An Approach to use Cooperative Car Data in Dynamic OD Matrix

Transcription

1 An Approach to use Cooperative Car Data in Dynamic OD Matrix Estimation L. Montero and J. Barceó Department of Statistics and Operations Research Universitat Poitècnica de Cataunya UPC-Barceona Tech Abstract. Traffic management appications are supported by dynamic modes whose input shoud be reaistic rea-time OD demand matrices in order to find efficient network state estimates and forecast their short-term evoution. OD matrices have been so far usuay estimated from historic and/or rea-time data coection and prior matrices. Some of those methods deveoped by the authors in previous works provide reaistic matrices to cope with day-to-day demand variabiity and rea-time traffic conditions. Off-ine time-siced OD matrices estimation based on a simuation-optimization Bieve- DUE approach has proved to provide appropriate initiaizations for on-ine and rea-time dynamic OD estimation methods based on specific versions of Kaman fitering whose input data requirements are traffic counts coected from traffic detection stations and other data suppied by ICT (Information and Communication Technoogies) sensors as for instance trave times between pairs of fixed ICT sensors. In this work we present a review of the contributions to the on-ine/off-ine estimation of Dynamic OD matrices and we examine how new data provided by cooperative vehices as the tracking aong trajectories giving trave times between intermediate points of OD trips can be incorporated into the Kaman fitering equations for on-ine dynamic OD estimation. Cooperative vehices can be considered as mobie sensors generating data from any point of the network the computationa burden of the adapted Kaman approach to cope with tracking data is examined in depth in order to guarantee the on-ine appicabiity of the proposed approach for a mid-sized urban network. Keywords: Demand Estimation Information Systems Advanced Transport Information Systems Kaman Fitering Cooperative car data 1 1. Introduction: Background motivation and objectives In the context of estimating passenger-car transport demand Origin-to-Destination (OD) trip matrices describe the number of trips between each origin-destination pair of transportation zones in a study area. For private vehices route choice modes describe how drivers seect the avaiabe paths between origins and destinations and as a consequence the number of trips using a given path (or path fow proportions). The route choice proportions can vary depending on the time-interva in dynamic modes since they depend on traffic states changing over time. Whie an average OD tabe for a whoe period of interest is acceptabe for an urban transportation panning study OD matrices for consecutive time intervas are required for appropriatey modeing and/or optimizing dynamic system operations. For a formuations of static traffic or transit assignment modes (Forian and Hearn 1995) as we as dynamic modes invoved in ATIS (Advanced Transport Information Systems) (see Ashok et a. 2000) the usua assumption is that a reiabe estimate of an OD matrix is avaiabe and constitutes an essentia input for describing the demand in predicting traffic state evoution over the network. Since OD trips are not directy observabe indirect estimation methods have then been proposed. These are the so-caed matrix adjustment methods whose main modeing hypothesis can be stated as foows (Cascetta 2001): if the assignment of an OD matrix to a network defines the number of trips in a network inks then the same OD matrix can be estimated as the inverse of the assignment probem as a function of the fows observed on the inks of the network. We focus on dynamic OD matrix estimation. In a previous research (Barceó et a. 2013) we have found that the quaity of the detection ayout and the quaity of the historic dynamic OD matrix are

