Investigation on entry capacities of single-lane roundabouts

Transcription

1 University o Wollongong Researh Online Faulty o Engineering and Inormation Sienes - Papers: Part A Faulty o Engineering and Inormation Sienes 014 Investigation on entry apaities o single-lane roundabouts Liang Ren Griith University Xiaobo Qu Griith University Shuaian Wang University o Wollongong, shuaian@uow.edu.au Hong Guan Griith University, h.guan@griith.edu.au Publiation Details Ren, L., Qu, X., Wang, S. & Guan, H. (014). Investigation on entry apaities o single-lane roundabouts. Applied Mehanis and Materials, Researh Online is the open aess institutional repository or the University o Wollongong. For urther inormation ontat the UOW Library: researh-pubs@uow.edu.au

2 Investigation on entry apaities o single-lane roundabouts Abstrat Bothheavy goods vehiles () and exiting vehiles an signiiantly aet the entry apaity o a roundabout. However, their eets have not been taken into aount in HCM 000 model.reently two studies have been arried out to address this issue: 1) Dahl and Lee (01) proposed an expetation theory based approahto inorporate the eet o s [1]; and)qu et al. (013) deriveda new roundabout apaity model by assuming that eah exiting vehile ould provide one entry opportunity or waiting vehiles []. In this paper, the two models are integrated using a senario-based approahtoanalyse the eets o not only exiting vehiles but also s. A omparative study indiates that HCM 000 model perorms well under low to mid trai onditions while it underestimates the apaities under high trai onditions in ombination with high proportions o exiting vehiles. Keywords entry, apaities, investigation, single, roundabouts, lane Disiplines Engineering Siene and Tehnology Studies Publiation Details Ren, L., Qu, X., Wang, S. & Guan, H. (014). Investigation on entry apaities o single-lane roundabouts. Applied Mehanis and Materials, This journal artile is available at Researh Online:

3 Investigation On Entry Capaities o Single-lane Roundabouts Liang Ren 1,a, Xiaobo Qu 1,b, Shuaian Wang, and Hong Guan 1,d, 1 Griith Shool o Engineering, Griith University, Gold Coast, QLD 4, Australia Shool o Mathematis and Applied Statistis, University o Wollongong, Wollongong, NSW 5, Australia a l.ren@griith.edu.au b x.qu@griith.edu.au wangshuaian@gmail.om d h.guan@griith.edu.au Keywords: Roundabout; Entry Capaity; Gap Aeptane Theory; Heavy Goods Vehiles Abstrat The heavy good vehiles () and exiting vehiles an signiiantly aet the entry apaity o a roundabout. However, their eets have not been taken into aount in HCM 000 model. Reently two studies have been arried out to address this issue: 1) Dahl and Lee (01) propose an expetation theory based approah to inorporate the eet o s [1]; and ) Qu et al. (013) derive a new roundabout apaity model by assuming that eah exiting vehile ould provide one entry opportunity or waiting vehiles []. In this paper, the two models are integrated using a senario based approah to analyse the eets o not only exiting vehiles but also s. A omparative study indiates that HCM 000 model perorms well under low to mid trai onditions while it underestimates the apaities under high trai onditions in ombination with high proportions o exiting vehiles. Introdution Along with inrease o trai demand, transport inrastrutures are designed and established to satisy higher requirements o saety, apaity and luidity [3-6]. A roundabout is a type o irular intersetion with one or more marked lanes in whih road trai is slowed and lows are almost ontinuously in one diretion around a entral island to several exits onto the various interseting roads [7-9]. Its detailed operations are usually not ormulated in transportation network modelling studies [10-15]. In reality, roundabouts ould substantially redue queue and delay under low volume onditions as vehiles are not required to perorm a omplete stop. Roundabouts allow U-turn within the normal low o trai, whih oten are not possible at other orms o juntion [16]. Further, roundabouts provide higher saety than signal ontrolled juntions in terms o not only requeny but also severity o aidents. Fortuijn (009) asserted that as the vehiles in a roundabout ould drive along the same diretion, the probability o rashes ould be redued thanks to the derease o onliting points [17]. Aordingly, roundabouts have been an inreasingly popular intersetion type, espeially in less populous suburbs [18,19]. Along with the wider use o roundabouts, the entry apaity is o more importane to transport agenies [0-]. Various models have been developed to estimate the entry apaities o roundabouts [3-5]. Highway Capaity Manual (HCM) 000 model is the most widely-used analytial model based on the gap aeptane theory [5], mathematially, exp( vτ / 3600) C000 = v (0) 1 exp( vτ / 3600) where C 000 is the entry apaity o an arm (veh/hr); v is the onliting irulating low (veh/hr); τ and τ are ritial gap and ollow-up time (s), respetively. In the above-mentioned model, the entry apaity is alulated as a untion o irulating trai, ritial gap, and ollow-up time, without taking into aount the low interations and vehile types [6]. In reality, as pointed out by Barry [7] and Dahl and Lee [1], the exiting lows and heavy goods vehile () have signiiant impats on the entry apaities. HCM 000 model treat the exiting vehiles as non-existent, whih are not ounted as irulating trai. Based on survey o 19 single-lane modern roundabouts in Queensland, Australia, Qu et al. (014) indiated that waiting vehiles will immediately (in an average o 1.4 seonds) enter the roundabout ater exiting vehiles turn their indiators on (usually more than 1 seond beore the atual turning movements) []. In other words, a waiting vehile might not neessarily wait or a ritial gap i an exiting vehile shows up. Aordingly, by assuming that eah exiting vehile ould provide one entry opportunity or waiting vehiles, a new roundabout apaity model (reerred to as NRC model I hereater) is proposed by Qu et al. by onsidering inluene o exiting vehiles [], mathematially expressed by

