Traffic flow of adaptive cruise control vehicles on highway with an on-ramp

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2 Traffi flow of adaptive ruise otrol vehiles o highway with a o-ramp Rui Jiag 1, Mao-Bi Hu 1,, Qig-Sog Wu 1, ad Yog-Hog Wu 1 Shool of Egieerig Siee, Uiversity of Siee ad Tehology of Chia, Hefei 3006, Chia Departmet of Mathematis ad Statistis, Curti Uiversity of Tehology, Perth WA6845, Australia Abstrat Reetly, adaptive ruise otrol (ACC) systems are equipped o some vehiles to provide oveiee ad omfort ad to alleviate the drivig burde of the drivers. This paper studies traffi flow features ear a o-ramp i a ar-followig model of ACC vehiles. I the ar-followig model ad the related gap aeptae model i the road mergig setio, (i) Traffi flow stability is always maitaied; (ii) There is o large aeleratio ad deeleratio; (iii) Safety is guarateed ad o ollisio happes eve without the itervetio of drivers. The depedee of the system apaity o the iflow rates o mai road ad o-ramp is studied. The effet of aggressive parameter is also ivestigated. The desired ad udesired traffi flow features are revealed. Keywords: Traffi flow; adaptive ruise otrol; o-ramp 1. Itrodutio Log distae drivig alog highway is tirig. Reetly, adaptive ruise otrol (ACC) systems are equipped o some vehiles to provide oveiee ad omfort ad to alleviate the drivig burde of the drivers (Va Arem et al., 006; Zhag ad Ioaou, 006; Ioaou ad Stefaovi, 005; Zheg ad MDoald, 005). A ACC-equipped vehile detets the presee of a preedig vehile ad measures the distae (rage) as well as the relative speed (rage rate) by usig a forward-lookig sesor. It automatially adjusts the vehile speed to keep a proper rage whe a preedig vehile is deteted (Ioaou, 003; VaderWerf et al., 001; Shladover, 000). Some riteria of a good rule of ACC vehiles (iludig ar-followig rule, lae hagig rule, rage poliy, gap aeptae rule, et.) are: (i) Traffi flow stability should be guarateed (Kikuhi et al., 003; Yi ad Horowitz, 005); (ii) There is o large aeleratio ad deeleratio; (iii) Safety should be guarateed ad o ollisio happes eve without the itervetio of drivers (Rakha et al., 001; Wag ad Rajamai, 004a). I this paper, we study traffi flow features ear a o-ramp i a ar-followig model of ACC vehiles, usig the ostat time headway poliy (Zhou ad Peg, 005; Wag ad Rajamai, 004b). The above metioed riteria are met i the ar-followig model ad the related gap

3 aeptae model i the road mergig road setio. The depedee of the system apaity o the iflow rates o mai road ad o-ramp is studied. The effet of aggressive parameter is also ivestigated. The paper is orgaized as follows. I the ext setio, the ar-followig model of ACC vehiles as well as the gap aeptae model at the road mergig setio is itrodued. Setio 3 presets ad disusses the simulatio results. The olusio is give i setio 4.. Model I this setio, we itrodue the ar-followig model of ACC vehiles ad the gap aeptae model at the road mergig setio. For the ar-followig model, the ostat time headway poliy is adopted. The dyamis of the ACC vehiles a be modeled by the followig equatio (Davis, 004) dv dt 1 x D = mi, v τ T max λ v + v (1) x Here v is the veloity of vehile, x is the positio of vehile. x = x 1 x is the distae headway betwee vehile ad its preedig vehile 1, v = v 1 v is the veloity differee betwee vehile ad vehile 1. τ is the vehile respose time, whih is typially 0.5- s. T is the preferred time headway i the ostat time headway poliy. D is the average legth of vehiles. λ is a parameter refletig the respose to the rage rate. Note the model of ACC vehiles is atually a full veloity differee model with the optimal veloity V x ) = mi(( x D) / T, v ) (Jiag et al., 001). Therefore, the stability of ( max ACC vehiles ould be maitaied provided that 1 λ V '( x ) = 1/ T < + for τ x x = v max T + D is met (Jiag et al., 001; Liag ad Peg, 000). x Furthermore, i order to provide omfort to the passegers, large aeleratio ad deeleratio are prohibited. I this paper, we restrit a dv dt a + +, ad set a = m/s ad a = 3 m/s. I order to avoid ollisio, the deeleratio a = 3 m/s is applied whe v a > v 1 a + x D () Here a is a omfortable deeleratio ad it is set to a = m/s. Therefore, v a deotes

