UNDERSTANDING TAXI DRIVERS MULTI-DAY CRUISING PATTERNS

Transcription

1 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns FANG ZONG, Ph.D. E-mal: Jln Unversty, College of Transportaton 5988 Renmn Street, Changchun, Jln, , Chna XIAO SUN, Prof. Correspondng author E-mal: Jln Unversty, Appled Technology College 5372 Nanhu Road, Changchun, Jln, , Chna HUIYONG ZHANG, Ph.D. E-mal: Jln Unversty, School of Management 5988 Renmn Street, Changchun, Jln, , Chna XIUMEI ZHU, Ph.D. E-mal: Jln Unversty, School of Management 5988 Renmn Street, Changchun, Jln, , Chna WENTIAN QI, M.S. E-mal: Suzhou Insttute of Constructon and Communcatons Suzhou, Jangsu, , Chna Traffc Management Orgnal Scentfc Paper Submtted: Sep. 25, 2014 Approved: Nov. 24, 2015 UNDERSTANDING TAXI DRIVERS MULTI-DAY CRUISING PATTERNS ABSTRACT Ths study nvestgates tax drvers mult-day crusng behavours wth GPS data collected n Shenzhen, Chna. By calculatng the nter-daly varablty of tax drvers crusng behavours, the mult-day crusng patterns are nvestgated. The mpacts of learnng feature and habtual feature on multday crusng behavours are determned. The results prove that there s varablty among taxs day-to-day crusng behavours, and the day-of-week pattern s that tax drvers tend to cruse a larger area on Frday, and a rather focused area on Monday. The fndngs also ndcate that the mpacts of learnng feature and habtual feature are more obvous between weekend days than among weekdays. Moreover, learnng feature between two sequent weeks s found to be greater than that wthn one week, whle the habtual feature shows recesson over tme. By revealng taxs' day-to-day crusng pattern and the factors nfluencng t, the study results provde us wth crucal nformaton n predctng taxs' mult-day crusng locatons, whch can be appled to smulate taxs' mult-day crusng behavour as well as to determne the traffc volume derved from taxs' crusng behavour. Ths can help us n plannng of transportaton facltes, such as stop statons or parkng lots for taxs. Moreover, the fndngs can be also employed n predctng taxs' adustments of mult-day crusng locatons under the mpact of traffc management strateges. KEY WORDS tax; mult-day; crusng pattern; GPS; 1. INTRODUCTION Tax s one of the maor transportaton modes n urban transportaton system. Yet, empty tax crusng results n sgnfcant amount of wasted energy and emssons. As we know, up to 40 percent of taxs daly mleage s spent wth no passengers on board [1]. The average dead mleage for taxs n Beng s 120 km per day, whch accounts for 40% of total daly mleage. Ths means that 13 ltres of fuel are used per day whle drvng wth no passengers [2]. Therefore, t s mportant to dentfy ways to make empty taxs cruse more effcently. Ths paper ams at learnng taxs mult-day crusng patterns and provdng mportant nformaton for tax drvers and transportaton managers to enhance taxs crusng effcency. By nvestgatng the factors that affect tax drvers crusng decsons and by examnng ther mult-day crusng behavours, we wll try to fnd the underlyng mechansms of taxs dayto-day crusng decsons. In recent years, massve progress has been made n travel survey wth the rapd development and applcaton of Global Postonng System (GPS) technology. As an advanced computer-based technque, GPS offers sgnfcant advantages over tradtonal survey methods n collectng travel data, especally ts ablty to capture mult-day data [3]. Many researchers pre- Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

2 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns sented studes on tax s drvng behavours by usng GPS data [4]. Ths study wll use mult-day GPS data collected from 2,536 tax drvers n Shenzhen, Chna. As GPS-collected data are not ready for drect use n crusng behavour analyss, some computer-based technques and methods wll be used, such as Quadrat Analyss and Entropy, n processng and analysng GPS data. Wth wde applcaton of GPS devces n mult-day travel survey, the analyss of mult-day travel behavour has been one of the hot ssues n transportaton studes. However, none of the researchers analysed the mult-day operatng patterns or modelled the process of day-to-day dynamcs of taxs crusng behavours. In ths paper an analyss of taxs mult-day crusng patterns wll be conducted. Two maor features of taxs day-to-day crusng behavours,.e., learnng from prevous pck-up experence (learnng feature) vs. obeyng crusng habts (habtual feature), wll be nvestgated. In partcular, we seek to answer three questons: 1) Is there varablty between tax drvers day-to-day crusng behavours? 