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Traffic demand estimation for lane groups at signal‐controlled intersections using travel times from video‐imaging detectors

2017; Institution of Engineering and Technology; Volume: 11; Issue: 4 Linguagem: Inglês

10.1049/iet-its.2016.0233

1751-9578

Dongfang Ma, Xiaoqin Luo, Wenjing Li, Sheng Jin, Weiwei Guo, Dianhai Wang,

Autonomous Vehicle Technology and Safety

IET Intelligent Transport SystemsVolume 11, Issue 4 p. 222-229 Research ArticleFree Access Traffic demand estimation for lane groups at signal-controlled intersections using travel times from video-imaging detectors Dongfang Ma, Dongfang Ma Institute of Marine Information Science and Technology, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorXiaoqin Luo, Xiaoqin Luo College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorWenjing Li, Wenjing Li Institute of Marine Information Science and Technology, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorSheng Jin, Corresponding Author Sheng Jin jinsheng@zju.edu.cn College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorWeiwei Guo, Weiwei Guo College of Electrical and Control Engineering, North China University of Technology, Beijing, 100144 People's Republic of ChinaSearch for more papers by this authorDianhai Wang, Dianhai Wang College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this author Dongfang Ma, Dongfang Ma Institute of Marine Information Science and Technology, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorXiaoqin Luo, Xiaoqin Luo College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorWenjing Li, Wenjing Li Institute of Marine Information Science and Technology, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorSheng Jin, Corresponding Author Sheng Jin jinsheng@zju.edu.cn College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this authorWeiwei Guo, Weiwei Guo College of Electrical and Control Engineering, North China University of Technology, Beijing, 100144 People's Republic of ChinaSearch for more papers by this authorDianhai Wang, Dianhai Wang College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, Zhejiang, 310058 People's Republic of ChinaSearch for more papers by this author First published: 23 March 2017 https://doi.org/10.1049/iet-its.2016.0233Citations: 31AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The purpose of this study is to present a new method for lane-based traffic demand estimation using travel times from video-imaging detectors. The method overcomes the following two shortcomings of loop-detector-based algorithms: the fact that the actual demand is unknown when detectors are located upstream from the stop lines within a short distance; and the difficulty in calculating the ratio between streams in different lane groups if detectors are located at the upper reaches of the links. First, the authors analyse a variety of travel time patterns and introduce the concept of a virtual cycle that satisfies the criteria that all vehicles entering into a link in one virtual cycle have just departed from a downstream stop line within a single signal cycle. Next, the authors improve the travel time reduction rate model for queued vehicles in each cycle, and enhance the algorithms to estimate the lane-based traffic demand under different conditions. Finally, all parameters are calibrated and the new models are evaluated. The results show that: the maximum, minimum and average deviations over 12 cycles are 38.50, 0.02 and 16.19%, respectively. The findings in this study have potential applicability for use in traffic control systems, especially where oversaturated conditions are present. 1 Introduction Traffic congestion has become one of the most serious problems in many big cities all over the world. During peak hours, a growing number of signal-controlled intersections are operating in oversaturated conditions, which results in the frequent presence of long queues and vehicle delays [1-3]. When oversaturated conditions persist for an extended period of time, it may be beneficial to apply different timing strategies than those used under usual conditions [4-7]. The topic of developing effective traffic signal timing plans under oversaturated conditions has attracted the interest of many researchers in recent years, and a series of representative findings have been reported, which can be divided into two categories according to their operational objectives: maximising throughput and managing queues [8-11]. The traffic demand for any approach or lane group is the same as the arrival rate from an upstream intersection, and it is a basic index that can be used to optimise the signal timing parameters. The accuracy of these parameters determines the effect of implementation of the signal timing plans. Most existing research is focused on traffic signal timing optimisation for a known traffic demand. However, the methods used to obtain this basic information are usually ignored, especially under oversaturated conditions. Three common types of devices are used to measure the traffic demand in traffic control systems: loop detectors, microwave detectors and video-imaging detectors. These devices operate by counting the number of vehicles passing through their detection areas. The number of vehicles counted by the detectors per unit time is called the traffic flow and corresponds to the traffic demand. The following problems may be