Study on Properties of Traffic Flow on Bus Transport Networks

Study on Propertes of Traffc Flow on Bus Transport Networks XU-HUA YANG, JIU-QIANG ZHAO, GUANG CHEN, AND YOU-YU DONG College of Computer Scence and Technology Zhejang Unversty of Technology Hangzhou, 310023, Chna P.R.Chna xhyang@zjut.edu.cn Abstract: - In ths paper, we nvestgate the statstcal propertes of traffc flow on the urban bus transport network (BTN) n the cty Hangzhou of Chna. To allevate the congeston and smulate propertes of traffc flow on BTN, we construct a model usng Hangzhou BTN whch consders the short walkng dstance between two nearby statons and the maxmum transfer frequency. We select four parameters to evaluate the characterstcs of traffc flow on the BTN. We fnd that the results obtaned from the smulaton model are smlar wth the theoretcal model rrespectve of congeston. If congeston s consdered, the stuaton s dfferent. Besdes, f we ncrease the departure frequency of the buses wth some large passenger flow lnes, t wll lead to the crtcal packets generatng rate ncreasng on the whole network tremendously. It ndcates that buses wth larger passenger flow are more mportant n the BTN, so we can ncrease the departure frequences to mprove the network performance. Our results provde a method to mnmze the congeston on BTN. Key-Words: - BTN, traffc flow, passenger flow, relevng congeston 1 Introducton Durng the last few years, studes of transportaton networks have drawn lots of attenton of network scholars[1]-[8]. These transportaton networks are called publc transportaton networks, n whch the nodes n the networks represent statons whle the edges are the lnks between two statons whch mean that we can reach from one staton to another drectly. These publc transportaton networks such as bus networks[9]-[12], ralway networks[13],[1] and arport networks[15],[16] affect our daly lfe and naton s economy n many respects[17], so they become the study focus of the scholars. In ths paper, we nvestgate the urban bus transportaton network (BTN) n cty Hangzhou of Chna. To our knowledge, the urban bus system s essental to mantan the normal operaton of the cty and takes an mportant role n our daly lfe. In the BTN, the nodes are bus statons and the edges are lnks connected by the bus routes between two statons. Through the research of the BTN, we can obtan many statstcal propertes of the bus networks. Although at present there have been a lot of prevous works on the BTN, they mostly focus on the statc characterstcs of the networks, the dynamc characterstcs are rarely dscussed. The problem of traffc flow on BTN s one of the mportant aspects n the research as t drectly reflects the performance of the bus networks. The traffc flow of networks has been wdely researched by many scholars[18]-[21], however they often explore t from abstract perspectve, or use the abstract model n ther research, or the defnton of traffc flow s too smple (for example they only consder node congeston or edge congeston). Although abstract method can help us fnd the common characterstcs n dfferent knds of networks, t may also lead to the E-ISSN: 222-2678 16 Volume 13, 201

