A SUGGESTED MODEL TO SIMULATE STORAGE LANE FOR VEHICLE QUEUE ON URBAN ROAD U-TURN

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1 A SUGGESTED MODEL TO SIMULATE STORAGE LANE FOR VEHICLE QUEUE ON URBAN ROAD U-TURN Muhammad Hadd 1, Hera Wdyastut 2 and Wahu Heranto 2 1 Departement of Cvl Engneerng, Insttut Teknolog Kalmantan, Indonesa 2 Departement of Cvl Engneerng, Insttut Teknolog Sepuluh Nopember, Indonesa E-Mal: hadd@tk.ac.d ABSTRACT U-turn wth hgh arrval rate and hgh traffc on urban road can decrease the Level of Servce (LOS) of road tself. To revtalze the current condton, storage lane for vehcle queue must be provde. To set length of storage lane, we should know the queue length. Based on current condton, queue occurs because servce tme or turnng movement s too long. The other factor of queue s hgh traffc on the opposte lane. Posson dstrbuton for arrval rate of vehcle on U-turn and model of servce tme of U-turn s used for ths research. Model of servce tme s ganed from cumulatve frequency dstrbuton of servce tme data from each U-turn. The result of smulaton s queue length and the mnmum length of storage lane On Pndugo U-turn, Nrwana U-turn, Galaxy U-turn whch are 150 meter (correcton factor:0.96s), 102 meter (correcton factor: 0.85s), and 114 meter (correcton factor: 0.95s), respectvely. Smulaton model s accepted when correcton factor s close to 0s. Based on the result, the Smulaton model of queue s accepted. Keywords: smulaton, servce tme, U-turn. INTRODUCTION A U-turn n drvng refers to performng a 180 rotaton to reverse the drecton of travel (Wkpeda). Medan openngs, however, may also become ponts of ncreased congeston of accdent exposure (Potts. et al, 2004). Therefore, f traffc safety on multlane hghways s to be preserved, the locaton of medan openngs must be gven careful consderaton (Potts, et al, 2004). Some factors that nfluence medan openng locaton nclude the followng (Potts, et al., 2004): Spacng between medan openngs, Stoppng sght dstance, Intersecton sght dstance, Operatng speeds, Length of turn lanes, Rght-turn conflct overlap, and, Sze and type of traffc generator. To desgn U-turn s consder aspects of geometrc desgn of road, as followng (Bna Marga, 2005): Functon of road, Classfcaton of road, Wdth of medan Wdth of lane Traffc volume each lane U-turn movement data Desgn of U-turn can be conducted f t fulflls some requrements and has specal study. The am of specal study s to antcpate traffc mpact that wll occur. To antcpate the mpact of U-turn traffc, ths research wll dscuss smulaton method of queue on U- turn to set the length of storage lane. Queue that occur on U-turn can decrease performance of road tself. For example, a segment of road has 2 lanes and the queue length of vehcle s 1 lane, automatcally the effectve wdth of road that can functon s only 1 lane. That s why ths smulaton model s needed. The Mddle East Rng Road (MERR), Surabaya has some problematc U-turn. Ths research determnes 3 (three) problematc U-turns. The man problem s the queue length that has mpact to road performance. Ths occur because the storage lane cannot accommodate vehcle queue. The problematc U-turns are: Pandugo U-turn (Fgure-1 and Fgure-2), Nrwana U-turn (Fgure-3 and Fgure-4), Galaxy U-turn (Fgure-5 and Fgure-5). Fgure-1. Satellte vew of Pndugo U-turn (Source: Google Fgure-2. Street vew of Pndugo U-turn (Source: Google 14391