2) What are the dfferences among mult-day crusng behavours? 3) How do the two factors,.e., learnng and habts, affect tax drvers day-today crusng behavours? The remander of ths paper s organzed as follows. Secton 2 presents a revew on the analyss of taxs crusng behavours n general. Secton 3 presents a descrpton of data and the study area. In Secton 4 the spatal dstrbutons of crusng traces and pckup ponts are examned. In Secton 5, the mult-day varablty of crusng patterns s calculated, and the dfferent mpacts of learnng feature and habtual feature n day-to-day crusng behavours are nvestgated. The paper s concluded wth Secton 6, n whch the fndngs are summarzed and the drectons for future research dscussed. 2. LITERATURE REVIEW The mult-day travel behavour analyss has been one of the hot ssues n transportaton research. However, none of the studes analysed the mult-day operatng pattern or modelled the day-to-day dynamcs of taxs crusng behavours. There re only a few researchers who consdered prevous operatng experence n modellng taxs drvng patterns. For example, Reference [5] modelled a tax servce system n urban areas, takng nto account the tax drvers knowledge of the transportaton network from ther day-to-day experence. Reference [6] found that drver s travel experence as well as a renewal of all acqurable traffc nformaton that can assst n confrmng the reference ponts n road network have nfluence on the route choce of the next trp. Reference [7] presented an experental approach to compute optmal paths, n whch path-plannng was supported by a flexble road network herarchy usng the experence of tax drvers. Other studes that nvestgated drvng experence are Yu et al. s work on modellng bus arrval tmes [8, 9] and vehcle s route choce [10], and Yao et al. s study on accdent detecton [11], etc. Several models were developed to nvestgate the day-to-day dynamcs of travel behavours, such as reference [12] proposed a stochastc process approach to analyse day-to-day dynamcs n a transportaton network. A key assumpton of the stochastc process s that the path choce probabltes are tme homogeneous, whch means that there are no tme-dependent varatons n drvers' perceptons. Ths approach was further extended by reference [13] to nclude day dynamcs. Reference [14] descrbed a smple route choce model over tme whereby decsons are based on the weghted average of prevous travel decsons utltes. Based on ths model, reference [15] proposed a myopc adustment model by allowng the weghts to vary across ndvduals. Reference [16] presented detaled dscussons regardng the habtual and varable behavour of ndvduals over tme. They noted that some behavours, when examned n a dsonted framework (say, a work trp examned n solaton of the overall daly actvty-travel pattern), are repeated on a day-to-day or week-to-week bass. However, when the overall daly actvty-travel pattern s examned n ts entrety, they found that a one-day pattern s not representatve of a person s routne travel. Prevous studes also proposed two maor features of mult-day travel decsons: learnng feature vs. habtual feature. Wth respect to learnng feature, some researchers mentoned above proved that tax drvers have the characterstcs of learnng, whch means that they wll update ther traffc nformaton from ther day-to-day experence and use the nformaton n route choce of the next trp [5, 6]. Besdes tax related studes there are also some researchers who modelled the learnng process of other travel behavours. For example, reference [17] proposed travellers decson-makng process based on Bayesan updatng by consderng day-to-day dynamcs of travel behavours. Reference [14] proposed a learnng model for route choce selecton. Reference [18] developed a learnng model for mode choce. The habtual feature has been also proved and utlzed by many studes related to travel behavour analyss. In many studes about mode choce modellng, the factor of habt was also taken as a maor varable [19, 20]. Reference [21] demonstrated that when behavours are well-practced and repeatedly performed, frequency of past behavour reflects habt strength and has drect effect on future performance. Reference [22] found that although most drvers thought that they had two or three alternatve routes, the maorty sad they always stuck to the same one. Ths also demonstrated the crucal role of habts n travel decsons. 468 Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

