Journal of Advanced Transportation

Volume 2018 (2018), Article ID 4106086, 14 pages

https://doi.org/10.1155/2018/4106086

## Traffic State Estimation Using Connected Vehicles and Stationary Detectors

^{1}Swedish National Road and Transport Research Institute (VTI), 581 95 Linköping, Sweden^{2}Department of Science and Technology, Linköping University, 601 74 Norrköping, Sweden

Correspondence should be addressed to Ellen F. Grumert

Received 29 September 2017; Accepted 2 December 2017; Published 10 January 2018

Academic Editor: Fernando García

Copyright © 2018 Ellen F. Grumert and Andreas Tapani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Real-time traffic state estimation is of importance for efficient traffic management. This is especially the case for traffic management systems that require fast detection of changes in the traffic conditions in order to apply an effective control measure. In this paper, we propose a method for estimating the traffic state and speed and density, by using connected vehicles combined with stationary detectors. The aim is to allow fast and accurate estimation of changes in the traffic conditions. The proposed method does only require information about the speed and the position of connected vehicles and can make use of sparsely located stationary detectors to limit the dependence on the infrastructure equipment. An evaluation of the proposed method is carried out by microscopic traffic simulation. The traffic state estimated using the proposed method is compared to the true simulated traffic state. Further, the density estimates are compared to density estimates from one detector-based method, one combined method, and one connected-vehicle-based method. The results of the study show that the proposed method is a promising alternative for estimating the traffic state in traffic management applications.

#### 1. Introduction

Density, speed, and flow are important measures for describing the characteristics of the traffic on a road segment. The density of traffic is defined as the number of vehicles located on a road segment. The speed can be defined either as the time mean speed, which is the mean speed of all vehicles passing a specific location within a given time interval, or as space mean speed, which is the mean speed of all vehicles travelling over a road segment at a certain point in time. Finally, the flow is defined as the number of vehicles passing a specific location within a given time interval. The three measures are commonly referred to as the traffic state. The traffic state is of special interest for traffic management systems based on automatic control. Examples of such systems are variable speed limit systems and ramp metering. The purpose of the traffic management system is to improve the traffic conditions during, for example, congested periods and incidents. The systems should be able to detect abrupt changes in the traffic state, such as lower speeds and flows and higher densities, and use this information as input to apply a suitable control strategy. Thus, representative real-time estimation of the traffic state is of importance.

The traditional way to measure and estimate the traffic state is by the use of stationary equipment, for example, loop detectors and radars. Due to recent development in vehicle technology, different types of connected vehicles are being introduced and the expectation is that in 2020 75% of newly produced vehicles will be equipped with technology that enables the possibility to connect to the surroundings [1]. The connected vehicles facilitate communication between vehicles and between vehicles and the infrastructure. This allows for frequent updates of individual vehicle measures such as their speed and position. Hence, it is possible to use connected vehicles in combination with stationary detectors, or as a standalone data source, to estimate the traffic state. This can also result in improved spatial estimates instead of the traditionally used point estimates.

In this study, we propose a method for estimating the traffic state based on vehicle-to-infrastructure communication. The required information is speed and positioning measurements from connected vehicles in combination with counts from stationary detectors. By assuming that the connected vehicles have the same distribution of speed as regular vehicles, the speed is estimated as an average of the speeds of the connected vehicles. The only connected vehicle data needed to estimate the density is information about the current road segment of the connected vehicles. This makes the method robust with respect to errors in the positioning data. Each connected vehicle continuously communicates its location, which is used to estimate the total number of connected vehicles on a specific road segment. Further, the number of connected vehicles passing stationary detectors is, together with the total number of passing vehicles, used to estimate the penetration rate of connected vehicles. Thereby, the total number of vehicles located on a segment can be estimated.

Our hypotheses are that the proposed method will result in (1) density and speed estimates that can capture the current traffic conditions on the road, (2) a possibility to use more sparsely placed stationary detectors without considerably reducing the performance of the density estimation, given that the share of connected vehicles is assumed to be approximately the same over the road stretch, and (3) precise and fast detection of changes in the traffic state, especially for higher penetration rates of connected vehicles. In real applications, the traffic state estimation is one component of a larger model system, often including both data assimilation and fusion techniques. The aim of this paper is to find a straightforward approach to estimate the density and speed by the use of connected vehicles and investigate how well the traffic state estimation can capture the actual traffic situation as a first step towards using the proposed method as such a component in traffic management applications.

To study these hypotheses, the proposed method is evaluated by the use of microscopic traffic simulation. The density estimates are compared to one detector-based method, one combined method, and one connected-vehicle-based method. The comparisons are done in order to investigate if the proposed method gives estimates that are comparable to estimates of existing methods. A simulation scenario with an incident is analyzed to study how well the proposed method can capture abrupt changes in the traffic state. Two different distances between the detectors are applied to examine how the method performs with sparsely placed detectors. To isolate the effects related to the method, we use a simple design of the road network and assume that no measurement errors exist in detector and connected vehicle data.