2 key controabe design factors. Another reevant design factor the penetration rate of the seected ICT technoogy which unfortunatey is not controabe. In our study we deat in particuar with Buetooth antennas to identify Buetooth devices set to discoverabe mode. So given a suitabe Buetooth sensor ayout and the most ikey used paths between BT sensors the historica measurements of the associated trave times between pairs of BT sensors for predetermined time-sices were incuded in an off-ine (simuation-optimization Bieve-DUE approach) to generate a set of initia OD matrices. These estimated time-siced OD matrices and the rea-time measurements are the inputs to on-ine procedures (inear Kaman fitering approach) to estimate dynamic OD matrices. The computationa testing of the dynamic OD matrix estimation was conducted by simuation and the most ikey used paths between OD pairs and between a BT antennas were assumed to be those computed by a Dynamic User Equiibrium achieved in our case by a mesoscopic traffic simuation conducted with the simuator Aimsun Meso. Aimsun Meso generates not ony the simuated fows and speeds at traditiona detection stations and BT antennas but aso the simuated trave time estimates from Buetooth antennas aong the corresponding paths (Barceó et a. 2014)(Buejos et a.2014). Amost 20 years ago memory space was expensive and unavaiabe on ordinary aptop computers. Because of this inear Kaman fitering (KF) approaches for estimating dynamic trip matrices were considered inefficient and unabe to satisfy the requirements of on-ine appicabiity. A inear KF prototype suited to the specific characteristics of the probem coded in MATLAB (Barceó et a 2013a and b) has proven to meet the requirements for on-ine appications using traditiona data coection and new ICT data. The off-ine dynamic OD matrix estimation procedure provides updated and high quaity timesiced OD matrices to be used as initia or seed matrices by the on-ine estimation procedure. As reported in (Barceó et a. 2013a) the quaity of this input is a key factor to achieve the fast convergence required for rea-time appications requiring a response fast enough to support them. A reevant exampe are the Rea-Time Traffic Management Systems whose decisions have to be supported and evauated by traffic modes based on the estimated dynamic OD matrices at short time-intervas typicay shorter that 15 minutes and forecasting is performed for time horizons of about 30 minutes. 2 HISTORICAL DATABASE (PROFILES/ BEHAVIORAL PATTERNS) INITIALIZATION HISTORICAL OD MATRIX (A) OFF-LINE GENERATION OF CANDIDATE TARGET OD MATRICES TARGET MATRIX GENERATION FOR SELECTED PROFILE NETWORK MODEL ADJUSTMENT PROCESS REAL TIME DATABASE OF TIME-SLICED OD SEED MATRICES (B) ON-LINE SELECTION OF TARGET REAL-TIME DATA SELECTION OF THE OD TARGET MATRIX FOR TIME SLICE k SELECTED TARGET FOR TIME SLICE k REAL-TIME DATA FOR TIME SLICE k REAL-TIME OD KALMAN FILTER ESTIMATOR PREDICTED FOR TIME SLICE k+1 DYNAMIC MODEL NETWORK STATE ESTIMATION & SHORT-TERM FORECASTING (C) REAL-TIME OD ESTIMATION AND ITS USES Figure 1: Methodoogica process for the estimation of time dependent OD matrices for rea-time appications

3 The reported research corresponds to a methodoogica framework whose conceptua ogic is depicted in Figure 1. The off ine generation of the seed OD matrices expoiting a sources of traffic data is described in Box-A and the on-ine process in Box-C with an intermediate seection process of the suitabe inputs in term of the observed evidence described in Box-B. The process in Box-A has been reported in (Barceó et a. 2014) (Buejos et a.2014) and process in Box-C in ([Barceó et a. 2013a and 2013b) the objective of this paper is to expore the way and expected improvements of expanding the off-ine and rea-time estimation processes when new data are avaiabe. Our interest addresses two main mobie data sources that are either currenty avaiabe or wi become avaiabe in the near future: GPS data and data from Cooperative Cars. The advantage that they are and presumaby wi become pervasive providing in this way a wide coverage of the traffic network whie the chaenge is that they are mobie and the data captures are randomy distributed in the space whie in time randomness can be reduced by samping poicies (e.g. reporting every t time units as in GPS data coection for exampe) or can be a continuous tracking. The research questions addressed in this paper are then find how the Kaman Fitering framework deveoped to dea with ICT data can be adapted to tacke with the new data and whether the computationa burden doesn t hinders the possibiity of the rea-time appications. 2. Proposed approach The scenario addressed in this research is a traffic network whose potentia data sources are iustrated schematicay in Figure 2 and wi be: Inductive oop detectors suppying: Traffic voumes (in vehices/hour) Occupancies (in time percent) and Spot speeds (in Km/h). With a given time resoution (e.g. 1 minute 5 minutes...). Magnetometers suppying: Individua vehice detection that can be aggregated to estimate traffic voumes at the desired time resoution Individua vehice s time on the detector that can be aggregated to estimate percent time occupancy at the desired time resoution Time headways between successive vehices passing over the detector. Buetooth/Wi-Fi antennas suppying: Time continuous samping of Buetooth/Wi-Fi devices passing through the detection obue of the antenna Trave times of individua devices between two antennas (tt AB = trave time between antenna BT A and antenna BT B ) Inductive Loop Detectors/Magnetometers Ce k Ce k+1 Ce k+2 3 T B i-th vehice in k-th ce Unequipped vehice GPS Equipped vehice Buetooth/Wi-Fi Antenna T B Buetooth/Wi-FI equipped vehice Cooperative vehice Figure 2: Potentia traffic data sources in the research scenario

