sabiliy a he macroscopic aalysis level. REFERENCE. Richard W. Rohery. Car Followig Models. Revised Moograph o Traffic Flow Theory. Ocober. Bracksoe M. ad M. McDoald. Wha Is he Aswer? Ad Come o Tha, Wha Are he Quesios? Trasporaio Research Par F, Vol., No , pp Bracksoe M. ad M. McDoald. Car-Followig: A Hisorical Review. Trasporaio Research Par F, Vol., No , pp Mehmood? 5. Edwi R. Boer ad Marika Hoedemaeker. Modelig Drivig Behavior wih Differe Degrees of Auomaio: A Hierarchical Decisio Framework of Ieracig Meal Models. 7 h Europea Aual Coferece o Huma Decisio Makig ad Maual Corol, December 4-6, 998. Valeciees, Frace. 6. Va Wisum, W. The Huma Eleme i Car Followig Models. Trasporaio Research Par F, Vol., No , pp Boer, E. R. Car Followig from he Driver s Perspecive. Trasporaio Research Par F, Vol., No , pp. -6

13 Tao, Wei ad Wag 8. Tao, Ruihua. peed Disurbace, Absorpio ad Traffic abiliy. Ph.D. Disseraio. Michiga ae Uiversiy Wei, Heg. Observed Lae-Choice ad Lae-Chagig Behaviors o a Urba ree Nework usig Video-Capure-Based Approach ad uggesed rucures of Their Models. Ph.D. Disseraio. Uiversiy of Kasas Garer, N., G. C. Messer, ad A. K. Rahi. Traffic Flow Theory. Chaper 4 of R. W. Rohery, Car Followig Models. Trasporaio Research Board pecial Repor 65, Trasporaio Research Board,, Page Todosiev, E. P.. The Acio Poi Model of he Driver Vehicle ysem. Repor No. A-3. Ohio ae Uiversiy, Egieerig Eperime aio, Columbus, Ohio, 963. Rohery, R. W., R. ilver, R. Herma ad C. Torer968, Aalysis of Eperimes o igle Lae Bus Flow. Operaio Research, 968, pp Tomer Toledo, H. N. Housopoulos, ad Be-Akiva, M.E. Modelig Iegraed Lae-chagig Behavior. I prepris of 8 d Trasporaio Research Board Aual Meeig, Washigo D.C., Jauary -6, 3 4. Yulog Zhag, Larry E. Owe, ad James E. Clark. A Muli-Regime Approach for Microscopic Traffic imulaio. A paper preseed a Trasporaio Research Board 77 h Aual Meeig i Washigo, D.C. Jauary -5, Gipps, P.G., A Model for he rucure of Lae Chagig Decisios. Trasporaio Research, B, pp Heg Wei, Eric Meyer, Joe Lee, ad Chue Feg. Characerizig ad Modelig Observed Lae- Chagig Behavior for Lae-Vehicle-Based Microscopic imulaio o a Urba ree Nework. Trasporaio Research Record No. 7,. pp 4-3

14 Tao, Wei ad Wag TABLE OF TABLE AND FIGURE TABLE : ummary of Variables i Miimum pacig Models for All udy cearios ad Cases...3 TABLE : Observed Maimum Acceleraios for -mph Icremes i Urba rees...4 FIGURE : Heurisic Driver Modelig Framework...5 FIGURE : ae-corol Acio-Epeced Chais Respodig o peed Disurbace...6 FIGURE 3: Illusraio of peed Disurbace ad Car-Followig cearios...7 FIGURE 3 co.: Illusraio of peed Disurbace ad Car-Followig cearios...8 FIGURE 3 co.: Illusraio of peed Disurbace ad Car-Followig cearios...9 FIGURE 4: Process of a peed Disurbace Propagaed hrough a Lie of Vehicles... FIGURE 5: Observed pacig ad Headway bewee Pairs of Vehicles a Corol Acio Times*... FIGURE 6: Accepable Gap Codiios i he Adjace Lae for Lag-Chagig Decisio-Makig...

15 Tao, Wei ad Wag 3 TABLE : ummary of Variables i Miimum pacig Models for All udy cearios ad Cases Disurbace-Effecig pacig Ef, f Disurbace-Edig pacig D, f cearios ad Cases Miim Ef Corol Acio Time Miimum E Corol Acio Time Car- Followig ceario a Car- Followig ceario b Car- Followig ceario c All cases N/A N/A [ ] Case : ad < > Case : ad < < Case 3: ad > > Case : > Case : < e coservaive regular = = = = = τ τ T = = = = = = Lae- Chagig ceario Case : < Case : > e coservaive regular l = duraio of lae chage = = l = = l Noes: The spacig whe he follower begis respose o speed disurbace is called Disurbace-Effecig pacig Ef The spacig whe he follower begis speed recovery from speed disurbace is called Disurbace-Edig pacig E

16 Tao, Wei ad Wag 4 TABLE : Observed Maimum Acceleraios for -mph Icremes i Urba rees Type Typical Maimum Acceleraio Rae o Level Road f/sec arig peed - 5 f/s - mph 5-9 f/s - mph 9-44 f/s -3 mph f/s 3-4 mph f/s 4-5 mph Two-way Oe-way Daa ource: vehicle rajecory daa observed i Kasas Ciy, Missouri, 998