encountered when measuring traffic demand using traffic flow data: (i) when these detectors are located a short distance upstream from a stop line, such as the Sydney coordinated adaptive traffic system (SCATS) [12] and the adaptive control Software-Lite (ACS) system [13], the traffic flow is only equal to the traffic demand under unsaturated conditions, since the maximum traffic flow collected by these detectors is limited by the capacity of the corresponding lane with the influence of a downstream signal. The actual traffic demand is unknown once the demand exceeds capacity, i.e. under oversaturated conditions; and (ii) when these detectors are located at the upper reaches of the links, such as the split-cycle-offset optimisation technique system [14], the traffic demand is accurately represented by the traffic flow for all traffic conditions. However, the traffic flow ratio due to movements between different lane groups cannot be calculated. There are two simple solutions that can be used to overcome these defects: (i) position two group detectors near the stop line and near the upper reaches, although the project cost is greatly increased with this strategy; (ii) obtain the total demand using the aggregate number of vehicles departing the lane groups at an upstream intersection who move into the link of interest, and calculate the turning proportion using the traffic flow data collected by the downstream detectors. This method is inaccurate if vehicles exit the share-lanes, as the detectors cannot determine the turning ratio in a share-lane. In addition, there is a widespread understanding that there are some potential correlations between data at different locations. Therefore, it is more feasible to meet the above objectives by mining these potential correlations. Travel times can be used to represent the overall process for vehicles passing through different detection areas, and therefore they should be able to reveal the potential correlations. In recent years, automatic violation detecting and recording systems (AVDRS) have become common in many big cities in China. The main purpose of installing these systems is to record red light violations. For this purpose, video-imaging detectors should be located about 10 m upstream from the stop line, as shown in Fig. 1. These detectors can collect many parameters including traffic flow, occupancy, vehicle license plates, departure times from stop lines and so on. Fig. 1Open in figure viewerPowerPoint Operational principles of an automatic detection and recording system for violations Since the locations of the detectors in an AVDRS are similar to those in the SCATS and ACS systems, these detectors cannot measure the actual traffic demands under oversaturated conditions. If the vehicle license plates from the upstream detector can be matched to those from the downstream detector, this can be used to obtain travel times for all vehicles in each lane or lane group [15]. As well as video-imaging detectors used in AVDRS, travel times can also be obtained by analysing the outputs of other devices such as wireless magnetic sensors, mobile sensors and so on [16-20]. In recent years, a very popular research topic has used arterial travel times to extract traffic flow parameters and estimate the traffic states. Ban et al. [21] studied intersection delay patterns by measuring sampled travel times, and represented these patterns using piecewise linear curves. Subsequently, the reasons that delay patterns were induced were analysed, and methods for computing real-time performance measures and estimating signal timing parameters, such as the maximum and minimum queue length in each cycle [22, 23], have been advanced using known delay patterns. For queued vehicles in each cycle, their travel times reduce linearly from a maximum value after the start of the red time, ignoring the passing behaviours. The decreasing trend, i.e. the travel time reduction rate in one cycle, has a positive correlation with the traffic demand, and can be fitted using linear forms [21]. In this paper, we aim to improve the relationship model between the travel time reduction rate of queued vehicles and the traffic demand in [21], and then present a new method to estimate the demand that can overcome the shortcomings of loop detector-based algorithms. This rest of this paper is organised into three parts. Section 2 first introduces the concept of a virtual cycle and analyses the relationship between the virtual cycles and signal cycles, and then presents a process to establish estimation models for lane-based traffic demand under three different conditions. Section 3 calibrates the parameters in the proposed models, and evaluates the new method using field survey data. The final section concludes this paper with a summary of our findings. 