Article

Robust Deep Learning Architecture for Traffic Flow Estimation from a Subset of Link Sensors

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Abstract

Traffic flow data are needed for traffic management and control applications as well as for transportation planning issues. Such data are usually collected from traffic sensors; however, it is not practical or even feasible to deploy traffic sensors on all of a network's links. Instead, it is necessary to extend the information acquired from a subset of link flows to estimate the entire network's traffic flow. To this end, this study proposes a robust deep learning architecture based on a stacked sparse autoencoders (SAEs) model for a precise estimation of the whole network's traffic flow with an already-deployed sensor set. The proposed deep learning architecture has two consequent components: a deep learning model based on the SAEs and a fully connected layer. First, the SAEs model is used to extract traffic flow features and reach a meaningful pattern of the relation between the traffic flow data and network structure. Subsequently, the fully connected layer is used for the traffic flow estimation. Then, the whole architecture is fine-tuned to update its parameters in order to enhance the traffic flow estimation. For training the proposed deep learning architecture, synthetic link flow data are randomly generated from the network's prior demand information. The performance of the proposed model is evaluated then validated using two real networks. A third medium real-size network is used to measure the robustness of applying the proposed methodology to this specific problem of traffic flow estimation.

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... In graphical form, it is how to select a line to sep-mainly answers where and how many traffic sensors of a specific type are to be placed in a network for a designated purpose [10,11]. Although TSLP studies differ in solution structures depending on the problem formulation, they share some common guiding lines (e.g., coverage rules and link flow independence) [12]. ...
... Recently, [12] obtained close results to these exact link flow inference methods with fewer sensor counting via deep learning neural networks. The proposed technique can learn the latent relationships among a network's flow elements to accurately predict the absent link data. ...
... Algorithm 2 initializes the problem with a set of paths equal to the number of O/D pairs (̅). The central core in steps (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) attempts to find the best solution to cover the considered paths while perturbing the search in each internal iteration. Two leading operators of diversification are used: tolerance probability (Tp) and neighbor search fraction (Nfs). ...
Article
In this study, we present exact and heuristics algorithms for a traffic sensors location problem called the screen line problem. It is a problem of how to locate traffic sensors on a transportation network where all the origin/destination node pairs are fully separated. The problem experiences two main complexity dimensions that obstruct finding an efficient solution algorithm for large-scale networks: its mathematical formulation, which is proved in the literature to be NP-hard, and an inherent combinatorial complexity due to the need for a network complete path enumeration. In this study, the problem is reformulated as a set covering problem. Thereafter, the dual formulation is recalled showing that the shortest path-based column generation method would yield as many paths as necessary and hence circumvent the intractability of the full path enumeration task. This path generation technique enables applying both the proposed heuristics and exact methods to the problem. In addition, the gap value between the heuristics and the exact algorithms is set to be examined statistically. For evaluation, three networks of different sizes were used to track the scalability of proposed algorithms. The methodology showed high efficiency to deal with up to 10,000 demand node pairs in addition to the capability of producing practical solutions with respect to normal traffic flow conditions. The proposed heuristics algorithm stipulates a gap value of less than 25% with more than 99% confidence.
... These models encounter difficulties in dealing with non-homogeneous distribution variables; besides, they are prone to statistical flaws when there is a correlation among the independent variables (le Cessie and Van Houwelingen 1994, Midi et al. 2010). The second approach is advanced ML methods that could capture the inherent characteristics of the input data interactions (Owais et al. 2020b, Moussa and. Despite their capabilities, they might fail to infer/prioritize the impact of each input variable on the output/ target variable. ...
... DL is recognized as one of the rapidly growing branches in ML. It is the technology where an exclusive architecture of multilayer "deep" neural networks is used (Ciregan et al. 2012, Owais et al. 2020b). DL has proved pre-eminent performance in many applications in transportation engineering, including incident detection and traffic congestion (Chakraborty et al. 2018a, Chakraborty et al. 2018b, traffic flow estimation (Owais et al. 2020b), transportation-networks-reliability-analysis (Nabian and Meidani 2018), and pavement performance detection (Zhang et al. 2017, Fan et al. 2018, Dorafshan and Azari 2020, Moussa and Owais 2020. ...