17 Tao, Wei ad Wag 5 FIGURE : Heurisic Driver Modelig Framework raegic Level Needs: O-D hores Pah raegy elecio: Plaig Pre-Trip Lik-Based Roue Roue Turig Corol Pois Tacical Level Objecive: Roue Keepig Tasks: afey, mooh Task chedule/aeio Maager E Roue Liks Keepig Local Asympoic abiliy Operaioal Level Objecive: aisfied Lae Yes Lae Keepig Car Followig Disurbace Absorpio Traffic codiios o curre ad adjace laes Roadway codiios o curre ad adjace laes peed Limi aisfyig Curre Lae? No peed Disurbac pacig Reducio Lae Chagig, he Lae Keepig

18 Tao, Wei ad Wag 6 FIGURE : ae-corol Acio-Epeced Chais Respodig o peed Disurbace peed disurbace by lead Vehicle Iiial ae of Comforable pacig a Accepable speed of he lead vehicle Uaccepable speed of he lead vehicle a arge-risk Yes Tolerable recovery period T? No No Adjace lae saisfied? Yes Yes Adjace lae saisfied? No ceario a Accepace/ o acio ceario b Reduce speed a Lae-Chagig ceario Eecue lae chage a before Reachig mi ceario c Immediaely reduce speed a τ Reach mi a T Reach mi sar recovery a ar Recovery a he ime lae-chagig duraio Reach mi sar recovery a Comforable spacig a T T

19 Tao, Wei ad Wag 7 FIGURE 3: Illusraio of peed Disurbace ad Car-Followig cearios A Recovered peed Disurbace: peed peed reducio peed recovery = - T ime Where, = speed of vehicle a ime, = speed of vehicle a ime, T = ime period of a speed disurbace developme ad recovery, Car-Followig ceario a:, peed T ime 3 Car-Followig ceario b: peed, T ime

20 Tao, Wei ad Wag 8 FIGURE 3 co.: Illusraio of peed Disurbace ad Car-Followig cearios 4 Car-Followig ceario c:, peed τ Where, = speed of he lead vehicle a ime, T ime = speed of he followig vehicle a ime, = speed of he followig vehicle a ime, τ = percepio-reacio ime of he followig driver, = ime poi before which he followig vehicle ravels a is origial speed, ad = ime poi a which he followig vehicle complees i speed reducio. 5 Possible Cases i ceario b:, peed 3 : sceario : ceario 3: ceario 3 T ime

21 Tao, Wei ad Wag 9 FIGURE 3 co.: Illusraio of peed Disurbace ad Car-Followig cearios 6 Possible Cases i ceario c:, peed : Case : Case Where, τ T ime = ime poi before ha he followig vehicle ravels a is origial speed, ad = ime poi a which he followig vehicle complees i speed reducio. 7 Lae-Chagig ceario: peed, l Fro Vehicle T ime Lag Vehicle Lae Chager Lead Vehicle Where, = ime poi before ha he followig vehicle begis lae chagig, ad = ime poi a which he followig vehicle complees i speed reducio

22 Tao, Wei ad Wag FIGURE 4: Process of a peed Disurbace Propagaed hrough a Lie of Vehicles Vehicles pacig peed disurbace propagaio peed T ime Where, = spacig bewee vehicles ad a ime, = spacig bewee vehicles ad a ime, = ime poi before ha he followig vehicle ravels a is origial speed, ad = ime poi a which he followig vehicle complees i speed reducio.

23 Tao, Wei ad Wag FIGURE 5: Observed pacig ad Headway bewee Pairs of Vehicles a Corol Acio Times* Observed pacig of Targe Fro Vehicles Vs. he Targe Vehicles peed Y - pacig of Targe Ahead Vehicles f Y - Headway of Targe Ahead Vehicles s Hadbook Mi pacig y = y = 6.484e X - Targe Vehicles peed a Corol Acio Time f/s Gaps of Targe ad Ahead Vehicles as A Lae Chace Begis Mimum pacig Lie Miimum afey pacig Epo. Mimum pacig Lie Power Miimum afey pacig Observed Headway of Targe Ahead Vehicles Vs. he Targe Vehicles peed Observed Mi Headway Coservaive Drivers Observed Mi pacig y = 3.668e -.49 y = Regular Drivers X - Targe Vehicles peed a Corol Acio Time f/s Observed Headway of Targe ad Ahead Vehicles as A Lae Chace Begis Epo. Mimum Headway Lie Poly. Mimum Headway Lie * Corol Acio Time: as he follower begis reducig speed due o he speed disurbace by he fro vehicle.

24 Tao, Wei ad Wag FIGURE 6: Accepable Gap Codiios i he Adjace Lae for Lag-Chagig Decisio-Makig Y = Gap f Lead ad Lag Gaps versus Lae-Chagers peed ad he Lag Vehicles peed Aalysis of Trajecory Daa Observed i Kasas Ciy, Missouri 998 Hadbook Mi pacig Coservaive Drivers Y =.3336X.6398 R =.9998 Observed Mi pacig Y = 7.979e.556X R =.9953 Regular Drivers Observed Lead Gap vs ubjec Vehicles peed Aggressive Criical Gap Power Miimum afey Gap Observed Lag Gap vs Lag Vehicles peed Miimum afey Gap Epo. Aggressive Criical Gap X = peed mph