The remainder of the paper is organized as follows. In Section 2, an overview of traffic state estimation methods is given with focus on density estimation. The proposed method for estimating the traffic state based on connected vehicles in combination with stationary detectors is presented in Section 3. The simulation setup and the evaluation method are described in Section 4, including an overview of the methods used for comparison. In Section 5, the performance of the proposed method is presented and compared to other methods. Finally, conclusions from the study and directions for further research are discussed in Section 6.

#### 2. Traffic State Estimation Using Connected Vehicles

The traditional way to estimate the traffic state is by the use of stationary detectors such as loop detectors and radar detectors, as described by Kurkjian et al. [2], Coifman [3], and Singh and Li [4]. This is limiting the estimation to specific points in space, and the conditions in between detectors remain unknown. Hence, the estimation will be a good representation of the traffic state on the road section only under steady-state conditions, that is, when there is no change in the traffic conditions in space and time. This is usually not the case, particularly not for bottlenecks or during incidents, and therefore the density estimated with these methods will most probably deviate from the true density on the section. Hence, to give enough information about the traffic conditions on a longer road section, the detector-based method does require densely placed detectors (see, e.g., the method proposed by Singh and Li [4]). Data assimilation and fusion techniques including a traffic model are common methods to get a picture of the traffic state also in between the detectors. A number of studies using different underlying traffic models and different filtering approaches exist in the literature (see, e.g., Kurkjian et al. [2], Muñoz et al. [5], Wang and Papageorgiou [6], Mihaylova et al. [7], Singh and Li [4], and Duret et al. [8]). Methods have also been proposed, where no underlying model and no filtering are needed. See, for example, Coifman [3], where reidentification of vehicles and the vehicle conservation law is used to estimate the density between two detectors. Darwish and Bakar [9] conclude that methods using different types of stationary detectors can estimate the traffic state accurately but they are often expensive to install and maintain and are limited to small areas. Also, the information is usually transmitted with delay, since it has to be processed through a traffic information center.

Lately, when more data sources have become available, connected vehicles have been used as input to the filtering approaches in order to update the modeled traffic state. See, for example, Herrera and Bayen [10], Work et al. [11], Yuan et al. [12], Seo et al. [13], Astarita et al. [14], and Bekiaris-Liberis et al. [15]. Other traffic state estimation methods making use of connected vehicle data without an underlying traffic model are presented by Herring et al. [16], Herrera et al. [17], Van Lint and Hoogendoorn [18], Qiu et al. [19], Ma et al. [20], Bhaskar et al. [21], Zhang et al. [22], Seo et al. [23], and Montero et al. [24].

When speed measurements from connected vehicles are available, the speed can be estimated by calculating an average of the speeds of the connected vehicles. This requires that the connected vehicles have the same distribution of speeds as regular vehicles, similar to what has been done in the works of Astarita et al. [14] and Bekiaris-Liberis et al. [15]. Otherwise, the speed estimate would be biased towards the average speed of the connected vehicles.

The density estimate using connected vehicles requires some more calculations. One way of estimating the density is by using connected vehicles together with traditional stationary detectors, here referred to as combined methods. For the combined methods, a weighted estimate based on both traditional detector measurements and connected vehicle measurements of, for example, speed, travel time, and/or location is used. Examples are the methods presented by Astarita et al. [14], Qiu et al. [19], Ma et al. [20], Bhaskar et al. [21], Zhang et al. [22], and Bekiaris-Liberis et al. [15]. The method by Qiu et al. [19], which was later extended by Ma et al. [20], detects the number of vehicles located within a segment. The density estimate is calculated by counting the number of vehicles that have passed the detector upstream of the segment at the times when a connected vehicle enters and exits a segment. According to Qiu et al. [19], the accuracy of the density estimates is better than when only stationary detector data is used to estimate density. Zhang et al. [22] use probe vehicle data and detector stations in order to estimate the space mean speed, and not density, on a road stretch. Astarita et al. [14] and Bekiaris-Liberis et al. [15] develop macroscopic cell transmission type models for the dynamics of the percentage of connected vehicles along the considered road. It is assumed that the connected vehicles move with the same average speed as the nonconnected vehicles, and hence no modeling of the speed dynamics is needed. In the work of Astarita et al. [14], the density is estimated by the percentage of connected vehicles based on counts of connected vehicles moving from one segment to another in the network and inflows measured at the ramps and at the boundaries of the network. Similarly, Bekiaris-Liberis et al. [15] use the penetration rate of connected vehicles, together with measurements of speed from the connected vehicles, the boundary flow, and the ramp flows measured through stationary detectors, to estimate the density. Also the combined methods do often require densely placed detectors to get good estimates. The methods are often based on retrospective measurements, such as travel time at an earlier point in time (see, e.g., Qiu et al. [19] and Ma et al. [20]). As a result, the density estimate might not reflect the current situation.