4 C exit exp( v τ / 3600) = v ρ+ 1 exp( v τ / 3600) () where C exit is the entry apaity onsidering exiting vehiles (veh/hr); v is irulating low inluding exiting vehiles (veh/hr); ρ is proportion o exiting vehiles. In addition, Dahl and Lee [1] analysed the eet o heavy good vehiles by adjusting ritial gap and ollow up time. I the entry low onsists o ars and s only, the ritial gap should onsider the eet rom both ar and truk, mathematially, τ = τ + τ (3),1q1,q where τ is the adjusted ritial gap (s); τ,1 and τ, are the ritial gap or ars and truks, respetively (s); q 1 and q denote the proportion o ars and truks within the entry low, respetively. Similarly, the ollowup times are inluened by various proportions in ars and truks at entry low. Dahl and Lee [1] pointed out that the ollow-up time varies depending on the type o two entering vehiles in a queue - the lead vehile and the ollowing vehile within the entry low. Four ases o vehile-ollowing onditions were assumed as ollow: 1) Car ollowed by ar (ar/ar) ) Car ollowed by truk (ar/truk) 3) Truk ollowed by ar (truk/ar) 4) Truk ollowed by truk (truk/truk) The adjusted ollow-up time is desribed as ollow: τ = τ q + τ q q + τ q q + τ q (4), 1, t 1, t 1, tt This equation an be rewritten as ollow: τ = τ q + ( τ + τ ) q q + τ q (5), 1, t, t 1, tt where τ is the adjusted ollow-up time (s); τ,, τ, t, τ, t and τ, tt are ollow-up times or a ar ollowing a ar (ar/ar), a truk ollowing a ar (ar/truk), a ar ollowing a truk (truk/ar) and a truk ollowing a truk (truk/truk), respetively (s). In this paper, a gap aeptane based analytial model is proposed to inorporate the eets o both exiting vehiles and s. A omparative study is urther arried out to analyse the results alulated by the HCM 000 model and the proposed models. Aording to the analyses, although the HCM 000 model is good approximations under low perentage o exiting lows or low irulating low onditions, their perormanes or other onditions are questionable. Proposed models Based on the pioneering work by Dahl and Lee [1], we inorporate this dierene in the gap aeptane proess. Table 1 presents two senarios o gap aeptane based on a simple lassiiation. Senarios 1 and reer to the ases that the lead vehiles in a queue are ar and truk, respetively. The probabilities o Senario 1 and ould be estimated by the proportions o ars and truks. Table 1 shows the ritial gaps, ollow up times, and apaities under eah senario. Note that the adjusted ollow-up time is still adopted in this model. The apaity under eah senario ould be estimated by either HCM 000 model or the NRC model I. Table 1 Senarios Senario ( k ) Lead vehiles (probability) Critial gap Follow up time Capaity o senarios q ) τ,1 C( τ, τ ) 1 Car ( 1 Truk ( q ) τ, Notes: Ck ( τ, j, τ ) denotes the apaity under Senario k. τ,1 τ, C( τ, τ ) Having had the probabilities and apaities or eah senario, the new model to estimate the roundabout apaity (reerred to as NRC model II hereater) presented as

5 where C( τ,,1 τ ) and (,, ) ( ( τ, i, τ ) ) ( i ( τ, i, τ ) ) = = (6) C E C q C i= 1 C τ τ are the roundabout apaity under Senarios 1 and, respetively. thus represents the expetation o the apaity under a ombined senario. (,, i ) C C τ τ an be estimated by either HCM 000 model or NRC model I. Aordingly, we then establish two proposed models as ollows: exp( vτ, / 3600) i C000 = qi v (7) i= 1 1 exp( vτ / 3600) where C 000 is the entry apaity (veh/hr) when only heavy good vehiles are onsidered based on HCM 000 model. This model is named as NRC model II hereater. v exp( v τ, / 3600) j Cexit = q j v ρ+ (8) j= 1 1 exp( v τ / 3600) where C exit is entry apaity (veh/hr) o onsidering both exiting vehiles and s; v is irulating low onsidering exiting vehiles; ρ is the proportion o exiting vehiles. This model is named as NRC model III. A omparative study To analyse the impat o ombined eet, the ield survey data olleted by Dahl and Lee [1] rom an approah o the Brattleboro roundabout are used in this study (see Table ). This study assumes the proportion o driver using indiator is 60%. The proportion o exiting vehiles is assumed to be 0.5. Roundabout Table Observed roundabout data rom Brattleboro Critial Gap (s) Car Truk, Follow up Time (s) t t, t t, t t, tt Brattleboro Soure: Dahl and Lee [1] Proportion o Truk We ompare the perormanes o our models: adjusted HCM 000 (Dahl and Lee s model in ombination with HCM 000), NRC model II, and NRC model III. As an be seen in Figure 1, the irst two models have a very similar estimation or the apaity o this roundabout. However, the apaity might be signiiantly underestimated under high trai onditions i the eets o exiting vehiles are ignored A Comparative Study Adjusted HCM 000 NRC II model NRC model III (ρ=0.5) Capaity (veh/hr) Cirulating Flow (veh/hr) Fig. 1 Capaity omparison between NRC models and HCM model