2 These U-turns are cause of the decreasng of road performance. The storage lane provded s not enough to accommodate the queue. Based on survey, the queue length that occur are: Pndugo U-turn : 150 meter Nrwana U-turn : 102 meter Galaxy U-turn : 114 meter Fgure-3. Satellte vew of Nrwana U-turn (Source: Google Fgure-4. Street vew of Nrwana U-turn (Source: Google Fgure-5. Satellte vew of galaxy U-turn (Source: Google All U-turn n ths study are a part of sngle weavng system. Queue that occur decrease length and wdth of weavng. The mpact s decreasng of sngle weavng and road performance. On Nrwana U-turn, the deprecaton of sngle weavng performance, whch s represented by Degree of Saturaton or V/C rato, s from 0.60 become 0.88 (Hadd et al., 2014). The am of ths research s to obtan queue length that can be used to obtan mnmum requrement of length of storage lane. To decrease the nfluences of queue length on road performance, provdng storage lane whch accommodate queue vehcle s needed. Mnmal length of storage lane s same as maxmum queue length that occur on U-turn. The reason for usng smulaton s because characterstcs of traffc each locaton dfferent. From ths research, the dfferences s the servce tme. Servce tme depends on opposte traffc volume. Hgh opposte traffc volume effects the maxmum servce tme on U-turn. Usually, determnng mnmum length of storage lane s based on rght turn vehcle (vehcle/mnute) and head dstance (meter). The value that s used s the mean value, both rght turn vehcle and head dstance. Usng the smulaton, we can generate varous servce tme each vehcle based on model of servce tme n each locaton. Usng smulaton s more accurate to obtan length of queue than usng smpler method. The length of queue from smulaton s useful to determne length of storage lane. LITERATURE REVIEW U-turn or medan openng s desgned to accommodate vehcle to undertake maneuver turnng to opposte drecton, crossng maneuver and rght turn maneuver. Illustraton of U-turn s shown by Fgure-7 below: Fgure-6. Street vew of galaxy U-turn (Source: Google Fgure-7. U-turn and the movement

3 Decelaraton lane Deceleraton Lane s a provded lane that has functon to decelerate vehcle to ext from contnuous traffc (Bna Marga, 1992). To desgn deceleraton lane, we can use equaton 1 below: ls 2 M s (1) Cumulatve frequency dstrbuton For obtan the data, we need to get the number of data that has value below or above from certan value that be compared that dfferent on certan nterval. So we used cumulatve frequency dstrbuton and used Ogve graph Fgure-8 to present the data (Harnald, 2005). Ls M s : length of storage secton (meter) : mean of rght turn vehcle (vehcle/mnutes) : mean of head dstance (meter) Based on Bna Marga (1988) the mnmum deceleraton lane s shown by Table-1 below. Table-1. Mnmum deceleraton lane length. Fgure-8. Cumulatve frequency dst. dagram (Source: Harnald, 2005). METHODS The method that usng on ths study s shown on Fgure-9 below: Decelaraton lane The algorthm for generatng Posson (λ) random varetes s based essentally on the relatonshp between the Posson (λ) dan expo (1/λ) dstrbutons (Law&Kelton, 1991). The algorthm s as follows: 1. Let a e, b=1, and = 0 U ~ 0,1 and replace b by 2. Generate bu 1 U 1. If b<a, return x=. Otherwse, go to step Replace I by +1 and go back to step 2. The algorthm s ustfed by nothng that x= f and only f 1 1 Y 1 Y (2) 1 The (statonary) Posson process wth rate λ>0 has Where Y 1/ lnu ~ exp 1 / and the Y s are ndependent property that the nterarrval tmes A t t 1 (where =1,2, n) are IID exponental random varables wth common mean (1/λ). Thus, we can generate the t s recursvely, as follows (Law&Kelton, 1991): 1. Generate U~U(0,1) ndependent of any prevous random varates 1 1/ 2. Return t t U The recurson starts by computng t 1 (recall that t 0=0). ln Fgure-9. Flowchart