3 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns Though the above studes proved that travel behavours have the learnng features and habtual features, none of them conducted a quanttatve comparson between them. Ths study wll present a quanttatve comparson between these two features, and measure the mult-day varablty of tax drvers crusng patterns. 3. DATA AND STUDY AREA The data used n ths study are GPS traces collected from 2,536 taxs durng a 9-day perod (November 18 th 2011 November 26 th 2011), n Shenzhen, Chna. The surveyed taxs account for about 17.14% of the total number of taxs and 76.64% of taxs wth on-board GPS equpment n Shenzhen. Each record n the dataset represents a GPS sgnal that was captured consecutvely at a 5-second nterval (Shenzhen Transport Informaton Center, 2011). The basc nformaton provded by the dataset contan taxs traces n longtude and lattude form, vehcle dentfcaton, operaton status (empty or occuped), tmestamp, spot speed, and azmuth. Durng the 9-day perod, 30,179,212 vald postons n total were recorded. In order to learn the mult-day crusng patterns as well as the features of crusng behavours, two types of ponts are selected from the GPS traces,.e., crusng traces (wthout passengers) and pck-up ponts (locatons whose operaton status s from vacancy to occupancy), n whch crusng traces represent tax drvers crusng patterns. The spatal correlatons among dfferent days crusng traces and pck-up ponts are used to represent learnng vs. habtual features. The study area of ths paper s the urban area of Shenzhen cty, whch s one of the four most developed ctes n Chna. It had a resdng populaton of mllon n 2013 and 10 dstrcts. The admnstratve dvson of Shenzhen s shown n Fgure 1. As GPS-collected data are not ready for drect use n crusng behavour analyss, one of the wdely used spatal analyss technques Quadrat Analyss wll be employed n data processng. Accordng to the theory of Quadrat Analyss, the entre study area s dvded nto cells. The area of each cell (Area g ) can be calculated as: Area g = 2A/Q (1), where A s the entre study area and Q s the number of traces that wll be analysed n the study area. The X and Y coordnates for the study area range from to and from 2, to 2,531.10, respectvely. Based on these ranges, the total area A can be calculated as 3, square klometres. Snce ths study s concerned wth drvers traces on one day, the average number of GPS traces of each drver per day,.e., 9,083, s taken as the value of Q. Thus, the area of each cell s then calculated as square klometres, wth each sde beng equal to km. Thus, the study area s dvded nto 96 50=4,800 cells. For X coordnate, there are ( )/0.93=94.92 segments, and for Y coordnate, there are (2, ,486.22)/0.93=48.26 segments. In order to cover the four sdes of the study area as well as to make the numbers of the segments ntegers, one cell s expanded for each sde of the study area. Ths yelds 96 and 50 segments for X coordnate and Y coordnate, respectvely. CBD Fgure 1 Admnstratve dvson of Shenzhen cty Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

4 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns 4. SPATIAL DISTRIBUTIONS OF CRUISING TRACES AND PICK-UP POINTS 4.1 Entropy By employng a parameter of entropy, whch s a measure of the uncertanty n a random varable [23], the basc characterstcs of spatal dstrbuton of crusng traces and pck-up ponts can be examned. If we defne a dscrete random varable Z as the event that one pont locates n a zone, then the entropy of Z,.e. H(Z), refers to the unpredctablty of event Z: 25 n n HZ ( ) = - ln( ) (2) = 1 N N n whch, n s the number of ponts n zone wth = 1, 2,, 25 (the study area s dvded nto 25 zones as shown n Fgure 1), N s the total number of ponts, that 25 n s N = n, then means the probablty that one = 1 N pont s located n zone, and 25 n = 1. = 1 N When all the ponts are located n one zone, we can get the mnmum value of H(Z), that s 0, whch means that event Z s most predctable, or ponts are most clustered concernng spatal dstrbuton. On the contrary, when all the ponts are located n 25 zones evenly, we can get the maxmum value of entropy, defned as H m, whch means that event Z s most unpredctable, or ponts are most dspersed concernng spatal dstrbuton. In ths study, H m = ln 25, whch s obtaned n 1 from probablty N = 25 for each zone. Then C can be ntroduced to represent the cluster degree of ponts: C = 1 - H(Z)/H m (3) As we know, C s a value between 0 and 1. The hgher the cluster degree C s, the more clustered the spatal dstrbuton of ponts s. Accordng to reference [24]' study, cluster degree>0.45 means that the data ponts are very clustered, and 0.4 < C 0.45 denotes that the data ponts are clustered, whle C 0.4 means that the ponts are dspersed. 