results obtaned from the model conflct wth the actual network. In our paper, we construct a model of traffc flow under some assumptons whch agree wth the actual stuaton to analyss the propertes of traffc flow of bus networks and then compare them wth the emprcal nvestgatons obtaned from bus systems n cty Hangzhou. The conclusons should be applcable for many real systems and helpful for the correspondng research of traffc flow. Ths paper s organzed as follows. In the next secton, the model of traffc flow s descrbed n detals. In secton 3, the results of the smulaton of theoretcal model and computer smulaton are provded and dscussed. Secton, presents our conclusons. 2 Model In the problem of traffc flow of networks, the packet s a basc concept. Every packet s generated wth nformaton of ts sources and destnatons. We name the par of the ntal node and the termnal node to be the OD par. Once a packet s generated, t wll be added to the networks and enters the lfe cycle. Then t tres step by step from the ntal node to reach the termnal node along one certan route. The lfe cycle s over after the packet reaches ts destnaton, then the packet s removed from the network. Durng ts lfe cycle, the move forward of the packet along the gven path generates traffc flow. In fact, the research of traffc flow comes down to analyss of the propertes of traffc flow on network components (nodes and edges) under dfferent stuatons. It s worth notng that the topology structure of networks, the dstrbuton of OD pars and the choce of the packet path all of them wll affect the traffc flow on networks. In Fg. 1, t shows that a blateral unweghted network exhbts dfferent propertes under the nfluence of the three factors mentoned above. So the analyss of the traffc flow should focus on these three factors. In order to obtan results agree wth the actual stuatons, we must make these factors approach to the actual stuatons. From the abstract vew, BTN has many common propertes wth lots of actual networks, such as small world characterstc, exponent degree dstrbuton or power degree dstrbuton and so on. But BTN has ts partcular propertes. Dfferent from many networks, the basc components of BTN are routes. In the actual moton of BTN, the basc components can be represented by buses whch are nterval drvng on every route wth fxed traffc capacty. Ths feature ndcates that we should apply dfferent method n study of BTN compared wth tradtonal model. 1 2 3 2 1 6 2 3 ( a ) ( b) 1 6 2 3 1 6 2 0 3 () c ( d) Fg.1 A blateral unweghted network nfluenced of three factors. (a). the topology structure of the network. (b). under even dstrbuton of OD pars, the dstrbuton of the traffc flow as all the packets move forward along the shortest path. (c). under gven dstrbuton of OD pars (the packets between node 3 and node s double than the packets between other pars), the dstrbuton of the traffc flow as all packets move forward along the shortest path. (d). under even dstrbuton of OD pars, the dstrbuton of the traffc flow as all packets move forward along the gven path (the shortest path whch excludes the edge between node 2 and node 3). For BTN, we can t change ts topology structure. For the dstrbuton of the OD pars of the network, we can obtan t through statstcal method. So we pay our attenton on the choce of the packet path. It s reasonable to use the shortest path along whch packets move forward n the networks to approxmately represent the actual path n tradtonal traffc flow models, such as n communcaton networks. But, for BTN, the packets represent passengers who travel through BTN. Passengers 8 6 E-ISSN: 222-2678 165 Volume 13, 201

choose path has nothng to do wth the lnks n networks but based on the basc components of BTN, namely, the routes. Ths makes the actual path often dfferent from the shortest path, as showed n Fg.2. So n the BTN model, we have to defne a passenger path to satsfy actual stuaton. 0.25 1 2 3 8 Fg.2 A BTN network formed by two groups of four routes. Each group s connected by sold lnes wth dfferent colors and contans two routes (the uplnk and the downlnk). Due to the statons n both routes of one group are the same, so ths network s symmetrc. The node 2 and node 8 s connected by purple dotted lne whch represents the dstance between them s smaller than the walkng dstance threshold, so they can walk to each other. The dstance of the each lne represents the physcal dstance between two statons. Accordng to the shortest path, node 1 should move to node 6 along the path 1-2-3-6, n fact passengers move along the path 1-2-3--5-6. Because the former case needs to take two buses, nstead the latter case just needs one bus. Tradtonally, BTN can be mapped nto two spaces: space P and space L [2], [9], [21]. In both spaces, one node represents one bus statons. In space P an edge connects a par of statons when there s a bus travelng between them. If passengers have to exchange routes or buses, the par of statons s connected by more edges. In space L, an edge between two statons exsts f they are consecutve statons on the route. Space L reflects the topology of BTN whle space P shows the characterstc of BTN transfer. Only f we fnd the shortest path between two nodes n space P, we can determne the least transfer tmes between the correspondng statons. 7 6 5 Ths method doesn't take nto account the weght of network, we trvally fnd the least transfer tmes but the path length may be very long. In ths paper, we propose weghted space P network (WSP) n whch the weght of random edge s equal wth the mnmum value of the actual drvng dstance on the route between the correspondng statons. Smlarly, we defne weghted space L network (WSL). We can obtan the shortest transferred path based on the least transfer tmes through evaluatng the shortest path of WSP. But the shortest transferred path obtaned from WSP may also have dfference wth the actual stuatons. Because n addton to the same staton transfer, there s also transfer n dfferent statons. In the latter case, passengers get off one bus at one staton and walk to another staton to take the next bus. Obvously, dfferent staton transfer consders more about spatally characterstc than the WSP network; t may help reduce the transfer dameter. Therefore n order to acheve the transfer n dfferent statons, we propose another network WSW whch contans the walkng nformaton between any two statons. In fact, passengers wll never accept long dstance walkng, so we just store the par of nodes between whch the walkng dstance s below a threshold(n ths paper, we set the threshold as 0.5km ). Combned WSW and WSP and based on the prncple of prorty on walkng, we get the best transferred path between any two statons. Fg.3 shows the path tree generated from node 1 n Fg.2. 0.25 2.0 1 2.0 3.0.0 5.0 2 3 5 6 8 7 Fg.3 The path tree of node 1. The sold lne represents the shortest path from one staton to another by bus; the dotted lne represents the elmnated path. The path of the sold lne s not 2.0 E-ISSN: 222-2678 166 Volume 13, 201