For the connected-vehicle-based methods, the connected vehicles are used to capture the surrounding traffic conditions at every point in space, and the methods are therefore not limited to fixed locations. Recent studies by Seo et al. [13, 23] investigate how the gap to a leading vehicle can be used to estimate the density on a road segment. The same method has been applied to an urban area in Montero et al. [24]. Further, the method is extended to also include measurements of the gap to the following vehicle. Another method is making use of vehicle spacings and speed as input data for estimating density [12]. This method requires a numerical model of the relationship between the traffic states to describe the changes in speed, flow, and density. Finally, Seo and Kusakabe [25] propose a method based on the number of vehicles located in between two connected vehicles to estimate the traffic conditions on the road. For methods using only connected vehicle data, the measurements used to estimate density are local, only including the connected vehicle and its surroundings, which might not necessarily reflect the density on a larger section of the road. Also, the methods often require identification of current lane, speed of the vehicle, distance to vehicle in front, and so forth.

To conclude, detector-based density estimation techniques make use of measurements from stationary detectors, usually consisting of flow and speed, to estimate density. However, the density estimates using stationary detectors are based on point estimates and are therefore limited due to the fact that the conditions in between detectors are not known. Therefore, the methods require densely spaced detectors to give density estimates that correspond well with the traffic conditions on the road. The detector-based method can be improved by including connected vehicle data. For combined methods, the need for continuous updates from connected vehicles can be limited; that is, it is enough with low frequency data communicated from the connected vehicles. However, the combined methods do usually still require densely spaced detectors and the information is sometimes based on retrospective connected vehicle measurements. The density estimates using only connected vehicle data are based on local density estimates including precise estimates of the density surrounding the connected vehicle. The connected vehicle density estimates are transmitted for further processing and converted to a density estimate of a larger area by including estimates from many connected vehicles. Hence, a representative density estimate can often only be reached with a high connected vehicle penetration rate or for a high flow level. Further, the connected vehicles are assumed to be able to continuously transmit information about their location, speed, gap to proceeding vehicle, and so forth.

#### 3. A Method for Estimating the Traffic State by Using Connected Vehicle and Detector Data

We propose a combined method for estimating the traffic state on the road. The connected vehicle data is based on vehicle-to-infrastructure communication. The method is straightforward and it is possible to estimate the speed and density accurately based on limited information from the connected vehicles. Measurements from sparsely placed stationary detectors can be used without reducing the performance of the estimates. The purpose of the method is to get fast and representative traffic state estimates that can also be used to identify changes in the traffic conditions. Before introducing the method, a few essential assumptions are given:(i)The connected vehicles are able to report their position, including information about their current road segment and speed, with a frequency of 1 Hz.(ii)The stationary detectors are able to count and report the total number of vehicles, , and the total number of connected vehicles, , passing the detector within a given aggregation time period, .(iii)The connected vehicles are assumed to have the same distribution of speeds as the nonconnected vehicles.

Hence, neither the equipment used for communication of information for the connected vehicle nor the type of stationary detector (radar, Bluetooth, loop, etc.) is defined and may vary as long as they fulfil the requirements presented above.

The traffic state estimation consists of two parts, a speed estimate and a density estimate for each segment on the considered road stretch. The speed estimates are based on simple calculations. It is assumed that the connected vehicles have the same distribution of speeds as the nonconnected vehicles. By communication of the individual speed of each connected vehicle located on segment at time , the average speed of connected vehicles, , can be calculated. Then, the average speeds at time are averaged over the aggregation time period, , to get the final speed estimate,where is the total number of connected vehicles on road segment .

The density estimates make use of the position of each connected vehicle to get the total number of connected vehicles at each road segment, , and for each time step, . The average number of connected vehicles, , in segment and for the aggregation time period, , is used to estimate the total density. The stationary detector data is used to estimate the penetration rate on segment as the number of connected vehicles, , divided by the total number of vehicles, . The penetration rate at the detector station located just upstream of segment is used as input for the density estimate at segment . The density estimate becomes

The new speed and density estimates are becoming available after the latest aggregation time period , based on the measurements within the same aggregation time period and, hence, the estimates are varying with time. The temporal indices in the density estimates have been suppressed to increase readability. The method is hereafter referred to as the Count Connected Vehicle (CCV) method. By assuming that the penetration rate is constant over a longer road section, detectors can be sparsely placed in order to have as little requirements on detectors as possible. In this case, each estimate of the penetration rate is applied to many segments before a new estimate of the penetration rate becomes available.

The information from the connected vehicles and the detectors is collected at each time step and communicated to a central unit, where it is being processed, resulting in time-dependent speed and density estimates. Finally, the estimates are aggregated over the aggregation time period . Figure 1 gives an illustration of the process. The local units are the individual connected vehicles and the detectors. The central unit can, for example, be a roadside unit or a traffic management center used for further processing of data.