2 Models In Fig. 2, symbol I represents a single link in an urban street network. Let SLD1 represent the stop line for lane group j at the downstream approach to link I, and SLU1, SLU2 and SLU3 represent the stop lines for straight-through, left-turning and right-turning vehicles from the east, south and north approaches to the upstream intersection, respectively. For convenience, SLU represents the set of SLU1, SLU2 and SLU3 here. Some vehicles will then pass through SLD1 after they leave SLU. Fig. 2Open in figure viewerPowerPoint Streams for license plate matches Fig. 3 shows the spatial and temporal variation of the trajectories for vehicles that leave link I through lane group j. The starting time of the red phase for the downstream intersection in cycle i is denoted here as the beginning of that cycle; uf,i is the vehicle speed without the influence of signals in cycle i (m/s); ri and gi are the red-light time and green-light time for lane group j in cycle i at the downstream intersection (s), respectively; is the length of cycle i for the downstream signal (s); Ti,1 and Ti,2 are the time points when the first queued vehicle and undelayed vehicle for lane group j in cycle i enter link I; ti,1 is the difference between Ti,2 and Ti,1 and is the time interval during which all queued vehicles for lane group j within cycle i enter their destination links (s); and ti,2 is the difference between Ti+1,1 and Ti,2 and is the time interval during which all undelayed vehicles in cycle i enter their destination road (s). During an oversaturated cycle i, no vehicles can pass through SLD1 without experiencing a delay, and therefore, the value of ti,2 is 0 and the two time points Ti+1,1 and Ti,2 coincide. The new concept of a virtual cycle is introduced here, which satisfies the condition that all vehicles leaving SLU must pass through SLD1 within one given signal cycle. Let represent the time length of virtual cycle i, then . In Fig. 3, A, B, C, D and E denote the corresponding virtual cycles for signal cycles i, (i + 1), (i + 2), (i + 3) and (i + 4), respectively. There is a consistent one-to-one match between the virtual and signal cycles, and the traffic flow collected by the upstream detectors in each virtual cycle can be regarded as the traffic demand for the corresponding signal cycles. The rate of reduction of travel time for queued vehicles in each cycle is influenced by the state of the traffic in the current and previous cycles, and the process of traffic demand estimation should be divided into different parts. Fig. 3Open in figure viewerPowerPoint Spatial and temporal variation processes of vehicles’ trajectories 2.1 Scenario 1: both the current and previous cycles are unsaturated In this situation, there are no residual queued vehicles at the beginning of the cycle, which is denoted as cycle i in Fig. 3. Si, which is the rate of reduction of travel time for delayed vehicles in cycle i, can be calculated analytically as [21]: (1) where, qi is the traffic demand for a single lane group in cycle i (pcu/s); kjam is the traffic jam density (pcu/m); uw,i is the start wave speed in cycle i (m/s) and p is the number of lanes in this lane group. The speed of vehicles without the influence of traffic signals is considered to be the free-flow speed in [22], which deviates heavily from actual conditions. There are many methods to describe the relationship between traffic flow and speed. Among them, one of the widely used models is a parabola [24], which is selected as an approximation here: (2) where a and b are undetermined parameters, which are both positive numbers that can be calibrated using actual data. Substituting (2) in (1) gives: (3) Since the values of p, b, a, uw,i and kjam are all positive, this gives: (4) Generally, the value of kjam, ranges from 0.1 to 0.2, p is 1. Assuming that the maximum stop time in this cycle is Ni,max, a difference in travel time for vehicles leaving link I in cycle i will have just emerged by the (i + 1 − Ni,max)th signal cycle. This situation is similar to Section 2.1, and the formula is the same as (7). In these situations, Ni,max can be determined by: (8) where Ω and k are digital variable symbols; Ω∊N+ and k ∊N ; τi,max is the maximum travel time in cycle i (s); and τf is the travel time without the influence of traffic signals for link I, which can be approximately represented by the average value of all non-queued vehicles within a certain time period. 2.3 Scenario 3: the current cycle is unsaturated but the previous cycle is oversaturated In this case, the residual queues from the previous cycle influence the discharge process in the current cycle, and delayed vehicles leaving SLD1 in this cycle have been queued for at least one or more previous cycles, which can be seen in cycle (i + 4) in Fig. 3. In this situation, i also denotes the serial number of the signal cycle. If there are different arrival rates during virtual cycles i, (i − 1), (i − 2),…, (i − Ni,max + 1), then the virtual cycle i can be divided into (Ni,max + 1) sections. Only vehicles that leave SLU within the last section, i.e. section (Ni,max + 1), can pass SLD1 without any delays, and the number of stops for those vehicles that enter link I in the ψ th section is given by (Ni,max − ψ + 1), ψ = 1, 2, …, Ni,max + 1. Meanwhile, vehicles that enter link I in the ψ th section require the same time interval from the time they start to move ahead in cycle (i − Ni,max + ψ + 1) until they pass the stop line in cycle i. The difference in travel time between these vehicles is due to the traffic signals in the (i − Ni,max + ψ)th cycle. Here, ψ = 1, 2, …, Ni,max. The rate of reduction in travel time in the previous Ni,max sections can be denoted by , , …, . The traffic demand in the ψ th section is then: (9) where . For section (Ni,max + 1), the travel times of the undelayed vehicles are approximately equal, and the rate of reduction is always zero for different traffic demands. Consequently, it is impossible to estimate the traffic demand using travel times in this section. Generally, the oscillation