marked completely, for example from node 1 to node ; the path can be through the red lne from node 1 va node 2 and node 3 to node. In our method, we not only gve the statons on the way from the ntal staton to the termnal staton, but also recessvely gve the bus lnes from one staton to the next. For example, n Fg.3, there s blue lne between node 1 and node 7, whch ndcates that lne 2 s the most optmal path. Though we can get the most optmal path, but t s just a knd of expectaton. In practce, when passengers travel from staton to staton j, they may not choose the shortest path, nstead they choose the path whch frst reach node and can reach node j drectly at the same tme the path length s smlar to the shortest path length. Because of passengers don t lke to take a roundabout bus. So we set a threshold T, when a passenger at one staton wants to reach another staton j by a bus, f the rato of the path length between two statons wth the length between two correspondng nodes n space P s smaller than T, he chooses ths bus. Here we defne the set of routes between any two neghbor statons j and k whch meets above requrement as LS, we wll use ths set n the subsequently analyss. The path defned above meets wth the actual stuaton, so we choose ths path as the passenger path and analyss the characterstc of traffc flow on BTN. Frst we defne the dstrbuton of OD pars as matrx POD. POD s a n n matrx n whch n represents the number of nodes of the network, for BTN t means the number of statons. A jk betweenness of any node as NB represents the number of packet paths va ths node. In the WSL, the betweenness EBj of any lnk whch connects node and node j represents the number of packet paths va ths lnk. The equaton (1) shows more detals of the defnton of whch NB and EB j n P mn represents the path of OD par mn., For BTN, NB = EB j = n Pmn m, n j n P NB and mn POD POD mn mn (1) EB j reflect the stuaton of passenger flow on statons and routes (where s congested and where s free n the network), ths nformaton can help to optmze the BTN network but t can t reflect the characterstcs of traffc flow completely. That s because the basc components of BTN are routes and buses on the routes, research wthout the basc components makes no sense. If we can get more nformaton of passenger flow of every bus route (whch routes are congested and whch routes are free n the BTN), then we can comprehend the characterstcs of traffc flow more. We defne the betweenness SB jk of any secton jk, on route as the number of packet paths va ths secton and shared by ths secton. Apparently, for any bus route whch belongs to the LS jk set of one component POD j s the probablty that randomly secton jk,, the shorter ts departure nterval tme s, generate a packet whose ntal node s and termnal node s j. The matrx POD can be obtaned by samplng survey of passengers at every staton. Combned matrx POD and passenger path, we can get the betweenness of every staton and every lnk n the WSL of BTN. We defne the the more lkely to share packet path on ths secton. For one route, we pay our attenton on the secton wth the largest passenger flow. We defne ts flow as SBB. SB jk and SBB can be expressed n equaton (2) n whch L represents the departure E-ISSN: 222-2678 167 Volume 13, 201