4 the distae traveled by vehile whe it deelerates with a. Next we preset the gap aeptae model at the road mergig setio. For simpliity, we assume the mai road is a sigle-lae road. We suppose a vehile o aeleratio lae ould hage to the mai road lae provided that the followig riterio is met (see Fig.1): v v v v+ γ ( ) < x D ad γ ( ) < x+ D (3) a a a a Here γ is a aggressive parameter, x + is the distae betwee the preedig vehile o mai road ad vehile o aeleratio road, x is the distae betwee vehile o aeleratio road ad the followig vehile o mai road. v is the veloity of vehile o aeleratio road, v is the veloity of the preedig vehile o mai road ad v is the veloity of the followig + vehile o mai road. detetor x_ x + detetor 1 v_ v + v mai road aeleratio lae Figure 1. Sketh of the o-ramp system. 00 time (s) positio (m) Figure. Trajetories of 40 vehiles. Iitially the vehiles are movig with veloity 30 m/s ad headway 60 m. The leadig vehile deelerates at t =0 with deeleratio - m/s util it reahes 0 m/s. Oe a see the followig vehiles deelerate aordigly ad the strig stability is maitaied.

5 3. Simulatio Results I this setio, the simulatio results are preseted ad disussed. I the simulatios, the parameters used are: v max = 30 m/s, T = 1.5 s, D = 7.5 m, τ = s, λ = 10.0 m/s Traffi stability Give the parameters, it a be verified that 1 λ 1 / T < + is always met whe τ x x x = 45 m. Therefore, traffi flow stability ould be always maitaied. This a also be see from Fig., where the leadig vehile of a platoo of vehiles with iitial headway x = 60 m deelerates to 0 m/s with deeleratio - m/s. Time (a) Time (b) Positio Time () Positio Positio Figure 3. Trajetories of vehiles o the mai road ear the o-ramp. (a) = 0. 5 α ; (b) = 0. 8 α ;

6 () α = Traffi flow ear a o-ramp I this subsetio, the traffi flow patters ad the flow rate o a highway with a o-ramp are studied. The o-ramp setup is show i Fig.1. The aeleratio lae is assumed to start from x = 500 m ad ed at x = 600 m. At the etrae of the mai road ad o-ramp, it is assumed that a vehile with veloity 30 m/s arrives with probability α ad β per 1.5 s, so that the maximum flow rate 400 vehiles/h ould be reahed o the mai road whe α = 1. Fig.3 shows the trajetories of vehiles o the mai road ear the o-ramp. The parameters are β = 0.4, γ = Oe a see that the vehiles a merge ito the mai road oly whe eough spae is available o the mai road. The vehiles o the mai road are oly slightly affeted by vehiles that merge from aeleratio lae, ad ogestio ever happes o mai road. With the irease of α, the flow rate o mai road ireases. As a result, the available spae log eough for the mergig of vehiles from aeleratio lae appears less frequetly. As a result, the mergig flow rate dereases. This a be see by omparig Fig.3(a) ad (b). Whe α 0.9, there is essetially o spae available for the mergig of vehiles. Cosequetly, a omplete jam appears o the o-ramp (see, e.g., Fig.3()). Fig.4 shows the depedee of system apaity (whih is reorded by detetor 1 dowstream of the mergig regio as show i Fig.1) o parameters α ad β. Oe a see that three regios are lassified i the spae of (α, β ). I regio A, both mai road ad o-ramp are i free flow state. The system apaity ireases with the irease of α ad/or β, ad it remais ostat provided α + β does ot hage. I regio B, o-ramp flow beomes ogested. I this regio, system apaity is essetially idepedet of α ad β. However, it is muh smaller tha the maximum flow rate of 667 vehile/s (i.e., 400 vehiles/h). I regio C, system apaity is idepedet of β ad it ireases with the irease of α util it reahes 667 vehile/s at α = 1.

7 0.7 apaity (vehile/s) β α β B C A α Figure 4. Depedee of system apaity o parameters α ad β. The bottom plot shows the projetio i the spae of (α, β ). Here γ =0.7.

8 0.7 q 1 (vehile/s) α β Figure 5. depedee of flow rate q 1 o parameters α ad β. Fig.5 shows the depedee of flow rate q 1, whih is reorded by detetor upstream of the mergig regio as show i Fig.1, o parameters α ad β. Oe a see q 1 is idepedet of β ad ireases liearly with α. Fig.6 shows the depedee of mergig flow rate, i.e., the flow rate of vehiles that suessfully merge ito the mai road from the aeleratio lae, o parameters α ad β. Oe a see that two regios are lassified i the spae of (α, β ). I the upper right part, the mergig flow rate is idepedet of β ad it dereases with the irease of α. I the lower left part, the mergig flow rate is idepedet of α ad it ireases with the irease of β. Next we ivestigate the effet of the aggressive parameter γ o the system apaity. Fig.7 shows the apaity at differet values of γ with a fixed β =. It a be see that with the derease of γ, the apaity ireases i the itermediate rage of α. This is beause more vehiles o aeleratio lae ould merge ito mai road with the derease of γ. However, to guaratee the safety of vehiles, γ aot be too small. Our simulatios show that if γ is set to 0.5, ollisio will happe without the itervetio of drivers.

