THE FOLLOW-UP TIME ISSUE ON SMALL ROUNDABOUTS

TRANSPORT PROBLEMS 2008 PROBLEMY TRANSPORTU Tom 3 Zeszyt 3 ElŜbeta MACIOSZEK*, Janusz WOCH Slesan Unversty of Technology, Faculty of Transport, Department of Traffc Engneerng Krasńskego St. 8, 40-019 Katowce, Poland *Correspondng author. E-mal: elzbeta.macoszek@polsl.pl THE FOLLOW-UP TIME ISSUE ON SMALL ROUNDABOUTS Summary. The follow-up tme was nvestgated. The am of ths analyss was to create a formula that allows the follow-up tme calculated usng the most mportant external parameters. The studes were based on emprcal data collected at small roundabouts localzed on Upper Slesa. The follow-up tme s the average tme gap between two cars of the mnor stream beng queued and entered the same major stream gap one behnd the other. Follow-up tmes were measured drectly by observng traffc flow. Resultng follow-up tmes were analyzed to determne ther dependence on parameters such as ntersecton layout, roundabouts dameter and left vsblty. These parameters were tested usng the conventonal calculaton method (regresson analyss). The dependence of follow-up tme was then ntegrated nto the own capacty estmaton method for small roundabouts localzed on urban areas. One of the bggest advantages ths dependence s that capacty and traffc flow on small roundabouts can be determned relably and approprately for actual stuatons. The new follow-up tme values for all range of external dameters of small roundabout 26 (22) 40 m have been presented n ths artcle. MINIMALNE ODSTĘPY CZASU POMIĘDZY POJAZDAMI WJEśDśAJĄCYMI Z KOLEJKI NA WLOTACH MAŁYCH ROND JEDNOPASOWYCH Streszczene. Wartośc mnmalnych odstępów czasu analzowane są główne podczas oblczeń przepustowośc skrzyŝowań regulowanych znakam drogowym, czyl skrzyŝowań bez sygnalzacj śwetlnej oraz rond. W przypadku rond, decydujący wpływ na przepustowość podporządkowanego wlotu jednopasowego lub dwupasowego mają welkośc natęŝeń nadrzędnych w obszarze kolzyjnym na jezdn ronda przy danym wloce (Q nwl ), granczny odstęp czasowy (t g ) odstęp czasu pomędzy pojazdam wjeŝdŝającym z kolejk na wloce podporządkowanym (t f ). Przy duŝych wartoścach natęŝeń ruchu na wlotach odstępy t f w głównej merze decydują o przepustowośc wlotów podporządkowanych. W artykule przedstawono wynk pomarów odstępów czasu pomędzy pojazdam wjeŝdŝającym z kolejk na wloce wraz z ch analzą statystyczną. Pomary wykonano na małych rondach zlokalzowanych na terenach zabudowanych zlokalzowanych na Górnym Śląsku. Wykorzystując analzę regresj korelacj welorakej uzyskano zaleŝność funkcyjną do wyznaczana mnmalnych wartośc odstępów czasu, która moŝe posłuŝyć w oblczenach przepustowośc wlotów na skrzyŝowanach regulowanych znakam drogowym. Typowe wartośc mnmalnych odstępów czasu pomędzy pojazdam wjeŝdŝającym z kolejk na wloce oblczone za pomocą oszacowanej funkcj przedstawono w artykule. Wartośc t f podano dla pełnego zakresu moŝlwych średnc zewnętrznych małych rond, czyl dla 26 (22) - 40 (45) m.

26 E. Macoszek, J. Woch 1. INTRODUCTION Usually capacty calculatons for unsgnalzed ntersectons controlled by Yeld or Stop sgns are based on gap acceptance theory. The fundamental parameters n ths theory are crtcal gaps and follow-up tmes. Consderng small roundabout wth two streams-one major and one mnor, the vehcles n the mnor stream can only pass the conflct area when the tme gap between the cars n the major stream s long enough (fg. 1). That means they can only enter the conflct area when the tme gap between the major vehcles s larger than ther crtcal gap t g. Therefore the crtcal gap t g s defned as follows: The crtcal gap (t g ) - s the mnmum tme gap between the vehcles of the major stream that s necessary for the vehcles n the mnor stream to enter the conflct area. In addton, several cars of mnor stream can only follow one behnd the other wthn a certan tme space, whch s called ther follow-up tme - t f. The follow-up tme (t f ) - s the average tme gap between two cars of the mnor stream beng queued and entered the same major stream gap one behnd the other. major stream conflct area mnor stream Fg. 1 Small roundabout wth two conflctng streams Rys. 1 Kolzyjne potok ruchu na małym rondze Typcal stuaton at hgh traffc volume n conflctng area durng merge manoeuvre was llustrated on fg. 2. Parameters lke t g and t f ndcate the dependence of traffc condtons at ntersectons wthout traffc sgnals on drvers behavor. Each drver watng n a mnor stream has to decde when t s safe to merge nto the conflctng traffc streams. The crtcal gaps and follow-up tmes take nto account the nfluence of external parameters, for example the geometrc desgn of the ntersecton or decsonmakng process. Capacty formulas based on gap acceptance theory have been mproved contnuously. Dfferent methods were developed by many scentsts lke: Segloch, Harders, Brlon and Grossman n Germany. Kyte, Tan, Mr, Hameedmansoor, Kttelson, Vandehey, Robnson and many other all over the world [1], [2], [4], [6].

