Fundamental Diagram Estimation Using Virtual Detection Zone in Smart Phones’ Application and CCTV Data Benny Hardjono1, 2 1
Faculty of Computer Science Universitas Pelita Harapan (UPH) Tangerang, Indonesia
[email protected] [email protected]
Abstract— Conventionally, Fundamental Diagrams, which consist of vehicle traffic flow and density pairs, are obtained from intrusive sensor such as inductive loop detectors. However these sensors are uncommon in developing countries as they are embedded in the roads, and consequently expensive to deploy and impractical to implement on busy roads. Our novel method, VDZ with CCTV snap shots can provide the data needed to construct Fundamental Diagrams and able to show zero speeds at jam density, which provide essential parameters for macroscopic traffic model. The results obtained, without the use of any intrusive sensor, have shown agreement with previous traditional method. Keywords—flow; density; virtual detection zone; fundamental diagram; non intrusive sensor; macroscopic model; capacity; free flow speed; wave speed; jam density; critical jam;
I. INTRODUCTION Capital cities in the world are in dire need to ease traffic jams, especially in the high ways. The cost of traffic jams has been presented in a number references [1][2][3]. One alternative is to make better use of existing roads, and existing traffic monitoring device. Concrete and manageable traffic data should be obtained so that the existing or future roads can be modeled, which in turn will help city planners and road designers to provide better accessible roads or improve existing ones. Unlike intrusive sensors for road traffic, which have to be embedded in to the road, non intrusive sensor (e.g. Closed Circuit Television or CCTV) can be placed around, in the traffic island or above the road. Non intrusive sensors are attractive as they have low maintenance cost [4], and longer life time [5]. Another non intrusive sensor is dedicated Global Positioning System (GPS) device or other GPS enabled device, e.g. GPS enabled smart mobile phone. They are readily available in taxis, delivery vehicles and in private cars. Consequently their availability either instructed or voluntarily, will not incur any capital cost on the government. Mobile phones as traffic sensor have been considered in [6] [7][8][9]. Virtual Detection Zone (VDZ) coined by the author, consists of longitude and latitude coordinates, which forms a
Rachmad Akbar2, Ari Wibisono2, Petrus Mursanto2, Wisnu Jatmiko2, and Aniati Murni Arymurthy2 2
Faculty of Computer Science Universitas Indonesia (UI) Depok, Indonesia
[email protected]
circle center. In other words, it is a virtual zone in a form of a circle with a certain radius. These zones, together with the map of destination, are sent by a computer server, as requested by an activated application (or agent) made for this purpose, in to GPS enabled smart phones. The radius is considered via an experiment in [10]. As the agent moves, it continues to monitor its current longitude-latitude coordinates and compares them to the pre-set-zones sent by the server. Once a client enters the pre-set zone, the agent gathers its current speed, as well as, Road_ID, VDZ_ID, and time stamp. The Road_ID. Direction is to be determined by the agent when 3 consecutive VD zones are valid. These components of information are then sent back to the server [10]. After obtaining initial traffic data for a certain target road, VD zones can be placed more frequently in dense areas [11] rather than sparse areas. These areas can be seen clearer using macroscopic model [12]. Cell Transmission Model (CTM) is adopted for our macroscopic model due to its similarity in dividing target road into cells and in our system each cell contains "zones". Macroscopic model can be used to see when or where a section of the road is jammed or the road’s behavior when, for example, certain road exits (off ramps) or entries (on ramps) are expanded or added to the main road. However, its parameters must be extracted first, from the traffic data and important ones come from Fundamental Diagram (FD). Traditionally FD, which consists of traffic flow and density pairs, is obtained from intrusive sensor such as inductive loop detectors. Our method is novel, to the best of our knowledge, because in the past FD have been constructed from loop detectors alone, or loop detectors with GPS enabled devices [13] and no attempt in real life, has been pursued using no loop detectors. Our smart phone agents, with Virtual Detection Zone (VDZ) application installed have gathered speeds in designated areas or zones. While from the existing CCTVs, which are already available in Jakarta (JKT) main roads, we can obtain number of cars along the same zones or density over a common distance (normalized to 1 km). This paper is a