4 Collectng data The Data needed n ths study s prmary data, such as: 1. Traffc Data 2. Servce Tme Data 3. Queue Data From feld observaton, the data that obtaned s shown by Table-2 below: Table-2. Observed data. Fgure-10. Cumulatve frequency dstrbuton of servce tme on Pndugo U-turn (Hadd, 2014). The observed data above s obtaned from feld observaton on each locaton on MERR Surabaya. Table-2 shows the maxmum value each data. Arrval rate s taken from peak hour volume of U-turn traffc. Based on table 2, peak hour volume on Pndugo U-turn s 509 vehcle/hour, 711 vehcle/hour on Nrwana U-turn, and 725 vehcle/hour on Galaxy U-turn. Servce tme data s a tme when the vehcle start to turn untl fnsh. Each locaton has mnmum and maxmum servce tme. On Pndugo U-turn, the mnmum servce tme s 2 seconds, and 18 seconds for maxmum value. Servce tme value on Nrwana U-turn s 3 seconds for mnmum value and 21 for maxmum one. For Galaxy U-turn, servce tme s 2 seconds for mnmum value and 26 seconds for maxmum one. The queue length s obtaned from maxmum queue durng observaton. The locatons of the observed U-turns are shown n Fgure-1 trough Fgure-6. Model of servce tme Model of Servce tme s obtaned by cumulatve frequency dstrbuton from data of servce tme. Each U- turn has one model of servce tme. Model of servce tme s an exponental equaton wth y as servce tme (sec) and x as generatng random number (0,1). The model of servce tme s used for smulaton of servce tme. By generatng random number, we wll get servce tme based on equaton model of each U-turn. From data of servce tme on Pndugo U-turn, we plot the cumulatve frequency dagram to get model of servce tme on Pndugo U-turn. The dagram of cumulatve frequency s shown n Fgure-10. From dagram of cumulatve frequency dstrbuton, we get the equaton of servce tme model whch shown by Equaton 3 below: y X e (3) Based on Fgure-10 determnant factor (R 2 ) s above or above 0.5. So that, the model of servce tme on Pandugo U-turn s accepted. Same as model of servce tme on Pndugo U-turn. Dagram of cummulatve frequency dstrbuton of servce tme on Nrwana U-turn s shown by Fgure-11 below: Fgure-11. Cumulatve frequency dstrbuton of servce tme on Nrwana U-turn (Hadd,2014). From dagram of cumulatve frequency dstrbuton we get the equaton of servce tme model Fgure-11 whch shown by Equaton 4 below: y X e (4) Based on Fgure 11 determnant factor (R 2 ) s above or above 0.5. So that, the model of servce tme on Nrwana U-turn s accepted

5 And for Galaxy U-turn, model of servce tme s shown by Fgure-12 below: Table-3. Result Pndugo U-turn smulaton. Fgure-12. Cumulatve frequency dstrbuton of servce tme on galaxy U-turn (Hadd, 2014). From dagram of cumulatve frequency dstrbuton we get the equaton of servce tme model whch shown by [Equaton 5] below: C AT NQ QL : Car : Arrval Tme (second) : Number of Queue (vehcles) : Queue Length (meters) y X e (5) Based on [Fgure-12] determnant factor (R 2 ) s above or above 0.5. So that, the model of servce tme on Galaxy U-turn s accepted. Smulaton and correcton factor Smulate of queue s as follow: 1. Arrval tme s based from random number and 1 Posson equatont t 1/ lnu. λ s arrval rate of vehcle (veh/sec) 2. Smulaton of servce tme s based on model of servce tme and random number 3. Queue wll occur when the arrval tme of vehcle s above of arrval tme of prevous vehcle and below of end tme of U maneuver one. 4. Generate correcton factor that representatve of reacton tme of drver. 5. If smulaton s not reach target (queue length based on data), back to step Smulaton s stop when arrval vehcle reach number of arrvng vehcle based on data. RESULT AND DISCUSSION Pandugo U-turn Procedure of smulaton of queue has dscussed above. In ths secton s dscuss about the result of smulaton. Pndugo U-turn has 1 lane that allowed s used to perform U maneuver. The result of smulaton s shown by Table-3 below. And the graphc of queue on Pandugo U-turn s shown by Fgure-13 below: Fgure-13. Queue length (meter) of Pndugo U-turn (Hadd, 2014). Based on Table-3 and Fgure-13 the smulaton result s 150 meter. The correcton factor or reacton tme of drver s 0.96 second. From the result the mnmum length of storage lane on Pndugo U-turn based on smulaton s 150 meter. Nrwana U-turn Dfferent from Pndugo U-turn, Nrwana U-turn s provde 2 lane that used as storage lane of U-turn. The smulaton has smulate the number of lane that taken by vehcle. To get the smulaton of decdng of number of lane, used random number. The random number s ust 1 and 2 to represented number of lane. The smulaton of 14395

