VOL. 5, NO. 11, November 2015 ISSN 22257217 ARPN Journal of Scence and Technology 20112015. All rghts reserved. http://www.ejournalofscence.org Study on Statstcal Dstrbuton of Bus Dwell Tme 1 ChangGyun Roh, 2 Bumjn Park* 1 Senor Researcher, Korea Insttute of Cvl Engneerng and Buldng Technology, Korea 2 Senor Researcher, Korea Insttute of Cvl Engneerng and Buldng Technology, Korea (*correspondng author) Emal: 1 rohcg@kct.re.kr, 2 park_bumjn@kct.re.kr ABSTRACT A bus servce comprses three elements: operaton, servce at a bus stop and watng for a sgnal. Servce at a bus stop comprses arrval at the stop, boardng and alghtng and departure from the stop. The tme requred for servce at a stop s defned as bus dwell tme. Bus dwell tme accounts for 9~11% of total bus operaton tme, and, thus, understandng Bus dwell tme accurately s very mportant n establshng and managng a bus operaton schedule. To ths end, the dstrbuton of the dwell tme of a bus route n downtown Seoul, whch has most complcated publc transportaton network n Korea, was dentfed n ths study. Consequently, Bus dwell tme shows a rghtskewed dstrbuton, whch wll be used as the base for effectve bus operaton. Keywords: Bus servce, dwell tme, BMS, BIS, dstrbuton 1. INTRODUCTION A bus servce comprses three elements: operaton, servce at a bus stop and watng for a sgnal. Servce at a bus stop comprses arrval at the stop, boardng and alghtng and departure from the stop, as n Fg 1. The tme requred from arrval at a stop to departure us called Bus dwell tme. Bus dwell tme s one of the three elements comprsng bus servces and s also a crtcal factor determnng servce qualty. That s, Bus dwell tme may ether ncrease or decrease the passenger's satsfacton. estmated together wth Fu's study (2003)[2] would be helpful n plannng and desgnng the bus routes. 2. RELATED STUDIES Bustranst servce relablty s closely dependent on bus operaton speed, dwell tme at a stop, the drver's layover tme and the length of the bus route. L and L (2006)[3] suggested dwell tme as the crtcal factor n determnng bus transt servce qualty. Accordng to Maloney and Boyle (1999)[1], dwell tme accounts for 9~11% of bus travel tme. Precedng studes on dwell tme have focused on ncrease as dependng on the number of passengers. Levnson (1983)[4] proposed fve seconds of mean tme and an ncrease of 2.75 seconds per passenger. Guenthner and Snha (1983)[5] asserted a relatonshp between dwell tme and the fare collecton system. Fgure 1: Dwell tme at a bus stop Bus servce management has so far focused on travel tme between stops. That s, management has been lmted to road operaton only among bus servce elements. As suggested n the study by Maloney and Boyle (1999)[1], Bus dwell tme accounts for 9~11% of total servce tme. Despte the mportance n determnng servce qualty, study on ths element has been relatvely lackng, compared to study of other elements. In ths study, the data on the dwell tme of the buses runnng n downtown Seoul was collected and analyzed. In Korea, realtme management of the bus servce s n process. Bus Management System (BMS) and Bus Informaton System (BIS) dwell tme was estmated usng the arrval and departure tme collected by BMS. Dwell tme The studes on dwell tme have been lmted to the mportance of dwell tme and ts effect on a bus operaton servce, and studes were conducted to prove the relatonshp between dwell tme and the number of passengers. In fact, a study on the statstcal dstrbuton of dwell tme has yet to be conducted, and dwell tme n establshng a bus operaton schedule has been lmted to applyng the mean value from smlar routes. 3. DATA Seoul cty ntroduced BIS and BMS n 2006, and, snce then, nformaton has mantaned a 95% level of accuracy. As n Fg 1, a total of 11 bus stops n downtown Seoul were ncluded n the revew. Bus stops were on between fve and 13 routes. Data were collected on May 19, 2009 (Tue) usng BMS and BMS data provded by the Seoul Transport Operaton and Informaton Servce Center (TOPIS) Out of 11 stops, 9, 10 and 11, where buses stop more frequently, were selected as prorty analyss stops, and Nos 5, 7 and 8, where the same buses stoppng at 9, 10 and 11 stop, were addtonally ncluded. 547