follow up to our previous research [10][12][14][15]. This time we propose not to care about penetration rate, simply because the CCTV along the road, which takes photos at about the same time, our agents pass by, will give enough evidence to support the speeds obtained from our agents. A dense road will naturally cause lower speed than a lesser dense one. The positional accuracy of GPS enabled smart phones has been tested in our previous paper [10] and the result agrees with [14][16]. The aim of this research is twofold. Firstly, to prove that our VDZ system can gather valid concrete vehicle traffic data. Secondly, to construct FD, and to obtain estimated parameters needed (e.g. free flow speed, critical density, and capacity) for a Cell Transmission Model (CTM), which is classified as macroscopic traffic model. II. RELATED WORKS FD is one of a number of ways to estimate road capacity. In [17] it is used to described the average behavior of a heterogeneous traffic. In fact FD has been assessed as one of the more promising method for practical use of traffic engineering besides product limit and empirical distribution methods [18]. In the Century mobile experiment [19][20] both loop detectors and 100 GPS enabled smart phones, Nokia N95, were utilized to obtain the real time traffic data. In other words, two types of sensors were used (intrusive and non intrusive). The experiment was carried out in a period of 8 hours, using 100 rented cars, as agents, over a 10 mile along I880 highway, in California, USA. However, no FD was constructed and no ground truth velocity was available. Only 30 Virtual Trip Lines (VTL), (17 were on the actual loop detectors) were incorporated in the smart phone’s application, sent by VTL server. Each agent sent the car’s location and speed every 3 second, as the car passed by a specific VTL. Video cameras were also employed, but only to provide exact travel time of individual vehicles through license plate reidentification, to ensure enough penetration rate [20]. It claimed that 2-3% agents out of total vehicles were required to provide accurate velocity measurement of the traffic flow. In other words, each VTL requires 2 pairs of longitude and latitude coordinates, while our VDZ system only needs one pair of longitude and latitude coordinate.
Fig.1. Sensors in smart phones, with VDZ and CCTV as part of an integrated intelligent transport system
From our previous work [10] we have already proposed and tested [14], an integrated system (Fig.1), which enables smart phone carriers to act like traffic sensor, by having an agent or application which gathers and then filters GPS data, due to zones’ data sent by the server. Time stamp, speed, and zone ID are among the parameters sent via the Cell phone Network back to the server. While the monitoring block is self explanatory. The validity of our VDZ system and ground truth (i.e. using speedometer) comparison have been presented also in [14].
III. CONVENTIONAL FD VS FD USING VDZ & CCTV The following are traffic parameters, commonly used in macroscopic model. Density (x, t) (1) is a ratio of the sum of vehicles per certain length of roadway which they occupy (i.e. in one mile or km). Conventionally, density can be computed, by dividing occupancy o(x, t), from loop detector, with the effective length (x, t) or also called G-factor (obtained by using double detector loops or estimation methods). (1) Flow f(x, t) (2), is a ratio or the number of vehicles travelling along a certain point of reference x, and during a certain period t. It is usually expressed as number of cars in an hourly rate. Flow can be accounted for, from volume (x, t) i.e. number of cars passing point x within a time interval [t-δt, t] measured by loop detector. (2) With these definitions, density, flow and speed are related, as shown in (3). (3) In essence, traditionally, flow and density (with adaptive G-factor [21][22]) are obtained by using loop detectors. However, VDZ in our method can measure speed more accurately than loop detectors. In our method, density is obtained from vehicle counting of the CCTV snapshots (normalized to 1 km) at about same time and place, of our VDZ data, and finally, flow is obtained by using (3). Since the number of vehicles in a particular road is conserved [23], all macroscopic traffic models are founded on the continuity equation for vehicle density ρ(x, t) per lane at position x and time t. There is a relationship between Conservation Law [24], Macroscopic Model [25] and the Road Topology, and many references can better explain this in detail. IV. RESULTS AND DISCUSSION Real data have been taken from 7 VDZ application users or agents (these small application is installed in GPS enabled Android based smart phones, owned by our volunteers) who have travelled to & fro Tangerang-Jakarta (26 km) toll road. Data collected & presented in this experiment, are from km 20.7 to -0.3 or 21 km in total, from 27 March to 28 May 2014,
including Saturdays and Sundays. During which over 7000 data points have been collected. The road is divided into 24 cells (length varies from 0.3 to 1.3km). There are 140 zones placed in total, in these 24 cells, which act like loop detectors. Densities are obtained from existing Jasa marga’s, 15 CCTVphotos’ (the unit is vpkml or vehicle per km per lane). While flows (unit is vphl or vehicle per hour per lane) are calculated from normalized densities (from CCTV photo), multiplied by their corresponding speeds (from VDZ) using (3). Some zones cover the entries and exits of the toll road, or both. In this paper we present the data from one direction of travel only, i.e. from Tangerang to Jakarta. There are 7 on ramps and 4 off ramps in the chosen direction.