4.2 Analysng spatal dstrbuton wth entropy The mean value of cluster degree C of crusng traces and pck-up ponts per person per day s calculated to be and , respectvely. Ths ndcates that both crusng traces and pck-up ponts exhbt a very clustered spatal dstrbuton. As the cluster degree C of pck-up ponts s bgger than that of crusng traces, we can nfer that pck-up ponts are more clustered than crusng traces n spatal dstrbuton. One potental reason s that the taxs pck-up ponts are also the start ponts of tax trps, and the spatal dstrbuton of the start ponts s related to the spatal dstrbuton of land use and populaton n the study area [25]. In the study area of ths paper,.e., Shenzhen cty, the hgh-densty area of land use and populaton s the area covered by Luohu and Futan dstrct (shown n Fgure 1). It s the clustered spatal dstrbuton of land use and populaton that leads to the aggregated spatal dstrbuton of taxs pck-up ponts. On the contrary, the spatal dstrbuton of crusng traces depends on tax drver s ndvdual crusng behavour, whch s much more a subectve factor, comparng wth land use and populaton dstrbuton whch are obectve factors. Beng the results of subectve decson behavours, crusng traces are then more dsaggregated than pck-up ponts n spatal dstrbuton. 4.3 Varablty n mult-day cluster degrees In order to dentfy the potental varablty n multday crusng patterns, we wll measure the changes among mult-day cluster degrees of crusng traces, and compare them wth those of the pck-up ponts. As the GPS traces recorded the crusng traces of dfferent days and dfferent taxs, the total varablty n GPS records contan both nter-daly varablty and nter-personal varablty. Therefore, n order to dentfy the varablty among mult-day crusng behavours, a dstncton should be made between nter-daly varablty and nter-personal varablty. Reference [26] and [27] provded the theory of TSS (total sum of squares) to measure and quantfy the nter-personal varablty and ntra-personal varablty n a travel survey data set. Fgure 2 shows the framework of TSS as adopted from ther work. Inter-personal varablty refers to the dfferences n the behavour among dfferent ndvduals on the same days. Behavoural dfferences among tax drvers may be explaned partally by dfferences n the characterstcs of ndvduals. By ncorporatng such characterstcs nto a model, one can account for systematc dfferences n behavour among ndvduals. The porton of nter-personal varablty that can be explaned systematcally through dfferences n soco-economc characterstcs s referred to as explaned varablty. The remander s referred to as unexplaned varablty. Smlarly, ntra-personal varablty (nter-daly varablty) may also be consdered as havng two components. The frst component s called systematc day-of-week varablty. Ths refers to the porton of ntra-personal varablty that may be attrbuted to systematc day-of-week effects. Intra-personal varablty that cannot be explaned by day-of-week effects s random and s referred to as resdual ntra-personal varablty. In ths study, the total ntra-personal (nter-daly) varablty as well as the total nter-personal varablty wll be quantfed by employng the TSS theory. The to- 470 Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

5 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns Total Varablty Inter-personal Varablty Intra-personal Varablty Explaned Varablty Unexplaned Varablty Systematc, Day-of-week Varablty Resdual Intra-personal Varablty Fgure 2 Methodologcal framework for measurng nter-personal/ntra-personal varablty tal varablty n varous measures of crusng patterns s splt nto two components whch are represented by approprate sums of squares. In ths representaton, the total varablty s represented by the total sum of squares (TSS), as follows: 2 ( ) (4) TSS = C - C where C s the cluster degree C of person on day, and C s defned as the overall sample mean of C per person per day. The nter-personal sum of squares (IPSS) s gven by: ( 2 ) (5) IPSS = J C - C where J s the number of days for whch ndvdual reported GPS crusng traectory, and C means the cluster degree C of person per day. The nter-daly sum of squares (IDSS) s gven by: 2 ( ) (6) IDSS = C - C C C Also, we have: = and J C = = JC J J C (7) (8) It can be readly seen that, TSS = IPSS + IDSS (9) Therefore, the rato IDSS/TSS provdes a measure of the proporton of total varablty n crusng patterns that may be attrbuted to nter-daly varablty. Smlarly, IPSS/TSS provdes a measure of the proporton of total varablty n crusng patterns that may be attrbuted to nter-personal varablty. The calculatng results of TSS parameters for cluster degrees of crusng ponts and pck-up ponts are shown n Table 1. The results ndcate that, for both crusng traces and pck-up ponts, the value of IPSS s greater than that of IDSS: the nter-personal varablty and nter-daly varablty can explan 66.27% and 33.73% of the total varablty n cluster degree of the crusng traces, respectvely; Smlarly, the nter-personal varablty and nter-daly varablty can explan 64.53% and 35.47% of the total varablty n cluster degree of the pck-up ponts, respectvely. Concernng the results of crusng traces, because IPSS accounts for 66.27% of the total varablty t ndcates that there s large varablty between dfferent tax drvers. In other words, dfferent types of tax drvers may have dfferent strateges for crusng locaton choce: some of them may cruse n a large area, whle some of them may choose a relatvely small area. In order to explan the nter-daly varablty n crusng traces and pck-up ponts, the mean values of cluster degree of dfferent days per person are calculated. The results are shown n Table 2. Table 1 TSS parameters for cluster degrees Item Cluster degree of crusng traces Cluster degree of pck-up ponts Value Rato Value Rato TSS IPSS IPSS/TSS: 66.27% IPSS/TSS :64.53% IDSS IDSS/TSS: 33.73% IDSS/TSS: 35.47% Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

6 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns Table 2 Mult-day cluster degrees Cluster degree of crusng traces Cluster degree of pck-up ponts Percent of devaton Percent of devaton Day Mean value C C -C 100% C Mean value C C -C 100% C Aprl 18 th % % Aprl 19 th % % Aprl 20 th % % Aprl 21 st % % Aprl 22 nd % % Aprl 23 rd % % Aprl 24 th % % Aprl 25 th % % Aprl 26 th % % Mean value C The results ndcate that there are two smlar characterstcs for the mult-day varablty of both crusng traces and pck-up ponts cluster degree: (1) the mult-day varablty s small,.e., the cluster degrees of dfferent days are smlar to each other; (2) there s a same day-to-day changng pattern,.e., the cluster degree reaches the mnmum on Aprl 22 nd (Frday). One of the reasons may be that on Frday passengers made tax trps not only for the workng purpose lke other weekdays, but also for other trp purposes, such as entertanment and mantenance, lke on weekend. Ths relatve complcated composton of trp purposes on Frday leads to the dsaggregated dstrbuton of both crusng traces and pck-up ponts. Concernng the maxmum of cluster degree, the value on Aprl 18 th (Monday) s the maxmal value n the mult-day cluster degrees of crusng traces. A potental reason s that most of the tax trps on Monday are workng trps, and tax drvers may choose a "Monday crusng mode" accordng to ther own crusng habts or land use characterstcs of the cty. It may be the relatvely regular "Monday crusng mode" that makes the dstrbuton of crusng traces more clustered than other days of the week. As for the pck-up ponts, the maxmum of cluster degree s the value on Aprl 24 th (Sunday). A potental reason s that most of the tax trps on Sunday are trps for entertanment or mantenance purposes startng from a hgh-densty area, such as the Central Busness Dstrct. Therefore, the pck-up ponts concentrate on the hgh-densty areas and present an aggregated dstrbuton. them n future crusng locaton choces. In ths paper, the spatal correlaton between current crusng traces and prevous pck-up ponts t &p - s chosen to represent the learnng feature. The footmark denotes current day and - refers to prevous day, t and p represent crusng traces and pck-up ponts, respectvely. Habts denote one s customary ways of behavng [21, 28]. In ths paper, the habtual feature presents that tax drvers wll accumulate some crusng habts from day-to-day crusng experence and follow the crusng habts conscously or unconscously n future crusng decsons. The smlarty n spatal dstrbuton between current crusng traces and prevous crusng traces (t &p - ) s taken as the habtual feature n crusng pattern. A dagram of the learnng feature and habtual feature s shown n Fgure 3. Habtual feature: t & t Learnng feature: t & p 5. LEARNING AND HABITUAL FEATURES OF CRUISING BEHAVIOUR The learnng feature means that tax drvers remember ther prevous crusng experence, learn from t, nfer potental pck-up locatons from t, and apply Current crusng traces Prevous pck-up ponts Prevous crusng traces Fgure 3 A dagram of learnng feature and habtual feature 472 Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