tme of route. SB jk = 1 PODmn 1 jk n P L mn l l LS jk SBB = max( SB ) jk L (2) The betweenness SB reflects the traffc flow on a certan secton of one bus route. There may be many buses on one bus route, so we can obtan the characterstcs of traffc flow of every bus on a certan secton. For any bus belongs to the bus route, we defne SBF jk as the average traffc flow on any secton jk, of ths bus. Obvously, proportonal to SBjk SBFjk s and also proportonal to ts departure nterval tme. Because f the departure nterval tme s less, there are more buses runnng at the same tme, the passenger flow assgned to every bus s fewer. For one route, we focus on the secton whch have the bggest passenger flow on every bus, we defne t as SBBF. SBBF can be expressed n equaton (3). 1 jk = jk / = mn 1 jk n P L mn l l LS SBF SB L POD SBBF = max( SBF ) jk 1 jk SBF jk and (3) Defntons of NB EB SBB SBBF n the above gve us ndex to analyss the characterstcs of traffc flow on BTN network. 3 Smulatons From the Internet we get the nformaton of BTN n Chnese cty Hangzhou whch contans routes statons and so on. We show the nformaton n Table.1. Accordng to these nformaton, we can generate WSP WSL and WSW networks and get transferred paths among statons. Based on the nformaton, we respectvely smulate the traffc flow of BTN n Hangzhou from theoretcal model and computer smulatons. The strategy of generaton of OD pars plays a vtal role n the smulatons of traffc flow, so we have to set the dstrbuton of the OD pars of passengers. In the process of smulatons, dfferent generaton strategy of OD pars wll produce dfferent results. We use the dstrbuton of statc OD pars to conduct our theoretcal smulaton. In our dstrbuton, every tme step we choose the startng pont of a new passenger accordng to the prorty of out-degree of statons. Namely, t s more lkely to be chosen f the value of the out-degree s bgger. Whereas, the termnal pont s chosen by the prorty of the n-degree of statons, namely t s more lkely to be chosen f the value of the n-degree s bgger. In ths paper, we defne the out-degree( od ) of any staton as the number of statons whch can be reached from staton through matrx WSL or WSW. The n-degree(d ) s defned as the number of statons whch reach the staton through matrx WSL or WSW. Therefore the possblty s a staton chosen to be the start pont and the possblty s a staton chosen to be the termnal pont. They can be respectvely expressed n equaton (). Table 1 Parameters of BTN n Hangzhou Cty SN RN AS AL Hangzhou 2750 509 20.3.19 Table 1 The parameters of BTN n Hangzhou. SN s the total number of statons. RN s the total number of routes. AS s the average number of statons belong to one bus route. AL s the average number of bus routes dstrbuted to one bus staton. P P O d = = j j od od d d j j () E-ISSN: 222-2678 168 Volume 13, 201

Ths selecton strategy s more realstc due to passengers wll be more n places where buses are ntensve. Accordng to P o vector and P d vector composed by each staton, we can get trp dstrbuton matrx POD as we show t n equaton (5). For every element POD j n the matrx POD, t can be expressed as POD = P P. o T d j o d j POD = P P (5) We stll need to do further treatment on the matrx POD. In addton to settng the dagonal elements as 0, we also need to set those elements whch can be reached by walkng from startng pont to termnal pont drectly or passengers have to take more than three buses as 0. In the above two cases, passengers can t reach the destnaton only by bus. The dealt matrx POD s normalzed to get dstrbutng matrx of OD pars whch wll be used n our smulatons. Wth the normalzed POD matrx and paths obtaned by calculaton, we can smulate the characterstcs of traffc flow on BTN n Hangzhou as our theoretcal model results. In order to smulate the actual stuaton better, we use our new strategy whch shortens the bus departure tme to half n the busest 10% bus lnes to smulate, namely we dvde bus routes nto two groups, group A and group B whch contans the busest 10% bus lnes. We set the departure frequences of group B twce than of group A. The rato of the number of routes n group A and n group B s 9:1. We obtan the characterstcs of BTN n Hangzhou wth our theoretcal model. The result s showed n Fg.. Fg. The characterstcs of traffc flow n BTN wth the theoretcal model. (a). the cumulatve probablty dstrbuton of NB, note that the parameter NB s normalzed, namely s the rato of NB wth the maxmum NB. (b). the cumulatve probablty dstrbuton of SBBF, note that the parameter SBBF s normalzed, namely s the rato of SBBF wth the maxmum SBB. (c). the sortng dstrbuton of SBB and SBBF, whch are shown n the blue and red lne respectvely. (d). the relaton between SBB and SBBF. Note that all parameters are normalzed. E-ISSN: 222-2678 169 Volume 13, 201