Fig.2. FDs of Tangerang to Jakarta toll road and road topology are entered into modified CTMsim (top menu added for directions and left/right slow lane road. Also all units are changed to km). Yellow area highlights, the last cell 24, and its input panel (bottom left). Note that cell 24, in km 20 to 21, geographically is toward Jakarta, while the blue and green inclined lines above long black block, from Left to Right, are the toll entries and exits respectively.
Fig.2 shows the road construction using CTMsim [26]. We have adopted and will modify CTMsim to include toll gates in km 9.7 to 8.7 or cell 13, in our next publication. However, since data, obtained from 7 volunteers are clustered in the hours of 5-9am and 16-20pm, of weekdays; we have purposely limit our observation during these periods. Photos in jpg format are regularly downloaded from jasamarga-live.com to our server over the period of our experiment. These 15 CCTVs, in fact take 3 seconds of video and snap shot photo every 10 minutes of our target road. This means the remaining 9 cells’ densities are estimated from neighboring VDZ data. Due to various view angles and very low resolution photos of the existing CCTV, unlike our previous experiments [14], vehicles have been counted manually over the measured distances and normalized to one km. Automatic ways, of vehicle counting and data analysis are in progress. Consequently, in this experiment we assume our data are valid (e.g. average speed, density and flow) only for second & fastest lanes or second & first lanes of the 3 lanes in km -0.3 to 8.2 or of the 4 lanes in km 8.2 to 20.7, sections of our target road. The density of our lane is therefore an average of these two lanes. In general, this is a rather fair assumption, as car owners do not want to travel along the slowest lane, whereby other heavy vehicles, like trucks are moving slowly.
Needless to say, our volunteers have agreed to drive in those 2 lanes to obtain better speeds. This is a common assumption. Similarly as applied in [17], in which case only the fourth lane of a certain Vehicle Detection Station (VDS), W4000, has been used to construct a Fundamental Diagram, we also use only cell 24 to construct our FD at km 20 to 21. There are 687 data points in this cell. Our data are imputed and aggregated by adopting [26] [27] [21]. Our modified rules are in the following. Firstly, zero speeds or lowest speeds and highest speeds in the zone are considered first. If at exact time (within seconds) of CCTV photo, the speed does not match the density, we consider CCTV photo within 3 minutes. Secondly, if not found, photos within 10 minutes window of the exact time are taken as nearest alternative which corresponds reasonably with the speed. Thirdly, if not found, we take known values of densities in the same cell by aggregating speed from the same day but a week before or a week after, i.e. weekday of the same time, or taking values at adjacent zones with similar speeds. Fourthly, if steps 1 to 3 are not possible, then adjacent VDZ zones with known speeds and densities, at similar times are considered. An experiment has been conducted using the following scenario. At zero speeds, when the circle of VDZ has become red, times on the smart phone are noted down. The result shows that the server times (i.e. due to phone network delay and write time on to our server’s hard disk) are lagging behind, up to 2-4 minutes than the real time of the smart phone, this result is quite reasonable. In Fig. 3, the distance which is used to calibrate the car density, of cell 23, over a km, is shown from a sample CCTV photo. This photo is taken on 11.35am, May 24th, 2014, from a CCTV camera at km 1.6 of the target road. Topological features, labeled A-D (white font coloured) in the photo, are taken as distance markers, in the process of distance calibration for the whole target road. A distance of 15m is measured from the bottom edge of the photo to A (from CCTV’s pole to A is 25m, not shown), while B is measured up to the lamp post (90m) at the centre of the road, D is a white advertisement board, and its post, C, becomes the marker for 137m distance, again from the bottom edge of the photo.