The follow-up tme ssue on small roundabouts 27 where: G - watng tme at Yeld lne, ε - moment, when vehcle s enterng from mnor road to man road of small roundabout, τ - vehcles arrval moments at conflctng areas, t g - crtcal gap, t f - follow-up tme, block - tme nterval, whch starts t g seconds before the major stream vehcle arrves and lasts untl the begnnng of the next major stream headway t t, antblock - the tme nterval between two blocks. An antblock starts when a headway g g t t starts and ends t g before the arrval of the next major stream vehcle. Mnor stream vehcles can enter the ntersecton durng antblock. Fg.2 Gap acceptance and queue dscharge at small roundabouts Rys.2. Proces wjazdów pojazdów z wlotu podporządkowanego na jezdnę małego ronda 2. THE EMPIRICAL STUDY Measurements were taken at 12 urban ntersectons. Traffc flow at these ntersectons was vdeotaped wth a tme sgnal recorded. The tme code helped dentfy each vehcle s arrval tme at a specfc pont along the road wthn 0.04 second. Each vehcle of a mnor stream was recorded n a database usng vehcle type, tme of arrval n front poston and tme of departure. These data were then used to record drvers follow-up tmes could be derved. Example of locaton places for followup tmes measurement has been presented n fg. 3. Defnng arrval and departure tmes turned out to be dffcult. Many mnor stream cars approached the yeld lne easly and stopped rght n front of the yeld lne. Other vehcles approached hestantly and rolled to stop slowly. To address these questons, generalzatons had to be made. Thus, after a seres of experments, the defntons were made accordng to the best knowledge of the researcher. Once defned however, the defntons were appled to all ntersectons consstently.

28 E. Macoszek, J. Woch Fg. 3. Example of locaton places for follow-up tmes measurement Rys. 3. Przykładowe lokalzacje stanowsk do pomaru odstępów czasu pomędzy pojazdam wjeŝdŝającym z kolejk na wloce 4. DETERMINING FOLLOW-UP TIMES The frst results were used to verfy the assumptons made for estmatng the crtcal values. The resultng follow-up tmes vared wthn relatvely wde margns as llustrated on fg. 4. These varatons were nvestgated to determne whether they are natural characterstcs of the follow-up tmes or f there are any systematc nfluences responsble for the varatons. The follow-up tmes were tested for ther dependence on several external parameters lsted n table 2. The crtcal values were tested usng a t-student test. The regresson coeffcent was tested usng a t-student test to determne whether t was dfferent from zero whch means that correlatons exst. The results of these tests were shown also n table 1. When a parameter turned out to have a sgnfcant nfluence on the follow-up tme t s ndcated by,,yes. In those cases, the coeffcent of correlaton s gven. From the coeffcent of correlaton one can see how sgnfcant the nfluence of the external parameter s on the follow-up tme. The bgger the coeffcent of correlaton s the stronger the correlaton between varables s. The other geometrc effects were not relevant because all measured ntersectons were desgned accordng to the quadelnes and there were no extreme condtons such as acute angles between ntersectons arms or uncharacterstc approach gradent etc.

The follow-up tme ssue on small roundabouts 29 Results from the determnaton of follow-up tmes Tab.1 1. Small roundabout n Śwerklanec The range of follow-up tmes 2.60 4.88 2. Tarnowske Góry II 3. Tarnowske Góry I 4. Bytom-Radzonków 5. Katowce 6. Mysłowce 7. Tychy I 8. Tychy II 9. Tychy III 10. Tychy IV 11. Pekary Śląske 12. Semanowce 1.64 3.00 1.16 4.04 1.52 4.32 2.50 4.84 2.76 3.92 1.16 4.04 1.92 3.96 1.20 3.32 1.44 3.60 2.00 3.84 1.56 3.76 0 1 2 3 4 5 6 7 8 9 10 follow-up tmes [s] The follow-up tme values obtaned from new formula was gven n table 3. The follow-up tmes was gven for man road lane wdth equal 4.0 m. Accordng to polsh gudelne, small roundabouts are ntersectons wth external dameter from range of 26 (22) - 40 (45) m. Values s brackets are