The subgraph (c) n Fg. ndcates that the maxmum of parameter SBBF s 0.5, because of the departure frequences of group A s twce than those of group B. The subgraph (d) n Fg. ndcates our theoretcal analyss whch contans two straght lnes. The lower one represents the route of group B whle the hgher one represents the route of group A. Furthermore, slope of the lower lne s one half of the hgher one, because the departure frequency of group B s twce than of group A. The result agrees wth our former theoretcal analyss. Next we contnue to do computer smulaton of traffc flow on BTN. In the program, a bus s restrcted by passengers and move along the gven bus route. Therefore we need three characters, the bus, the passengers and the system. For the runnng bus, t has four actons, drve, reach, drop off passengers and pck up passengers. For the passengers, t has four actons, walk reach get on the bus and get off the bus. For the system, t also has four actons, generate new passengers generate new buses recycle reached passengers and recycle reached buses. Our model s worked by tme steps, frst we assume that dfferent buses drve at the same speed and dfferent passengers walk at the same speed and ther speed don t change over the tme. Meanwhle, we gnore the tme of buses reachng the staton and drvng out and the tme of passengers gettng on and gettng off. In order to ensure these three characters runnng well, we have to rule that the drvng dstance of a bus n one tme step s no longer than the mnmum value of the lnks n WSP network. In every tme step, the detals are showed as follows: (1)The system generates the same number of new passengers accordng to matrx POD and sends new buses for the routes whch have new demand based on the departure tme nterval. (2)Explot the drvng dstance n one tme step to update all the drvng buses. For the buses whch have reached the statons, we record ther reachng state, passengers gettng off and the change of the state of the passengers. Moreover, for the buses whch have reached the destnaton, we recycle them. (3)Explot the walkng dstance of passengers n one tme step to update the state of walkng passengers. ()Accordng to the record, passengers of correspondng statons get on and change ther state. Based on the process above, the passengers who don't reach the destnaton have three states: walkng watng or on one bus. These three states correspond to three sets: the set of walkng passengers the set of watng passengers and the set of passengers on bus. Obvously, there s only one set of walkng passengers, every staton have a set of watng passengers whle every drvng bus has a set of passengers on bus. The changes of state of passengers mentoned above are all about extractng passengers from one set and puttng them nto another set (Besdes the changes also contan the recovery of passengers who have reached ther destnaton). Wth the MATLAB software, we do the smulaton on BTN. We propose a new parameter, the passenger capacty of bus whch helps to better understand the congeston on BTN. In practce, congeston wll happen on BTN due to the passenger capacty of one route s lmted. When a bus stop at one staton, f passengers who want to get on are more than the rest of passenger capacty after some passengers get off, some passengers can t get on the bus. If the stuaton s serous, t causes congeston. To deal wth ths problem, we randomly choose the same number of passengers from the watng set of the bus route to the rest of passenger capacty to get on the bus. After ntroducng the bggest passenger capacty, the congeston of BTN appears. An mportant E-ISSN: 222-2678 170 Volume 13, 201

parameter to evaluate the congeston s the crtcal number of nodes n the network. Apparently, when packets generatng rate R c. It measures the R s less than R, W = 0 and η = 0, the network c network s capacty. At R c, the phase transton s n free. When R s larger than R, η > 0, the c occurs when the network s state changes from freedom to congeston. When the packet generate rate R s less than R c, the number of new generatng packets are equal wth new reachng packets that means the network s free. When the packet generate rate R s larger than R, due to the lmtaton of the capacty of nodes or edges, the number of new generatng packets s larger than new reachng packets. The number of packets n lfe cycle becomes larger and larger and fnally causes the congeston. The traffc flow can be expressed as follow: C W ηρ ( ) = lm t ρn t c (6) Where W= Wt ( + 1) Wt ( ), W represents the average value of W. Wt () represents the number of packets exst at tme t. N represents the total network congest. We choose the same POD matrx and path wth the theory smulaton and set the bggest passenger capacty of every bus to be the same. Then we smulate and obtan the crtcal packets generatng rate of BTN n Hangzhou. Next we smulate two typcal states of network, the free state and the congested state. The results are showed n Fg.5 and Fg.6. At the free state, we can fnd that the result of computer smulaton s smlar wth the results n the theoretcal model. But because of the lmtaton of the bggest passenger flow of any secton on one route and the bggest passenger flow of every bus on the secton, the result at congested state n the computer smulatons are dfferent from the theoretcal model. As we all know, the capacty of a bus s lmted, so as subgraph (c) n Fg.6 shows, SBB and SBBF are lmted by the bggest passenger flow of a secton and the capacty of a bus. But due to the departure frequences of group B are twce than group A, the parameter SBB s also doublng. E-ISSN: 222-2678 171 Volume 13, 201

Fg.5 The characterstcs of traffc flow n BTN wth the smulaton model at free state. (a). the cumulatve probablty dstrbuton of NB, note that the parameter NB s normalzed, namely s the rato of NB wth the maxmum NB. (b). the cumulatve probablty dstrbuton of SBBF, note that the parameter SBBF s normalzed, namely s the rato of SBBF wth the maxmum SBB. (c). the sortng dstrbuton of SBB and SBBF. Parameter SBB and SBBF are also normalzed, whch are shown n the blue and red lne respectvely. (d). the relaton between SBB and SBBF. Note that all parameters are normalzed. E-ISSN: 222-2678 172 Volume 13, 201