6 Conlusions The heavy good vehiles () and exiting vehiles an signiiantly aet the entry apaity o a roundabout. However, their eets have not been taken into aount in HCM 000 model. To inorporate the eet o s, Dahl and Lee (01) propose an expetation theory based approah [1]. To analyse the eet o exiting vehiles, Qu et al. (013) derive a new roundabout apaity model by assuming that eah exiting vehile ould provide one entry opportunity or waiting vehiles []. In this paper, the two models are integrated in order to take into aount not only exiting vehiles but also s. A omparative study indiates that 1) HCM 000 model perorms well under low to mid trai onditions; ) HCM 000 model underestimates the apaities under high trai onditions in ombination with high proportions o exiting vehiles; and 3) the proposed model outperorms other models. It should be pointed out that all three models give similar results under low to mid trai onditions (irulating low < 700 veh/hour). Aordingly, as a uture work o this researh, the at-apaity ield data should be olleted to veriy the perormanes o proposed models under high trai volume onditions (irulating low > 700/hour). Aknowledgements This researh is inanially supported by Griith NRG sheme. Reerenes [1] J. Dahl, and C. Lee: Transportation Researh Reord Vol. 31 (01), p. 34. [] X. Qu, L. Ren, S. Wang, and E. Oh: Submitted to Journal o Transportation Engineering, (013). [3] X. Qu, Y. Kuang, E. Oh, and J. Sheng: Trai Injury and Prevention Vol. 15 (014), p. 80. [4] Q. Meng, and X. Qu: IEEE Transations on Systems, Man, and Cybernetis, Part C: Appliations and Reviews Vol. 4 (01), p [5] X. Qu, Q. Meng, Y.H. Wong, and Y. Vivi: Expert Systems with Appliations Vol. 38 (011), p [6] Q. Meng, X. Qu, K.T. Yong, and Y.H. Wong: Risk Analysis Vol. 31 (011), p [7] B. Hellinga, and A. Sindi: Transportation Researh Reord Vol. 91 (01), p. 56. [8] F Xu, and Z.Z. Tian, Transportation Researh Reord Vol. 071, (008), p [9] T.Z. Qiu, and D. Yin: Transportation Researh Reord Vol. 65 (011), p. 44. [10] S. Wang: Transportation Researh Part C Vol. 3 (013), p. 61. [11] S. Wang, Q. Meng, and Z. Liu: Transportation Researh Part B Vol. 47 (013), p. 77. [1] S. Wang, Q. Meng, and H. Yang: Transportation Researh Part B Vol. 50 (013), p. 4. [13] Z. Liu, Q. Meng, and S. Wang: Transportation Researh Part C Vol. 31 (013), p. 83. [14] Z. Liu, and Q. Meng: Journal o Advaned Transportation Vol. 47 (013), p [15] Z. Liu, Y. Yan, X. Qu, and Y. Zhang: Transportation Researh Part C Vol. 35 (013), p. 46. [16] A. Flannery: Transportation Researh Reord Vol (001), p. 76. [17] L.G. Fortuijn: Transportation Researh Reord Vol. 130 (009), p [18] S. Jin, X. Qu, D. Wang: Physia A Vol. 39 (013), p [19] Y. Bie, D. Wang, and X. Qu: IET Intelligent Transport Systems Vol. 7 (013), p. 8. [0] T. Wei, J.L. Grenard., and H.R. Shah: Transportation Researh Reord Vol. (011), p. 1. [1] S. Jin, D. Wang, C. Xu, Z. Huang: Physis Letters A, Vol. 376 (01), p [] J. Bie, H.K. Lo, and S.C. Wong: Journal o Advaned Transportation, Vol.44 (01), p. 45. [3] S.C. Wong: Transportation Researh Part B Vol. 30 (1996), p [4] J.M. Diah, M.Y.A. Rahman., M.A. Adnan, and H.L. Khoo: ASCE Journal o Transportation Engineering Vol.137 (011), p [5] Transportation Researh Board (TRB). Highway Capaity Manual 000. [6] T. Wei, and J.L. Grenard: Transportation Researh Reord Vol. 57 (01), p [7] C.D. Barry: Calibration o the HCM 010 Roundabout Capaity Equations or Georgia onditions. Master thesis. Georgia Institute o Tehnology, 01.