4 Additionay there wi be avaiabe at the site data from GPS equipped vehices providing: Vehice s identity Time tag (data coected every t time units) Map-matched vehice s position Speed (in Km/h) Heading (in º from due north; i.e. north = 0 ). Physica cooperative vehices are not yet avaiabe in the envisaged scenario the research pan consists of the microscopic simuation mode of an urban scenario in which data coection is conducted emuating the technoogies by means of specific ad hoc APIs and scripting. Concerning the Cooperative vehices they are based on the specifications about the oca data reated to traffic conditions that cooperative vehices wi coect by the sensors equipping them making them aware of oca traffic conditions surrounding a cooperative vehice that is the approach assumes that cooperative vehices continuousy measure: Its position speed and acceeration (ongitudina and transversa) The distances and reative speeds a surrounding vehices as depicted in the Figure 3. Additionay equipped vehices (red vehices in Figure 3) exchange this information between them. Figure 3: Surrounding awareness of an equipped vehice 4 Adopting the usua terminoogy in traffic fow theory et s assume a coupe of vehices a eader denoted by and a foower denoted by f. From the cooperative data gathered at time t assuming that the cooperative vehice is the red one in Figure 3 the system wi get (see aso Figure 4): The reative distance d f between the foower and the eader The reative speed v f between the foower and the eader The foower s map matched position (x f y f ) f d f (x f y f ) (x y ) Figure 4: Loca traffic reated data coected by an equipped vehice These are the data that assuming a hypothetica feet of cooperative vehices is emuated have been used to estimate by simuation oca densities and speeds and their changes over time to estimate oca traffic state and identify congestion generation (if necessary I can add here a ist of reated pubications) assuming that the penetration of the cooperative technoogy is arge enough. Data from Cooperative vehices provide oca speed and position at the corresponding time tag aow tracking the trajectory of each cooperative vehice. Time tags of recorded data aow estimating trave times between pairs of points aong the trajectory of the vehice this is the characteristic used to adapt the specific Kaman Fiter deveoped in (Barceó et a. 2013a) to expoit the trave times between pairs of BT Antennas without knowedge of the paths used between antennas. The information

5 about these paths provided by tracking the Cooperative vehices adds a new feature to the suppied data. How to dea with the subpath information in the framework and the benefits of this new source has been the aim of this research. 3. Mode Formuation Cooperative cars are mobie sources and the network framework wi be considered as covered by Virtua Cooperative Car sensors (VCC sensors). Each VCC sensor is referred to a junction or to a ink section in dense urban areas. For test site with ong inks severa VCC sensors have been proposed providing a compete and non-redundant coverage of the network inks. A threshod parameter has been defined as the maximum ength in a section to be covered by a virtua cooperative sensor (for the current tests it is set to 130 m). VCC sensor might have an active or non-active state VCC data is considered for active states and the active state occurs when a Cooperative vehice in the coverage area of the virtua sensor. We need to rey on this activity state since ony active sensors are considered in the KF approach that we have deveoped this aows us to skip the computationa burden reated to sensor definition. Of course VCC on/off activity is a dynamic feature that can vary each interva (an interva is usuay considered between 0.5sec to 3 min). Cooperative vehice OD data are assumed to be unknown. The tota number of origin and/or destination centroids (reated to transportation zones) is I; the tota number of ICT sensors is P ocated at in the inner network; the tota number of VCC sensors is V; and the tota number of paths corresponding to the most ikey used paths obtained by a DUE (Dynamic User Equiibrium) from the historic OD matrix in the horizon of study is K. QR is the number of pairs of ICT sensors (rs) pus individua sensor counts qr to be considered. QV is the tota number of pairs of VCC sensors (rs) pus individua VCC sensor counts qv ony those active wi be considered in a given interva k in the KF equations. Q is the number sensors (ICT rea sensors pus VCC virtua sensors). We finay estimate OD trips between OD pairs for a cars but OD path trips for ICT equipped cars and Cooperative car has to be internay considered and the percentage of ICT equipped vehices for each sensor technoogyas not between transit-stops. 5 ~ k q~ r k qv ~ k Q Q k qr k qv k ~ y q k G k k : ~ y q k G ~ g k k g G zk k z~ k u h rsk t rs k Tabe 1. Definition of mode variabes : Historic tota number of cars Cooperative cars and ICT equipped cars first detected at r reated to centroid i in fow conservation at time interva k. Tota number of cars Cooperative cars and ICT equipped cars first detected at r reated to centroid i in fow conservation at time interva k. : Historic and actua number of cars crossing at time interva k the q sensor or destination sensor s for a pair of either ICT o VCC sensors q=(rs) : Tota number of current G k and historic G ~ k cars as we as the current g k and historic ~ k ICT equipped cars accessing centroid i at time interva k and heading towards j using path e. g : State variabes are deviates of cars from centroid i during interva k headed towards centroid j using ~ G k G k G k. path e with respect to average historic data : The current and historic measurements of equipped / Cooperative cars during interva k a coumn vector of dimension Q (counts) pus L (fow conservation equations). Expansion equations. : Fraction of cars that require h time intervas to reach sensor s at time interva k from sensor r during time intervak h 1 t k ht. Time-varying mode parameters. Obtained from ICT equipped and/or Cooperative cars : Average measured trave time for ICT equipped and/or Cooperative that reach sensor s at time interva k from sensor r The state variabes G (k) are assumed to be stochastic in nature and OD path fow deviates at the current time k are reated to the OD path fow deviates of previous time intervas by impementing an autoregressive mode of order r <<M; the state equations are: ΔG r k 1 DwΔGk w 1 wk w1 where w(k) is zero mean with diagona covariance matrix W and k D w are transition matrices which describe how previous OD deviates G (k-w+1) affect current fows G (k+1) for w = 1 r. In (1)