7 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns As Fgure 3 shows, the relatonshp between t and p -, such as the dstance between current crusng trace and prevous pck-up pont, s selected to represent the learnng feature of crusng behavour. Smlarly, the relatonshp between t and t - can be seen as tax drver s habtual feature n crusng decson. 5.1 Analysng the dstance between hot spots One of the most drect approaches to measure spatal correlaton between spatal ponts s to calculate the dstance between them. To do ths, we frst dentfy the hot spots of crusng traces and pck-up ponts for each drver and each day, and then take the hot spots as representatons of crusng traces and pck-up ponts, respectvely, for dstance calculaton. Accordng to the theory of hot spot analyss, we calculate the number of crusng traces and pck-up ponts for each tax and each day n each cell of the study area. The centrod of the cell wth the largest amount of crusng traces or pck-up ponts s noted as the hot spot of crusng traces or pck-up ponts, respectvely. Then one tax s one day s crusng traces and pck-up ponts can be represented by ther calculated hot spot. The dstance between the hot spots of current crusng traces and prevous pck-up ponts can be defned as D(t, p - ), and the dstance between the hot spots of current crusng traces and prevous crusng traces s noted as D(t, t - ). The mean value of D(t, p -1 ) and D(t, t -1 ) per drver s calculated as 6.94 km and 6.20 km, respectvely. -1 and denote sequental two days n the 9-day perod. Ths ndcates that the dstance between today s crusng traces and yesterday s crusng traces s smaller than that between today s crusng traces and yesterday s pck-up ponts. Ths reveals that, concernng the dstance between hot spots, habtual feature s a more mportant factor than learnng feature n tax drvers crusng locaton choce. In order to measure mult-day varablty of learnng feature and habtual feature, the theory of TSS mentoned above s adopted. In equatons (4) to (8), the cluster degree related parameters can then be swtched to dstance related parameters whch present dstances among hot spots of mult-day crusng traces and pck-up ponts. The results of TSS analyss for dstance between hot spots are shown n Table 3. The IDSS and IPSS value of D(t, p -1 ) reveals that there are both nter-personal and nter-daly varabltes concernng tax drvers learnng feature. However, the nter-personal varablty s a lttle bt greater than the nter-daly varablty. Ths reveals that dfferent types of tax drvers have dfferent crusng behavours concernng the learnng feature. In other words, dfferent tax drvers are found to have dfferent levels of ablty to learn from prevous pck-up experences. Therefore, when measurng tax drvers learnng feature, not only mult-day varablty but also varablty among dfferent types of drvers should be consdered. The ratos IDSS/TSS and IPSS/TSS for D(t, t -1 ) show that the nter-daly varablty accounts for 63.27% of total varablty and the nter-personal varablty covers 36.73% of total varablty. Ths shows a larger varablty of mult-day habtual feature than that of nter-personal habtual feature. In other words, t proves that a tax drver has dfferent crusng habts on dfferent days of the week. The mult-day changes of crusng habts should be consdered n crusng patterns analyss. Therefore, further analyss of mult-day varablty s conducted by calculatng mult-day dstance between t &t -1 and t &p -1 hot spots. The results are shown n Table 4. Table 3 TSS parameters for dstances between hot spots Item D(t, p -1 ) D(t, t -1 ) Value Rato Value Rato TSS 3,081,451 2,832,022 IPSS 1,586,149 IPSS/TSS: 51.47% 1,040,226 IPSS/TSS: 36.73% IDSS 1,495,303 IDSS/TSS: 48.53% 1,791,797 IDSS/TSS: 63.27% Table 4 Statstcs of dstance between mult-day hot spots Tme D(t, p -1 ) D(t, t -1 ) Value (km) Standard devaton Value (km) Standard devaton Mean value per day Day of week Between days of two consecutve weeks Between two consecutve weekdays Sunday and Saturday Saturday and Frday Between Mondays Between Tuesdays Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