9 merge flow rate (vehile/s) α β β α Figure 6. Depedee of the mergig flow rate o parameters α ad β. The bottom plot shows the projetio i the spae of (α, β ).

10 0.7 apaity (vehile/s) γ=0.7 γ= γ= α Figure 7. System apaity at differet values of γ with a give β =. 4. Colusios I this paper, we have studied the traffi flow ear a o-ramp i a ar-followig model of ACC vehiles, usig the ostat time headway poliy. I the ar-followig model ad the related gap aeptae model at the road mergig setio, (i) Traffi flow stability is always guarateed; (ii) There is o large aeleratio ad deeleratio; (iii) Safety is guarateed ad o ollisio happes eve without the itervetio of drivers. It is foud (i) the traffi flow o the mai road is essetially idepedet of the traffi flow o the o-ramp, ad o ogestio appears o the mai road; (ii) I otrast, the traffi flow o the o-ramp depeds o the traffi flow of the mai road. Whe the mai road traffi reahes the maximum flow rate, there is o gap that ould be aepted by the vehiles o the o-ramp. As a result, o vehile ould merge ito the mai road. (iii) With the derease of flow rate o the mai road, the apaity of the system dereases; (iv) The apaity depeds o the aggressive parameter i the gap aeptae model. With the derease of the parameter, the apaity is ehaed. Nevertheless, whe the parameter is smaller tha a threshold, the safety ould ot be guarateed ad ollisio might happe. Feature (i) is desired but feature (iii) is udesired, whih eeds to be removed. Oe possibility is usig other rage poliy, whih eeds further ivestigatios. Moreover, i our future work, we eed to osider the situatio that the mai road has more tha oe lae. Akowledgemet: We akowledge the support of Natioal Basi Researh Program of Chia (No.006CB705500), the Natioal Natural Siee Foudatio of Chia (NNSFC) uder Projet Nos , , , the NCET ad the FANEDD. Y.-H. Wu akowledges the support of the

11 Australia Researh Couil through a Disovery Projet Grat. Referees: Davis LC, (004) Effet of adaptive ruise otrol systems o traffi flow. PHYSICAL REVIEW E 69 : Art. No Ioaou P, (003) Adaptive ruise otrol systems speial issue. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 4 : 113. Ioaou P ad Stefaovi M, (005) Evaluatio of ACC vehiles i mixed traffi: Lae hage effets ad sesitivity aalysis. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 6 : 79. Jiag R, Wu QS, Zhu ZJ, (001). Full veloity differee model for a ar-followig theory. PHYSICAL REVIEW E 64 : Art. No Kikuhi S, Uo N, Taaka M, (003) Impats of shorter pereptio-reatio time of adapted ruise otrolled vehiles o traffi flow ad safety. JOURNAL OF TRANSPORTATION ENGINEERING-ASCE 19 : 146. Liag CY ad Peg H, (000) Strig stability aalysis of adaptive ruise otrolled vehiles. JSME INTERNATIONAL JOURNAL SERIES C 43 : 671. Rakha H, Hakey J, Patterso A et al., (001) Field evaluatio of safety impats of adaptive ruise otrol. ITS JOURNAL 6 : 5. Shladover SE, (000) Progressive deploymet steps leadig toward a automated highway system. TRANSPORTATION RESEARCH RECORD (177): Va Arem B, Va Driel CJG, Visser R, (006) The impat of ooperative adaptive ruise otrol o traffi-flow harateristis. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 7 : 49. VaderWerf J, Shladover S, Kourjaskaia N, et al., (001) Modelig effets of driver otrol assistae systems a traffi. TRANSPORTATION RESEARCH RECORD (1748): Wag J ad Rajamai R, (004a) The impat of adaptive ruise otrol systems o highway safety ad traffi flow. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 18 : 111. Wag J ad Rajamai R, (004b) Should adaptive ruise-otrol systems be desiged to maitai a ostat time gap betwee vehiles? IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 53 : Yi JG ad Horowitz R, (006) Marosopi traffi flow propagatio stability for adaptive ruise otrolled vehiles. TRANSPORTATION RESEARCH PART C 14 : 81. Zhag JL ad Ioaou P, (006) Logitudial otrol of heavy truks i mixed traffi: Evirometal ad fuel eoomy osideratios. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 7 : 9. Zheg PJ ad MDoald M, (005) Maual vs. adaptive ruise otrol - Ca driver's expetatio be mathed? TRANSPORTATION RESEARCH PART C 13 : 41. Zhou J ad Peg H, (005) Rage poliy of adaptive ruise otrol vehiles for improved flow stability ad strig stability. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 6 : 9.