30 E. Macoszek, J. Woch permssble n exceptonal stuatons. In table 3 the typcal values of external dameter are hghlghted n bold. Dependence of follow-up tmes on external parameters Tab. 2 External parameter Dependence 1 Three or four armed small roundabouts no 2 Exstence of sland on mnor road no 3 Sght dstance no 4 Mnor road wdth no 5 External dameter of small roundabout yes R = -0.99 6 Major road wdth yes R = -0.72 Tab. 3 Follow-up tme values recommended for one-lanes small roundabouts localzed n urban areas D z [m] 22 23 24 25 26 27 28 29 30 31 32 33 t f [s] 3.32 3.30 3.28 3.26 3.24 3.22 3.20 3.18 3.16 3.14 3.12 3.10 D z [m] 34 35 36 37 38 39 40 41 42 43 44 45 t f [s] 3.08 3.06 3.04 3.02 3.00 2.98 2.96 2.94 2.92 2.90 2.88 2.86 4. CONCLUSIONS The paper provdes detaled nvestgatons on the varous factors that affect on follow-up tme. The nvestgaton was based on the database establshed durng the traffc flow parameters measurements on few small roundabouts localzed on urban area. The step-wse regresson analyss was conducted to nvestgate the potental factors affectng the follow-up tme. General observatons of the varous factors can be summarzed below: - It was found that the major factors affectng follow-up tme nclude ntersecton geometry lke small roundabout external dameter and major lane wdth. - Wth the ncrease of major stream volume drvers tend to seek smaller gaps. - Wth the ncrease of small roundabouts external dameter, the follow-up tme value tends to decrease. - Wth the ncrease of major lane wdth the follow-up tme value tends to decrease. It was due to the ncrease of the easness of the movement manoeuvre. - Follow-up tme of heavy vehcles s found to be consstently hgher than for passng cars. - It was proved after control measurements that the follow-up tme values proposed n the artcle can be used n small roundabouts capacty calculaton.

The follow-up tme ssue on small roundabouts 31 Although the regresson analyss provded nsghts on the relatonshps among varous factors, practcal engneerng judgment stll played an mportant role whle recommendng the fnal set of follow-up tme values. For example the other few factors appeared to be sgnfcant n the regresson analyses were not ncluded n the fnal recommendatons. These factors were dealt wth specfcally n other parts of the capacty analyss procedure. The newly recommended follow-up tme values have been adopted n the own method for small roundabouts capacty calculatons. Bblography 1. Brlon W., Troutbeck R., Tracz M.: Revew of Internatonal Practces Used to Evaluate Unsgnalzed Intersectons. Transportaton Research Crcular 468. Transportaton Research Board, Washngton, 1997. 2. Brlon W., Wu N., Bondzo L.: Unsgnalzed Intersectons n Germany a State of the Art 1997. Thrd Internatonal Symposum on Intersectons wthout Traffc Sgnals. Portland, Oregon, July, 1997, p.61-70. 3. Hagrng O.: Roundabout entry capacty. Bulletn 135. Department of Traffc Plannng and Engneerng, Lund, 1996. 4. Kyte M., Tan Z., Mr Z., Hameedmansoor Z., Kttelson W., Vandehey M., Robnson B., Brlon W., Bondzo L., Wu N., Troutbeck R.: Capacty and Level of Servce at Unsgnalzed Intersectons. Natonal Cooperatve Hghway Research Program (NCHRP), Washngton, 1996, p. 3-46. 5. Metoda oblczana przepustowośc rond. Instrukcja oblczana. Generalna Dyrekcja Dróg Krajowych Autostrad, Warszawa, 2004. 6. Tan Z., Troutbeck R., Kyte M., Brlon W., Vandehey M., Kttelson W., Robnson B.: A Further Investgaton on Crtcal Gap and Follow-Up Tme. Transportaton Research Crcular E-C018: 4 th Internatonal Symposum on Hghway Capacty. Bochum, Germany, 2000, p. 397-408. 7. Transportaton Research Board. Specal Report 209: Hghway Capacty Manual. Natonal Research Councl, Washngton, 1997. 8. Troutbeck R.: Estmatng the Crtcal Acceptance Gap from Traffc Movements. Research Report 92-5. Queensland Unversty of Technology, Brsbane, 1992. 9. Wenert A.: Estmaton of Crtcal Gaps and Follow-Up Tmes at Rural Unsgnalzed Intersectons n Germany. Transportaton Research Crcular E-C018: 4 th Internatonal Symposum on Hghway Capacty. Bochum, Germany, 2000, p. 409-421. 10. Woch J.: Nowe ujęce przepustowośc drog z porównanem model. Zeszyty Naukowe Poltechnk Śląskej, s. Transport, Glwce, z. 47, 2003, s. 43-72. Receved 24.01.2008; accepted n revsed form 22.09.2008