8 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns The smaller the dstance, the larger s the correlaton between the two types of spatal ponts. Concernng habtual feature, the results show that, for two consecutve days, the habtual feature between Sunday and Saturday s the largest, whle that between two weekdays s the smallest. Ths ndcates that the mpacts of habts are more obvous between weekend days than among weekdays. The dstances between t &t -1 hot spots of two consecutve weeks reveal that there are also crusng habts between two consecutve weeks. However, the mpacts of crusng habts of two weeks s smaller than those wthn one week. The results reveal a smlar pattern of nter-daly learnng feature n one week as the one of the habtual feature, that s, the learnng degree between Sunday and Saturday s the largest among learnng degrees between two consecutve days n one week, whle that between two weekdays s the smallest. Ths ndcates that the mpacts of learnng feature are more obvous between weekend days than among weekdays. In other words, tax drvers consder more yesterday s pck-up experence on Sunday than on other days of the week. The dstances between t &p -1 hot spots of two sequent weeks reveal that tax drvers also accumulate crusng knowledge from pck-up ponts of last week. Moreover, the learnng degrees between two consecutve weeks are greater than those wthn one week. Ths reveals that learnng feature does not decay over tme as habtual feature does. 5.2 Analysng frequency of the hot spots n the same cell Besdes dstance between hot spots, the probablty of t &p -1 hot spots vs. t &t -1 hot spots beng n the same cell s also adopted to measure mult-day learnng feature vs. habtual feature of crusng behavour, respectvely. In detal, the probablty that the hot spots of current crusng traces and prevous pck-up ponts are n the same cell s defned as P(t, p -1 ), and s taken as a parameter to measure the learnng feature of the crusng behavour. Smlarly, the probablty that the hot spots of current crusng traces and prevous crusng traces are n the same cell s defned as P(t, t -1 ) n order to be adopted n examnng habtual feature of crusng behavour. P(t, p - ) and P(t, t - ) are gven by: Pt (, p ) = - I = 1 d I tp (10) where d tp s an ndcator parameter, d tp = 1 f drver s hot spots of crusng traces on day (current) and pckup ponts on day - (prevous) are n a same cell, and d tp = 0 f ther hot spots of crusng traces on day and pck-up ponts on day - are not n the same cell. I s the total number of tax drvers. Pt (, t ) = - I = 1 d I tt (11) where d tt s another ndcator parameter, d tt = 1 f drver s hot spots of crusng traces on day and crusng traces on day - are n the same cell, and d tt = 0 f the hot spots of crusng traces on day and crusng traces on day - are not n the same cell. The results (shown n Table 5) ndcate that 41.69% of the tax drvers chose the same crusng area (hot spot) accordng to prevous day s crusng area, whle only 13.75% of tax drvers chose the same crusng area as prevous day s pck-up hot spot. Ths ndcates that tax drvers prefer to obey crusng habts more than to learn from prevous pck-up knowledge. Ths fndng s smlar to the result obtaned from the hot spot analyss presented above. The results also show smlar mult-day varablty of learnng feature and habtual feature: the mpacts of learnng feature and habtual feature between Sunday and Saturday s the largest among the values between two consecutve days n one week, respectvely, whle that between two weekdays s the smallest. Moreover, the dfference between learnng feature and habtual feature s that learnng feature between two consecutve weeks s greater than that wthn one week, whle the habtual feature presents recesson over tme. 6. CONCLUSION Ths study nvestgates tax drvers mult-day crusng behavours by usng GPS data collected n Shenzhen. Our results show that the nter-daly varablty can account for 33.73% of the total varablty n cluster degree of the crusng traces. Ths answers the Table 5 Probabltes of dfferent hot spots beng n the same cell Tme P(t, p - ) P(t, t - ) Mean value per day Between two consecutve weekdays Day of week Sunday and Saturday Saturday and Frday Between days of two consecutve weeks Between Mondays Between Tuesdays Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