VOL. 5, NO. 11, November 2015 ISSN 22257217 ARPN Journal of Scence and Technology 20112015. All rghts reserved. Thus, dwell tme analyss was conducted wth sx stops. Data collecton was made from 07:00 tll 19:00 for 12 hours, and dwell tme analyss consderng operatonal characterstcs was conducted by tme zone, mornng peak (07:00~09:00), nonpeak (12:00~14:00) and afternoon peak (17:00~19:00). A total of 15 routes use these bus stops as n Table 2. The operatonal characterstcs of the buses usng these stops are as n Table 2. Buses are n operaton wth a headway of four to fve mnutes. http://www.ejournalofscence.org whch was attrbutable to a large dfference n dwell tme between peak tme and nonpeak tme. Thus analyss of dwell tme separately by peak tme and nonpeak tme would be ratonal. Table 4 shows the result of dwell tme analyss by bus route. Dwell tme by route was 37.2 to 73.0 sec and standard devaton dstrbuton was 59.1 at 8.4. As a result of analyzng dwell tme by bus and by stop, mean value was around 1 mnute showng low varaton but hgh devaton. Thus devaton would be ncreased when applyng the mean value equally to bus operaton schedule. Ths study s ntended to revew the statstcal dstrbuton characterstcs of dwell tme and propose the optmal dwell tme based on revew. To that end, dwell tme was plotted by classfyng t nto mornng peak, afternoon peak and nonpeak tmes, and the outcome was used to dentfy the characterstcs of dwell tme dstrbuton. Should dwell tme follow normal dstrbuton, usng a mean value would be approprate, but, when skewed, usng a mode or medan value would be ratonal. Table 2: Headway of buses Headway (weekdays) Fgure 2: Bus stop data collecton: CBD n Seoul, Korea Table 1: Bus stop valdaton and the results of route selecton Class. Bus Stop / ID # of Bus 5 7 8 9 10 11 Natonal Polce Staton (02110) Gwanghwamun (01125) Seoul Museum of Hstory (01123) Seodaemun (01168) Dongnmmun (01170) Dongnmmun (01171) 701, 702, 703, 750, 752 370, 470, 471, 601, 720, 704 370, 470, 471, 601, 704, 710, 720 171, 370, 470, 471, 601, 701, 702, 703, 704, 710, 720, 750, 752 370, 470, 601, 703, 710, 750 171, 471, 701, 702, 704, 720, 752 Where, mnmum headway s based on peak tme whle maxmum headway s based on nonpeak tme. Dfference n headway between peak tme and nonpeak tme was 2 mnutes to 10 mnutes n maxmum. The longer the headway the larger the dfference between maxmum headway and mnmum headway, lke bus No. 704 and 752. Such nterval s dependent on rdershp. Extended nterval was attrbutable to less rdershp. Table 4 shows the statstcal analyss results of dwell tme by bus stop. A mean dwell tme was 37.7sec to 47.4 sec and the devaton was not sgnfcant. On the contrary, dwell tme by stop was 5 sec to 73sec, more than 15 tmes n dfference, Max. (a) Mn. (b) (a) (b) 171 6 10 4 370 4 7 3 470 6 11 5 471 4 6 2 601 6 10 4 701 8 10 2 702 4 10 6 703 6 10 4 704 10 20 10 710 6 13 7 720 7 10 3 750 4 12 8 752 4 14 10 4. ANALYSIS Dwell tme was calculated as below: where t t t depart t : dwell tme for a bus arrve 548
VOL. 5, NO. 11, November 2015 ISSN 22257217 ARPN Journal of Scence and Technology 20112015. All rghts reserved. t depart : tme of a bus departng from a stop t arrve : tme of a bus arrvng at a stop t > t ) ( depart arrve Table 3 shows the statstcal analyss result of dwell tme by bus stop. The mean dwell tme was 37.7 sec to 47.4 sec, and the devaton was not sgnfcant. Table 3: Dwell tme dstrbuton at bus stop Class. 5 7 8 9 10 11 total # of Data 938 1,048 1,346 1,438 712.0 874 6,356 Max. 179 158 144 175 264 161 264 Mn. 8 7 6 5 6 8 5 Ave. 41.8 39.8 47.4 45.9 37.7 43.8 43.4 St. Dev. 21.4 13.4 18.6 17.6 21.4 24.3 19.6 Var. 456.5 178.9 344.2 310.5 457.5 589.3 383.0 http://www.ejournalofscence.org As a result of analyzng dwell tme by bus and by stop, the mean value was around one mnute, showng low varaton but hgh devaton. Thus, devaton would be ncreased when applyng the mean value equally to the bus operaton schedule. Ths study s ntended to revew the statstcal dstrbuton characterstcs of dwell tme and propose an optmal dwell tme based on revew. To ths end, dwell tme was plotted by classfyng t nto mornng peak, afternoon peak and nonpeak tmes, and the outcome was used to dentfy the characterstcs of dwell tme dstrbuton. Should dwell tme follow normal dstrbuton, usng a mean value would be approprate, but, when skewed, usng a mode or medan value would be ratonal. 