D
C B A
137m mm 90m 15m mm
Fig.3. Example of distance calibration from a CCTV photo, with topological features (A-D). These photos are provided freely by jasamarga-live.com. The header, in purple ellipse, on top, consists of km 1.6 (location of cell 23) and the snap-shot time 2015-05-24 11:35:52.
Road topology and these distances were cross checked using, google maps, gpsvisualizer.com, GPS devices as in [10] and odometers (in car and walking stick odometer). In Fig. 4, a captured screen of our own VDZ application (taken from Samsung G-tab 1, 7 inch screen, as agent), shows the zones (green circles) sent by the server, and the car speed and VDZ time. These green circles change to red and back to green one at a time, immediately after the agent in the vehicle enters and then leaves the circle/zone. This feature is added to show that data has been captured correctly.
Fig. 5. Data gathered from our VDZ and CCTV system can help us construct the FD of cell 24, in km 0.7 to -0.3 (Tangerang-JKT) with brown ellipse containing Jam Density.
Both [20] and [17] neither show zero speeds in traffic jam state or jam density (see brown ellipse in Fig. 6) in their FDs.
Fig. 4. VDZ GPS coordinates of Tangerang-Jakarta, in green circles, shown via VDZ application on Samsung Galaxy Tab 1, as agent. These cells are part of 22 (zone 217, left) – up to part of cell 24 (zone 216, right).
One clear advantage of our method is the capability of the VDZ system to read GPS location and zero speeds (Fig. 5). While loop detectors cannot read zero speeds, i.e. at full stop vehicles produce no change of inductance in the loop detectors, as shown in Fig.6. As a contrast Fig. 5 is compared to Fig. 6 [20]. It can be observed that our FD data can touch zero speeds at Jam Density near 117.7 vpkml (in brown ellipse). The free flow speed (v=51.7 km/h, green line) and wave speed (w= -39.3, purple line), both inclined, are obtained using least squared method [26] as in Fig. 5. The curvy red line shows that a 4th order polynomial can give 82.07% best fit (R2), to cell 24 data. Two other estimates are Critically Jammed (green dashes, vertical line) = 52 vpkml and Capacity = 2650 vphpl (black dashes, horizontal line). These figures are similar to what obtained in [21]. Fig. 6 shows data from Vehicle Detection Station (VDS) 400669 on I-880 Southbound, accumulated over 92 days’ data [20]. Like our data, each dot on the plot corresponds to one observed density and flow pair. Another set of data to compare with our data, are recorded on the fourth lane of the A1 highway between Roissy Airport and Paris. In this reference [17], measurements are taken on a six minutes period. Only few measurements corresponding to a time series are plotted, which explains an uncommon scattering.
Fig. 6. A sample of actual scatter plot taken from [21] which can be turned into a FD as in Fig 5. Note that none of the Flow-Density points touch the horizontal axis (no zero speeds at jam density) – brown ellipse is added by author.
Fig. 7 shows that our traffic data can help in constructing the required FDs for the whole target road (24 cells or 24 FDs).