in traffic demands between any two sequential sections is small, and it is reasonable to assume that the traffic demand in the final section is equal to the corresponding value in section Ni,max, that is . The total number of vehicles entering link I by moving from SLU to SLD1 during this virtual cycle, Qi, gives: (10) If we let ti,2 in cycle i be also denoted as , the average traffic demand for the overall signal cycle is then: (11) where Θ is the set of 1 and 2, and Θ = 1 when ψ < Ni,max + 1, else Θ = 2. As traffic demands usually have a low oscillation within a short time period of, e.g. one cycle, the traffic demand for a lane group can be estimated using the average rate of reduction in travel time for all delayed vehicles in one cycle. The average reduction rate in cycle i can be denoted by , then (11) can be rewritten as: (12) where . 2.4 Generic model for the traffic demand In summary, the traffic demand for a single lane group in cycle i under different conditions can be calculated using: (13) If the oscillation in traffic demands within a signal cycle can be neglected, then the estimation model is given by: (14) In both models, the parameters of the start wave speed, the traffic jam density and the values of a and b can all be regarded as undetermined constants, which can be calibrated using actual survey data. Thus, the only variable is the rate of reduction of travel times for queued vehicles in each cycle, which enables the proposed method to be very easily used in actual applications. The rate of reduction can be derived by analysing the travel times, and can be calculated reliably even under oversaturated conditions, which addresses the first defect that was mentioned above for loop-detector-based algorithms. Meanwhile, video-imaging detectors can be used to record the license plates and the time stamp when each vehicle passes through the stop lines together with the lane number. Thus, vehicle travel times and the rate of reduction can be obtained for each lane or lane group, which addresses the second deficiency described for loop-detector-based algorithms. 3 Assessment It is clear that the assumptions that we have been used for the proposed models have some degree of deviation from reality. For example, some drivers may be reckless or conservative, which will result in their travel times deviating from the average significantly. In this case, the reduction rate will be incorrectly calculated using linear fitting, leading to errors in the traffic demand estimation. As a result, it is necessary to present a numerical case study in order to assess the precision of the proposed models for actual applications. 3.1 Data collection The first step in the case study was to design an investigation to obtain the relevant data, including the license plate data and the time stamp when vehicles are passing through the stop line. An area along Zijinhua Road, Hangzhou, China, was selected, which is shown in Fig. 4. Detailed information on this area is as follows. (i) Two intersections were included, namely, Zijinhua–Shenhua Road intersection and Zijinhua–Pingshui West Street intersection. (ii) There are three lanes at each approach to the two intersections. (iii) Two lanes are included at the upstream entrances of every link. (iv) The length of the section between the two intersections is approximately 480 m. (v) The downstream intersection implements a fixed-time strategy, and two signal plans are included in this survey period, shown as in Fig. 4c and d. (vi) The influence of the secondary road is ignored, since its traffic flows are very low. (vii) There is only one bus route and a bus stop within this section, and the proportion of buses is low. (viii) There are no roadside parking spaces. Fig. 4Open in figure viewerPowerPoint Investigational site The investigation was launched on 18 January 2016. For this study, the objective was to estimate the traffic demand for the straight-through lane group at the southern approach of intersection #2. Therefore, a total of six cameras were placed at the straight-through lane group on L1,1, the right-turning lane group on L1,2, and the straight-through lane group on L2,1, as shown in Fig. 4. Cameras 1–5 were set up to obtain license plates and the corresponding time stamps, while camera 6 was used to record colour changes of the traffic lights for the downstream signal. 3.2 Parameter calibration 3.2.1 a and b A microwave detector had previously been installed on the Zijinhua road prior to our investigation by the local transport authorities in Hangzhou. This detector can record traffic flow data and vehicle speeds at a minimum time interval of five seconds. The detector was located approximately 110 m from intersection #2. To obtain to fundamental diagram between the traffic flow and travel speed, the interval to calculate them must be long enough to cover variations in traffic signal cycle times. Referring to other existing articles [25-27], we selected 5 min used most frequently as the time interval here. The data collected by the microwave detector was exported from traffic police management data centres and a control platform in Hangzhou every five minutes, between the hours of 6:00 PM and 6:00 AM on 18 January 2016. Some abnormal data was collected by the microwave detector itself, which was first eliminated. Two principles were used for the elimination process: (i) All samples with a speed above 65 km/h were