5. DISTRIBUTION OF DWELL TIME Dwell tme dstrbuton n the mornng peak, afternoon peak and nonpeak tmes s as n Fgs 3, 4 and 5. In all cases, the mean value was greater than the medan value as rghtskewed (postve skewness), whch mples a problem when applyng the mean value as equally as dwell tme. Table 4: The mean and standard devaton of dwell tme Class. Bus Stop / ID Dwell Tme (Ave., St. Dev.) 171 370 470 471 601 701 702 703 704 710 720 750 752 5 Natonal Polce Staton (02110) 64.3, 27.7 47.1, 26.6 58.3, 38.4 7 Gwanghwamun (01125) 40.8, 10.1 42.7, 11.9 45.6, 22.6 41.7, 12.3 39.5, 15.1 8 Seoul Museum of Hstory (01123) 53.4, 22.6 44.5, 14.9 52.5, 20.7 62.5, 22.0 48.3, 25.1 48.0, 17.1 9 Seodaemun (01168) 63.7, 26.9 64.0, 27.9 57.4, 26.2 63.2, 15.3 61.5, 28.0 64.1, 10.8 72.8, 24.2 67.5, 25.0 73.0, 20.0 55.4, 25.1 66.4, 33.6 66.7, 16.2 67.9, 25.2 10 Dongnmmun (01170) 51.2, 19.4 51.0, 28.5 68.7, 59.1 51.1, 35.3 47.9, 20.4 11 Dongnmmun (01171) 52.2, 36.5 44.9, 20.4 45.1, 26.8 37.2, 8.4 44.5, 20.6 51.3, 23.0 68.6, 35.4 Table 4 shows the result of dwell tme analyss by bus route. Dwell tme by route was 37.2 to 73.0 sec, and the standard devaton dstrbuton was 59.1 at 8.4. On the contrary, dwell tme by stop was 5 sec to 73 sec, more than a dfference of 15 tmes, whch was attrbutable to a large dfference n dwell tme between the peak tme and the nonpeak tme. Thus, analyss of dwell tme separately by the peak tme and the nonpeak tme would be ratonal. A rghtskewed dstrbuton means a case n the form of a long tal at the rght sde. In such a case, an excessvely large value may be appled when usng a mean value. Partcularly n the afternoon peak, a rghtskewed dstrbuton wth a concentraton of passengers appeared. 549
VOL. 5, NO. 11, November 2015 ISSN 22257217 ARPN Journal of Scence and Technology 20112015. All rghts reserved. http://www.ejournalofscence.org Fgure 3: Mornng peak Fgure 4: Nonpeak Fgure 5: Afternoon peak 550
VOL. 5, NO. 11, November 2015 ISSN 22257217 ARPN Journal of Scence and Technology 20112015. All rghts reserved. 6. CONCLUSION In ths study, the dstrbuton of dwell tme at a stop was dentfed by plottng. A mean value was adopted for dwell tme used for the bus operaton schedule because the dwell tme dstrbuton was assumed to follow a normal dstrbuton. As a result of plottng the dwell tme dstrbuton of the buses n the operaton, a skewed dstrbuton, nstead of a normal dstrbuton, was found. Such a pattern appeared n the afternoon peak. The cause and result of the characterstcs of the afternoon peak are as follows. In general, the passengers are concentrated n a certan tme zone, and the headway of a bus s shortened, whch promotes quck servce at stops. Thus, the mode appears as a small value. On the contrary, a bus often provdes a boardng and alghtng servce at stops over an extended tme because of the concentraton of passengers. Thus, when establshng the operaton schedule by applyng the mean value of dwell tme at stop, the devaton would possbly be sgnfcant. Accordng to the outcome from ths study, the mode or medan value would be more ratonal for dwell tme at a stop n the case of stops wth such characterstcs. The modes at mornng peak, afternoon peak and nonpeak tmes were all smlar to each other, ndcatng 34~35 seconds. When applyng the same value rrespectve of the tme, usng the mode would be more approprate. As a result of revewng the plot result, dwell tme follows a gamma dstrbuton nstead of a normal dstrbuton. Hence, a dwell tme estmaton model usng gamma dstrbuton s proposed for further study. http://www.ejournalofscence.org REFERENCES [1] Maloney, M. & Boyle, D. (1999). Components of travel tme on the Glendale Beelne bus network. Transportaton Research Record, 1666, 23 27. [2] Fu, L. (2003). On plannng and desgn of flexroute transt servces. Transportaton Research Record, 1791, 59 66. [3] L, M.T. and L, S.C. (2006). A smulaton model for estmatng bus dwell tme by smultaneously consderng numbers of alghtng and boardng passengers at stop level. Transportaton Research Record, 1971, 59 65. [4] Levnson, H.S. 1983. Analyzng transt travel tme performance. Transportaton Research Record, 915, 1 6. [5] Guenthner, R. P. and K. C. Snha. 1983. Modelng bus delays due to passenger boardngs and alghtngs. Transportaton Research Record, 915, 7 13. 551