Fig. 7. FDs of the whole toll road Tangerang-JKT, in modified CTMsim [26]
For future work, our actual data should be compared with the macroscopic simulation (e.g. post km vs. speed time contour). To make the VDZ system less prone to privacy attacks, VD zones can be placed more efficiently i.e. more in dense areas than in sparse areas. Also less number of VDZ in sparse areas means more efficient in the use of battery power, and efficient in the use of memory i.e. no need to place too many VDZ [28]. This system is designed to avoid map mismatching phenomenon [10][29][30][31][32]. These issues need to be explored further to make sure that the whole system works well in practice. V. CONCLUSION Our VDZ system has been able to gather valid concrete traffic data, and combined with CCTV data, have helped us in constructing estimated Fundamental Diagrams for a real target road, using no intrusive sensor at all. Our results have shown agreement with previous results using traditional method, and the system is able to show zero speeds at jam density.
[12]
[13]
[14]
[15]
[16] [17] [18]
Acknowledgment The author would like to thank Pelita Harapan University (UPH) for giving a full scholarship to pursue a PhD degree at Universitas Indonesia since September 2011. Some useful discussions are also gratefully acknowledged with Kie Van Ivanky Saputra, PhD. (UPH).
[19]
[20]
References [1]
[2] [3] [4] [5] [6] [7] [8]
[9]
[10]
[11]
“Tackling congestion by making better use of England’s motorways and trunk roads,” House of Commons London, 2005. [Online]. Available: http://www.publications.parliament.uk/pa/cm200405/cmselect/cmpu bacc/134/134.pdf. [Accessed: 21-Dec-2012]. “Highway Statistics 2010 – Highway Statistics – Office of Highway Policy Information,” 2010. [Online]. Available: http://www.fhwa.dot.gov/policyinformation/statistics/2010/. D. Schrank, T. Lomax, and B. Eisele, “Urban Mobility Report,” 2011. P. T. Martin, “Detector Technology Evaluation (MPC-03-154),” 2003. G. Leduc, “Road Traffic Data : Collection Methods and Applications,” Luxembourg, 2008. S. Cheung, “Traffic Surveillance by Wireless Sensor Networks : Final Report,” Berkeley, 2007. M. Berman, “Cell Phone Location System,” Tallahassee, 2007. B. Hoh, T. Iwuchukwu, Q. Jacobson, D. Work, A. M. Bayen, R. Herring, J. C. Herrera, M. Gruteser, M. Annavaram, J. Ban, I. C. Society, and S. Member, “Enhancing Privacy and Accuracy in Probe Vehicle-Based Traffic Monitoring via Virtual Trip Lines,” IEEE Trans. Mob. Comput., vol. 11, no. 5, pp. 849–864, 2012. X. J. Ban and M. Gruteser, “Mobile Sensors as Traffic Probes : Addressing Transportation Modeling and Privacy Protection in an Integrated Framework,” in 7th International Conference on Traffic & Transportation Studies, 2010, no. 732, pp. 1–17. B. Hardjono, A. Wibowo, M. F. Rachmadi, and W. Jatmiko, “Mobile phones as traffic sensors with map matching and privacy considerations,” in Micro-Nano Human Science (MHS), 2012, pp. 450–455. B. Hoh, M. Gruteser, H. Xiong, S. Member, and A. Alrabady, “Achieving Guaranteed Anonymity in GPS Traces via UncertaintyAware Path Cloaking,” IEEE Trans. Mob. Comput., vol. 9, no. 8, pp. 1089–1107, 2010.