6 queue s not dfferent from Pndugo U-turn. The result of smulaton of queue on Nrwana U-turn s shown by Table-4 below: Table-4. Result Nrwana U-turn smulaton. Galaxy U-turn Smlar wth Nrwana U-turn, ths locaton has 2 lane that provde to turnng movement. And the result of smulaton s shown by Table-5 below. Table-5. Result of galaxy U-turn smulaton. C : Car AT : Arrval Tme (second) NL : Number of Lane (1 or 2) NQ : Number of Queue (vehcles) QL : Queue Length (meters) And the graphc of queue on Nrwana U-turn s shown by Fgure-14 below: C : Car AT : Arrval Tme (second) NL : Number of Lane (1 or 2) NQ : Number of Queue (vehcles) QL : Queue Length (meters) And the graphc of queue on Galaxy U-turn s shown by Fgure-14 below: Fgure-14. Queue length (meter) of Nrwana U-turn (Hadd, 2014). Based on Table-4 and Fgure-14 the smulaton result s 102 meter. The correcton factor or reacton tme of drver s 0.85 second. From the result the mnmum length of storage lane on Pndugo U-turn based on smulaton s 102 meter. Fgure-15. Queue length (meter) of galaxy U-turn (Hadd, 2014). Based on Table-5 and Fgure-15 the smulaton result s 114 meter. The correcton factor or reacton tme of drver s 0.95 second. From the result the mnmum 14396

7 length of storage lane on Galaxy U-turn based on smulaton s 114 meter. CONCLUSIONS From the result above, the mnmum requrement length of storage lane based on queue length smulaton on Pndugo U-turn s 150 meter wth correcton factor 0.96s, 102 meter on Nrwana U-turn wth correcton factor 0.85s and 114 meter on Galaxy U-turn wth correcton factor 0.95s. Based on the smulaton, the correcton factor s close to 0s, ts means the method of smulaton of queue length on U-turn can be used to obtan the length of storage lane. Correcton factor represents the reacton tme of drver and s added to endng tme of maneuver. If the correcton factor or reacton tme s closer 0s, the model s closer to real condton. Ths research does not consder the opposte drecton traffc flow and motorcycle. Opposte drecton traffc flow s represented by servce tme or necessary tme for vehcle to maneuver. If the servce tme s too long, t shows that the vehcle s watng on the opposte traffc to maneuver. The smulatng queue of motorcycle s dffcult because of unpredctable maneuver of motorcycle tself. [7] Law, A. M., & Kelton, W. D. (1991). Smulaton Modelng and Analyss (2 nd ed.). USA: McGraw-Hll, Inc. [8] Potts. et al Safety of U-turn at Unsgnalzed Madan Openngs. Washngton. D.C: Transportaton Research Board. NCHRP Report 524 [9] REFERENCES [1] Bna Marga Perencanaan Geometrk untuk Jalan Perkotaan. Jakarta: Departemen Pekeraan Umum. [2] Bna Marga Perencanaan Geometrk untuk Jalan Perkotaan, Jakarta: Departemen Pekeraan Umum. [3] Bna Marga Perencanaan Putaran Balk, Jakarta: Departemen Pekeraan Umum. [4] Hadd, Muhammad Analsa Penggunaan Laur pada U Turn d Jalan MERR II Surabaya dan Pengaruhnya terhadap Panang Antran, Kapastas dan Knera Ruas Jalan. Thess. Surabaya: ITS Surabaya. [5] Hadd, Muhammad; Wdyastut, Hera and Heranto, Wahu Smulas Antran Kendaraan pada U- turn dan Dampak Terhadap Knera Jalan Perkotaan. The 17 th FSTPT Internatonal Symposum, August 22 nd -24 th Jember Unversty. Forum Stud Transportas Perguruan Tngg. Volume 2, No. 1, 2014, Page 318. [6] Harnald Prnsp-Prnsp Statstk untuk Teknk dan Sans. Jakarta: Penerbt Erlangga