6 our tests we assume simpe random waks to provide the most fexibe framework for state variabes if no convergence probems are detected. Thus our first tria is r=1 and D w becomes the identity matrix. The reationship between the state variabes and the measurements invoves time-varying mode parameters (congestion dependent since they are updated from sampe trave times provided by ICT and Cooperative vehices) in a inear transformation that considers: The number of ICT equipped cars first detected in the system at rea sensor r reated to origin zones through expicit fow conservation equations during time intervas in k... k-m qr k. The number of Cooperative cars first detected in the system at virtua sensor r reated to origin zones through expicit fow conservation equations during time intervas in k... k-m qv k. The number of cars reated to origin zones i during time interva k q k. H<M time-varying mode parameters in form of fraction matrices u h rs k where the H adaptive fractions are updated from measures provided by ICT sensor and Cooperative car data. Direct sampes of trave times aow the updating of discrete approximations of trave time distributions. At time interva k the vaues of the observations are determined by those of the state variabes at time intervas k k-1 k-m. Δz k F( k) G( k) v( k) (2) where v( k) is white Gaussian noise with covariance matrix R. F(k ) maps the state vector G(k) k onto the current bocks of measurements at time interva k: counts of cars at sensors either ICT or VCC active sensors accounting for time ags and congestion effects. The soution shoud provide estimations of the OD matrix between OD pairs for each time interva up to the k-th interva once observations of equipped and cooperative cars up to the k-th interva are avaiabe. KF prediction of OD trips up to some intervas ahead must be considered in order to feed a dynamic transit assignment too that wi provide the forecasted trave times and traffic variabes in the short-future. 6 The key aspect reies on how to combine Cooperative car data for subpaths (counts) to OD path fows affected by time-varying parameters. Time-varying parameters reated to trave times from ICT equipped cars have to be updated with considering a the possibe paths between a pair of sensors but time-varying parameters updated from Cooperative cars data are updated knowing the exact used route that can affect to severa OD path trave times. Figure 5 shows the fowcharts between the dynamic estimation KFX4 too and the emuation of data. We have competed deveopment of API emuating the cooperative data fow the KFX4 fitering too impemented in MATLAB is in process of programming. Once avaiabe the estimation and forecasting too (KFX4) coud be vaidated using medium size network the testing of the fitering too is being performed using Vitoria s network.

7 EMULATION OF DATA COLLECTION CALIBRATED MICROSCOPIC SIMULATION MODEL OF THE SITE SELECTED SIMULATED DATA SIMULATION FRAMEWORK KALMAN FILTER OD ESTIMATOR ESTIMATED SYNTHETIC EVALUATION PROCESS RESULTS REPORT 4. Acknowedgments Figure 5. Conceptua Framework for the Computationa Experiments 7 The research is funded by TRA C03-02 of the Spanish R+D Nationa Programs. 5. References: 1. Forian M. Hearn D.: Network Equiibrium Modes and Agorithms. In: Chapter 6 in M.O. Ba et a. Eds. Handbooks in OR and MS Vo.8 Esevier Science B.V (1995). 2. Ashok K. Ben-Akiva M.: Aternative Approaches for Rea-Time Estimation and Prediction of Time- Dependent Origin-Destination Fows. In: Transportation Science vo.34 no.1 pp (2000). 3. Barceó J. Montero L. Buejos M. Linares M.P. Serch O. : Robustness And Computationa Efficiency Of A Kaman Fiter Estimator of Time Dependent OD Matrices. Transportation Research Record pp (2013a). 4. Barceó J. Montero L. Buejos M. Serch O. Carmona C.: A Kaman Fiter Approach for the Estimation of Time Dependent OD Matrices Expoiting Buetooth Traffic Data Coection. In: GITS Journa of Inteigent Transportation Systems vo. 17(2) pp (2013b). 5. MatLab (R2012a) by MathWorks Inc. ( (2012). 6. J. Barceó L. Montero M. Buejos M.P. Linares (2014b). A practica proposa for using origindestination matrices in the anaysis modeing and simuation for traffic management Paper presented at the 93rd TRB Annua Meeting incuded in the CD-Compendium of Papers 7. M.Buejos J.Barceó L.Montero (2014) A DUE based bieve optimization approach for the estimation of time siced OD matrices Internationa Symposium of Transport Simuation 2014 Procedia Socia and Behaviora Sciences. 8. Cascetta E. Transportation Systems Engineering: Theory and Methods. Kuwer Academic Pubishers Norwe Mass. 2001