removed, as the speed limit on this road is 60 km/h; (ii) samples giving traffic flows of <0.075 veh/s when the speeds were <40 km/h were also disregarded. There are two reasons for this: (i) unless an accident or another unusual situation has occurred, there must be congestion in the downstream approach when the speed near the microwave detector is 0.075 veh/s under oversaturation conditions when the saturated flow rate is 0.5 veh/s, i.e. 0.15*0.5 = 0.075 veh/s. Thus, samples with a traffic flow of 40 km/h should be regarded as normal data. In this case study, no samples had a speed above 65 km/h, and no samples were removed based on the first principle. Meanwhile, total seven points were abandoned with the second principle. The measured errors about the traffic flow data during the whole day was about 2.43%. Fig. 5 illustrates the relationship between the traffic demand and the speed without the influence of signals after noise has been removed. Fig. 5Open in figure viewerPowerPoint Speed-flow relationship Based on the data in Fig. 5, the values of a and b are found to be 0.0758 and 0.004463, respectively, with the coefficient of determination (denoted as R2) being 0.6155, signifying that the goodness-of-fit of this fitting equation is acceptable. 3.2.2 Traffic jam density kjam Although a large number of studies have calculated the traffic jam density parameter for highway or freeway traffic flow, this parameter should also be re-calibrated for discontinuous flows that are influenced by traffic signals in urban street networks. In addition, all of the parameters are determined by actual data in this study to ensure the confidence level of the assessment results. For a single cycle, the parameter kjam can be calculated using the ratio of queued vehicles to queue length at a single time point. As the value of this parameter will oscillate over different cycles, the average value in the survey period is adopted in the assessment process. The traffic jam density kjam,i in cycle i is: (15) where ns,i is the number of vehicles in the longest queue in cycle i (veh); xe,i is the distance from the tail of the longest queue to the stop line (m); xh,i is the distance from the first queued vehicle to the stop line (m). If total of ϓ cycles are included in the survey period, then the average traffic jam density, kjam, is given by: (16) 12 cycles were included in this survey, and the values of the traffic jam density for different cycles are presented in column 2 in Table 1, with an average value of 0.1440 veh/m. Table 1. Calculation of traffic jam density, saturated headways and normal speeds Cycles no. k jam Φi − 4 u m,i u w,i 1 0.1497 8 19.96 2.50 2.24 6.70 4.46 2 0.1402 7 16.04 2.29 2.60 5.77 6.76 3 0.1468 3 7.76 2.59 2.48 6.05 4.66 4 0.1409 2 5.16 2.58 2.20 6.82 4.61 5 0.1425 6 11.32 1.89 2.36 6.36 8.97 6 0.1452 8 16.60 2.08 2.64 5.68 7.98 7 0.1374 5 13.24 2.65 2.44 6.15 4.97 8 0.1439 8 20.24 2.53 1.96 7.65 4.28 9 0.1375 10 21.92 2.19 2.40 6.25 7.07 10 0.1469 7 18.40 2.63 2.16 6.94 4.13 11 0.1479 9 22.20 2.47 2.28 6.58 4.70 12 0.1493 9 20.80 2.31 2.40 6.25 5.40 Ave 0.1440 — — 2.39 2.35 6.43 5.67 3.2.3 Starting wave speed uw It is accepted that there are only minimal fluctuations in the start wave speeds for different cycles, and that this parameter can be regarded as being constant for any particular lane group. Generally, the start wave speed is deemed to be equal to the free-flow speed with the following two assumptions: (i) the flow-density relationship satisfies Greenshields model; and (ii) the speeds in front of and behind the vertical line (the location where each vehicle starts to move ahead) are both equal to the free-flow speed [28]. This is appropriate for continuous traffic flow on highways or freeways; however, in urban street networks, the average speed of the vehicles between the downstream stop line and the vertical line is far less than the free-flow speed, and the corresponding start wave speed is also much lower than the free-flow speed. Qu et al. [29] proposed a new estimation method based on the kinematic characteristics of queued vehicles, which gives a relative error of <7% according to actual verification. As shown in [29], the start wave speed in cycle i, uw,i, is: (17) where hc,i is the average saturated headway in cycle i (s) and um,i is the normal speed after the queued vehicles have completed their acceleration process (m/s). Due to stoppages caused by red lights, a certain percentage of green time is used to discharge queued vehicles, so that the headway between any two consecutive queued vehicles approaches the saturated headway. Taking the reaction times of drivers at the beginning of the green phase into consideration, the first two or three headways are usually greater than the saturated headway. Therefore, only the fourth to the last headway are selected to observe saturation headways within each cycle. Assuming that there are Φi vehicles blocked by a traffic signal in cycle i, the average value of the saturated headways can be estimated by: (18) where and are the time points when the last and the fourth queued vehicles pass through SLD1, respectively; and the saturated headways are listed in column #5 in Table 1. Meanwhile, a detection range is set in the opposite direction to the vehicles that are moving away from the stop line, and its length is denoted as D (∼15 m in this paper), as shown as in Fig. 4. The time taken for the queued vehicles to