[21] [22] [23] [24] [25] [26] [27] [28] [29]
[30] [31] [32]
B. Hardjono, A. Nurhadiyatna, P. Mursanto, and W. Jatmiko, “Development of Traffic sensor system with Virtual Detection Zone,” in International Conference on Advanced Computer Science and Information Systems (ICACSIS), 2012, pp. 19–23. J. C. Herrera, D. B. Work, R. Herring, X. (Jeff) Ban, Q. Jacobson, and A. M. Bayen, “Evaluation of traffic data obtained via GPSenabled mobile phones: The Mobile Century field experiment,” Transp. Res. Part C Emerg. Technol., vol. 18, no. 4, pp. 568–583, Aug. 2010. B. Hardjono, A. Wibisono, A. Nurhadiyatna, I. Sina, and W. Jatmiko, “Virtual Detection Zone in smart phone , with CCTV , and Twitter as part of an Integrated ITS,” Int. J. Smart Sens. Intell. Syst., vol. 6, no. 5, pp. 1830–1868, 2013. I. Sina, A. Wibisono, A. Nurhadiyatna, B. Hardjono, W. Jatmiko, and P. Mursanto, “Vehicle Counting and Speed Measurement Using Headlight Detection,” in International Conference on Advanced Computer Science and Information System (ICACSIS), 2013, p. 6. P. A. Zandbergen and S. J. Barbeau, “Positional Accuracy of Assisted GPS Data from High-Sensitivity GPS-enabled Mobile Phones,” J. Navig., vol. 64, no. 03, pp. 381–399, Jun. 2011. B. Schnetzler and X. Louis, “Anisotropic second-order models and associated fundamental diagrams,” Transp. Res. Part C Emerg. Technol., Oct. 2011. M. M. Minderhoud, H. Botma, and P. H. L. Bovy, “Assessment of Roadway Capacity Estimation Methods,” Transp. Res. Rec. J. Transp. Res. Board, vol. 1572, pp. 59–67, 1997. S. Amin, S. Andrews, S. Apte, J. Arnold, J. Ban, M. Benko, A. M. Bayen, B. Chiou, C. Claudel, C. Claudel, T. Dodson, O. Elhamshary, Batina, Gruteser, Herrera, Herring, Hoh, Jacobson, Kumar, Iwuchukwu, Lew, Litrico, and Luddington, “Mobile Century Using GPS Mobile Phones as Traffic Sensors : A Field Experiment,” in 15th World Congress on Intelligent Transportation Systems, 2008, pp. 8–11. J. C. Herrera, D. B. Work, R. Herring, and X. Jeff, “Evaluation of Traffic Data Obtained via GPS-enabled Mobile Phones : the Mobile Century field experiment,” in Transportation Research, 2009, no. June, pp. 1–30. G. Dervisoglu, G. Gomes, and R. Horowitz, “Automatic Calibration of the Fundamental Diagram and Empirical Observations on Capacity,” Transp. Res. Board, no. January, pp. 1–14, 2009. R. Horowitz, X. Sun, L. Muñoz, and M. Zhang, “Design , Field Implementation and Evaluation of Adaptive Ramp Metering Algorithms Final Report (TO 5503),” 2006. D. Helbing and M. Treiber, “Numerical Simulation Of macroscopic Traffic Equations,” in Computing in Science & Engineering, H. Gould and J. Tobochnik, Eds. 1999, pp. 89–99. R. Leveque, Numerical Methods for Conservation Laws. Birkhauser, 1992, p. 214. C. Braban-Ledoux, “METACOR – A Macroscopic Modelling Tool for Corridor Application to the Stockholm test site,” Stockholm, 2000. A. A. Kurzhanskiy and P. Varaiya, “CTMSIM — An interactive macroscopic freeway traffic simulator,” Berkeley, CA, 2008. CalTrans, An Introduction to the California Department of Transportation Performance Measurement System (PeMS), no. May. CalTrans, 2013, p. 193. K. Lin, “Energy-Accuracy Trade-off for Continuous Mobile Device Location,” ACM, pp. 285–297, 2010. M. A. Quddus, W. Y. Ochieng, and R. B. Noland, “Current Map Matching Algorithms for Transport Applications : State-of- the art and Future Research Directions,” Transp. Res. Part C Emerg. Technol., vol. 15, no. 5, pp. 1–30, 2007. M. Quddus, W. Ochieng, and R. Noland, “Integrity of Map Matching Algorithms,” Transp. Res. Part C Emerg. Technol., vol. 14, no. 4, pp. 283–302, 2006. Y. Zhao, B. Song, and J. Li, “A Map Matching Algorithm in GPSbased Car Navigation System,” Third Int. Conf. Intell. Inf. Hiding Multimed. Signal Process. (IIH-MSP 2007), pp. 77–80, Nov. 2007. M. A. Quddus, W. Y. Ochieng, L. Zhao, and R. B. Noland, “A general map matching algorithm for transport telematics applications,” GPS Solut., pp. 1–27, 2003.