Fg.6 The characterstcs of traffc flow n BTN wth the smulaton model at congested state. (a). the cumulatve probablty dstrbuton of NB, note that the parameter NB s normalzed, namely s the rato of NB wth the maxmum NB. (b). the cumulatve probablty dstrbuton of SBBF, note that the parameter SBBF s normalzed, namely s the rato of SBBF wth the SBB. (c). the sortng dstrbuton of SBB and SBBF, note that whch are shown n the blue and red lne respectvely. (d). the relaton between SBB and SBBF. Note that all parameters are normalzed. are shown n table 2. Next, we contnue to compare the dstrbutons of theoretcal model and smulaton model at free state and at congested state, the results are showed n Fgure.7. From the subgraphs (a) and (b), we can fnd that the theoretcal model and the smulaton model have approxmate dstrbutons. From the subgraphs (c) and (d) n Fgure.7, we can fnd that the dstrbutons of the two parameters whch value the characterstcs of traffc flow of the networks tend to be dfferent, whch means the state of the networks have mportant nfluence on the traffc flow. Fnally, we calculate the crtcal packets generatng rate usng three dfferent strateges and make three comparsons among three dfferent strateges, whch Table 2 Dfferent crtcal packets generatng rate wth dfferent strateges strategy 1 2 3 CG 22.93 23.39 6.23 In Table 2, CG s the crtcal packets generatng rate. Strategy 1 ndcates that the departure frequency of all lnes s the same. Strategy 2 ndcates that the departure frequences of the 10% lnes whch are randomly selected are doublng. Strategy 3 ndcates that the departure frequences of the 10% lnes whch have the bggest passenger flow are doublng. In ths paper, we use Strategy 3 as our strategy to smulate. E-ISSN: 222-2678 173 Volume 13, 201

We can fnd that when the departure frequences of the 10% lnes whch have the bggest passenger flow are doublng, the crtcal packets generatng rate doubles correspondngly. It ndcates that buses wth large passenger flow are more mportant, we should shorten the bus departure tme approprately to mprove the BTN propertes. Fg.7 The comparson of the dstrbutons of parameters obtaned from the theoretcal model and the smulaton model at free state and congested state. (a). the comparson of NB at free state. (b). the comparson of SBBF at free state. (c). the comparson of NB at congested state. (d). the comparson of SBBF at congested state. Note that all parameters are normalzed. Conclusons In our work, we propose a model for traffc flow on BTN, and smulate the characterstcs of the traffc flow from two aspects: the theoretcal and computer smulaton. The smulaton results tally well wth our theoretcal analyss rrespectve of congeston. If congeston s consdered, the stuaton s dfferent. Therefore, we should take congeston nto account when studyng the BTN. In the model we ntroduce some parameters to measure the propertes of traffc flow on BTN, such as NB EB SBB and SBBF. These parameters help us to optmze the BTN even f we only know the matrx POD. For example, based on SBBF, we reduce the departure frequency of buses on less mportant routes and ncrease the departure frequency of buses on mportant routes to reasonably assgn resources and mprove the ablty to deal wth congeston. We beleve that such nsghts wll be helpful explorng the ways to optmze problems of traffc flow. E-ISSN: 222-2678 17 Volume 13, 201

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WSEAS Transactons on Systems, Vol. 11, No. 12, 2012, pp. 691-702. [18] Penn, A; Hller, B; Banster, D, Confguratonal modellng of urban movement networks, Envronment and Plannng B-Plannng & Desgn, Vol. 25, No. 1, 1998, pp. 59-8. [19] Stathopoulos, A; Karlafts, MG, A multvarate state space approach for urban traffc flow modelng and predcton, Transportaton Research Part C-Emergng Technologes, Vol. 11, No. 2, 2003, pp. 121-135. [20] Sun, SL; Zhang, CS; Yu, GQ, A Bayesan network approach to traffc flow forecastng, IEEE Transactons on Intellgent Transportaton Systems, Vol. 7, No. 1, 2006, pp. 12-132. [21] Yuen, J. K. K.; Lee, E. W. M.; Lo, S. M., An Intellgence-Based Optmzaton Model of Passenger Flow n a Transportaton Staton, IEEE Transactons on Intellgent Transportaton Systems, Vol. 1, No.3, 2013, pp. 1290-1300. E-ISSN: 222-2678 176 Volume 13, 201