9 F. Zong, X. Sun, H. Zhang, X. Zhu, W. Q: Understandng Tax Drvers Mult-day Crusng Patterns frst queston that we proposed n Secton 1: there s varablty between tax drvers day-to-day crusng behavours. By nvestgatng the TSS statstcs of cluster degrees of mult-day crusng traces, the second queston proposed n Secton 1 s answered. Our fndngs reveal that there are mnor dfferences among cluster degrees of mult-day crusng traces. The cluster degree reaches the mnmum on Aprl 22 nd (Frday) and the maxmum on Aprl 18 th (Monday), whch reveals that tax drvers tend to cruse a larger area on Frday but a focused area on Monday. To answer queston 3, we conducted a comparson of the mpacts of learnng and habtual feature on dayto-day crusng traces. The results show that dfferent types of tax drvers obey the prevous pck-up experence n dfferent degrees. At the same tme, a tax drver has dfferent degrees of crusng habts on dfferent days of a week. Ths suggested that we should pay attenton to the varablty among dfferent types of drvers concernng learnng feature, whle consderng the day-of-week characterstc for the habtual feature of crusng behavours. The results also show smlar mult-day varablty of learnng feature and habtual feature: the mpacts of the two features are more obvous between weekend days than among weekdays. However, learnng feature between two consecutve weeks s greater than that wthn one week, whle the habtual feature presents recesson over tme. By revealng taxs' day-to-day crusng pattern and the factors nfluencng t, the study results provde crucal nformaton n predctng taxs' mult-day crusng locatons. In detal, the probablty can be calculated that a drver wll choose a locaton as today's crusng locaton by consderng ther crusng locatons and pck-up ponts n the prevous days. Ths fndng can be appled to smulate taxs' mult-day crusng behavour. Moreover, when makng a traffc management strategy, we can also employ the study results n predctng taxs' adustments of mult-day crusng locatons under the mpact of the strategy. Ths work also makes a contrbuton n determnng the traffc volume derved from taxs' crusng behavour n the study area. Ths fndng s essental for plannng of transportaton facltes, lke stop statons or parkng lots for taxs. It should be ponted out that only learnng feature and habtual feature are consdered n ths paper. In realty, there may be other factors, such as last dropoff locaton, land use characterstcs [29] and traffc condton [28, 30, 31], that have potental effects on taxs crusng behavour. Further study should be conducted to model the mpacts of these factors. Besdes, n order to get more nformaton concernng mult-day crusng patterns, the GPS data of more days should be used n the future study. ACKNOWLEDGEMENTS The research s funded by the Natonal Natural Scence Foundaton of Chna ( ), the Humanty and Socal Scence Youth foundaton of Mnstry of Educaton (14YJC630225), the Chna Postdoctoral Scence Specal Foundaton (2014M551191) and Jln Unversty outstandng youth fund (2013JQ007). Specal thanks to the anonymous revewers whose valuable comments helped tremendously to mprove ths paper. 出租车的多日巡航行为研究 宗芳 1, 孙晓 2, 张慧永 3, 朱秀梅 3, 祁文田 4 1 吉林大学交通学院长春中国 2 吉林大学应用技术学院长春中国 3 吉林大学管理学院长春中国 4 苏州建设交通高等职业技术学校苏州中国 本文应用深圳市的出租车车载 GPS 数据分析了出租车的多日的空载巡航行为 通过计算出租车各日巡航点空间分布特征值间的变化, 分析总结了巡航行为的多日变化规律 对比分析了司机的学习性和习惯性对巡航行为的影响 研究结果表明出租车逐日的巡航行为间具有一定差异 : 他们倾向于在周五巡航更大的区域范围, 而周一的巡航区域比较集中 ; 另外, 周六和周日之间学习性和习惯性的影响较每周工作日之间的表现更明显 ; 同时, 两周之间的学习性比一周内的影响更大, 而习惯性的影响具有随时间增长而衰减的特征 本文的研究成果体现了出租车的多日巡航行为决策机理, 对于提出有效措施提高出租车的巡航效率具有一定借鉴意义 关键词 出租车 ; 多日的 ; 巡航行为 ;GPS REFERENCES [1] Empty cabs waste fuel, cause polluton. Shangha Daly 2011 Feb 16; Avalable from: cn/envronment/ /16/content_ htm [2] L JZ. Optmal ncentve for transportaton management under a symmetrc nformaton. Journal of Chongqng Jao Tong Unversty (Natural Scence). 2007;26(5): [3] Castro PS, Zhang D, L S. Urban traffc modellng and predcton usng large scale tax GPS traces. Proceedngs of the 10th Internatonal Conference on Pervasve Computng; 2012 June 18-22; Newcastle, UK. Sprnger-Verlag Berln Hedelberg; p [4] Lu L, Andrs C, Bderman A, Ratt C. Uncoverng tax drver's moblty ntellgence through hs trace. Seventh Annual IEEE Internatonal Conference on Pervasve Computng and Communcatons; 2009 March 9-13; Galveston, Texas. [5] Km H, Oh J-S, Jayakrshnan R. Effect of Tax Informaton System on Effcency and Qualty of Tax Servces. Transportaton Research Record: Journal of the Transportaton Research Board. 2005;1903: Promet Traffc&Transportaton, Vol. 27, 2015, No. 6,

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