12 Third Iteratioal Symposium of Trasport Simulatio 008 (ISTS08) file://h:\idex.htm 页码,1/ Third Iteratioal Symposium of Trasport Simulatio 008 (ISTS08) Lists of Papers A Lae Chagig Model for Urba Arterials - Charisma F. Choudhary A Marosopi Estimatio Method of Platoos Behaviors i Cogestio - Niolas Chiabaut A Modular Tool for Preditio of Desig Choies Impat o Railway Servie Depedability - Giovai Dazzi Advaed Modelig ad Simulatio for Trasport Quality ad Depedability Assessmet - Ekehard Shieder Aggregatio Algorithms i a Vehile-to-Vehile-to-Ifrastruture (VVI) Itelliget Trasportatio System Arhiteture - Jeffrey Miller Approahes for Modellig Commerial Freight Traffi Regardig Logistis Aspets - Uwe Clause Coflit i Oe-Lae Roudabout: Keep The Priority or Keep Calm? - Auberlet JM Level Crossig Based o Stohasti Petri Nets Models ad Soial Eoomi Data - W. Zheg Explorig Crowd Dyamis uder Emergey Coditios: Simulatio Perspetives ad Experimets with Paikig Ats - Niraja Shiwakoti Headway ad Vehile Size Optimizatio i Urba Bus Trasit Networks - Luigi dell Olio Mesosopi Simulatio for Trasit Operatios - Tomer Toledo Mesosopi Simulator Data to Perform Dyami Origi-Destiatio Matries Estimatio i Urba Cotext - Emmauel Bert Mirosopi Pedestria Simulatio Model for Flow Evaluatio Iorporatig Atiipatory Behaviour - Miho Asao Mirosopi Traffi Simulatio: Towards a Simulatio Iludig Motorylists - Espié S Modellig Pedestrias i ad Aroud Etrae Poits: A First Coept Foussig o Automated Revolvig Doors - Wiie Daame Modellig Publi Trasport Stops by Mirosopi Simulatio - Rodrigo Ferádez Naosopi Traffi Simulatio: Ehaed Models of Driver Behaviour for ITS ad Telematis Simulatios - Hussei Dia Optimal Coordiatio of Publi Trasit Vehiles Usig Peratioal Tatis Examied by Simulatio - Yuval Hadas Partile-Filter Traffi State Estimatio ad Sequetial Test for Real-Time

13 Third Iteratioal Symposium of Trasport Simulatio 008 (ISTS08) file://h:\idex.htm 页码,/ Traffi Sesor Diagosis - Jaques Sau Pedestria Flow at Bottleeks Validatio ad Calibratio of VISSIM s Soial Fore Model of Pedestria Traffi ad its Empirial Foudatios - Tobias Kretz Pedestria Route Choie Self-Orgaizatio - Kardi Tekomo Presriptive Route Guidae as a Traffi Maagemet Measure i the Curret State of Pratie - Ir. F. S. Zuurbier Realtime Optimal Cotrol of Railway Traffi - Stefa Wegele Roudabout Delay Estimatio with Simulatio Models: DRACULA, VISSIM, ad SITRA-B+ - Mahmoud Saffarzadeh Route Swithig i Mirosopi Traffi Simulatio - Ir. Freek Faber Sigapore Kallag-Paya Lebar Expressway (KPE) Phase 1: A Tuel Cogestio Maagemet Strategy Derived Usig VISSIM - Dave Keea Sytheti Household Travel Survey Data Simulatio - Yogpig Zhag Traffi flow of adaptive ruise otrol vehiles o highway with a oramp - Rui Jiag Traffi Miro-Simulatio Assisted Uderpass Desig - Blake Xu Trasport data, models, aalysis, ad kowledge developmet - Jeffery Arher Travel Behavior Model for Traffi Miro-Simulatio System: A Mahie Learig Approah - Chog Wei Use of Simulatio-Based Foreast for Real Time Traffi Maagemet Deisio Support: The Case of the Madrid Traffi - Alexadre Torday Usig a LWR Model with a Cell Based Kalma Filter to Estimate Travel Times - Ir. C.P.IJ. va Hisberge