... It is the technology where an exclusive architecture of multilayer "deep" neural networks is used (Ciregan et al. 2012, Owais et al. 2020b). DL has proved pre-eminent performance in many applications in transportation engineering, including incident detection and traffic congestion (Chakraborty et al. 2018a, Chakraborty et al. 2018b, traffic flow estimation (Owais et al. 2020b), transportation-networks-reliability-analysis (Nabian and Meidani 2018), and pavement performance detection (Zhang et al. 2017, Fan et al. 2018, Dorafshan and Azari 2020, Moussa and Owais 2020. Several studies have already employed DL in the traffic safety analysis. ...
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... One of the oldest ML techniques is Artificial Neural Networks (ANNs) paradigm that is developed by [50]. Over the last two decades, ANNs have increasingly been applied to develop predictive models from data due to their ability to recognize and learn the trends of data as well as the latent relationships among them [51]. That makes them an excellent substitution for the typical physical models to analyze complex relationships involving multiple input variables [52,53]. ...
... A fast-growing branch in ML is the Deep learning (DL) technology, in which a unique architecture of multi-layer ''deep" neural networks is utilized [51,74]. DL has shown superior performance in a wide range of applications in civil engineering; traffic flow estimation [51,[75][76][77][78], traffic congestion and incident detection [79][80][81], transportation network reliability analysis [82][83][84][85], pavement crack detection [86][87][88], and structural damage detection [89,90]. ...
... A fast-growing branch in ML is the Deep learning (DL) technology, in which a unique architecture of multi-layer ''deep" neural networks is utilized [51,74]. DL has shown superior performance in a wide range of applications in civil engineering; traffic flow estimation [51,[75][76][77][78], traffic congestion and incident detection [79][80][81], transportation network reliability analysis [82][83][84][85], pavement crack detection [86][87][88], and structural damage detection [89,90]. DL superior performance relies on its ability to learn high-complex features (representations) of the row data than other ML tools [91][92][93]. ...
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... Despite their usefulness in collecting different traffic measures, it is not always practical to install them in all network links. Thus, the problem becomes: how many sensors are needed, where to locate them, and how to estimate and predict the missing measures (Owais, Moussa, and Hussain, 2020). ...
... The methods vary according to the chosen statistical approach, such as least squares (Bell, 1991;Cascetta, 1984), maximizing entropy (Lam and Lo, 1991;Wong, et al., 2005), maximum likelihood (Spiess, 1987;Hai Yang, Sasaki, Iida, and Asakura, 1992), and Bayesian inference (Li, 2005;Tebaldi and West, 1998;Wei and Asakura, 2013). Deep learning is also used for the link flow estimation problem because it estimates the network flows from a subset of installed counting sensors using randomly generated synthetic flow data for the training stage (Owais, Moussa, et al., 2020). ...
... While we have assumed that the network sensors are provided and fixed, we would assume that there is no certain information about the O/D demand and consequently the link-node pair mapping matrix. To track the observability levels for this set of sensors, we used the method of synthetic demand generation presented in (Owais, Moussa, and Hussain, 2020) to generate 100 versions of the A matrix trying to capture the variation in the path choice within the network in real practice. The levels of observability through these 100 iterations are depicted in Fig. 5. ...
Article
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... As an important branch of machine learning, neural network models, including artificial neural networks (ANN), fuzzy neural networks (FNN), and radial basis neural networks (RBFNN), are equipped with a multinode network memory function to extract more complex nonlinear feature information from the historical traffic flow. Deep learning models deepen the hierarchical structure of neural networks [18,19], and this multi-hidden layer network improves the value density of feature information in the process of multilevel parameter transfer, abstracts the low-level feature distribution into high-level feature information, and strengthens the feature representation ability of the model in comparison to traditional neural networks, which can learn the deeper traffic flow evolution laws. Deep belief networks (DBNs) [20] expand the network depth by multilayer stacking based on restricted Boltzmann machines, whose hidden layer units are trained to capture the correlation of higher-order data exhibited at the visual layer, thereby enabling the network to more closely approximate the real system energy state of the data. ...
... Let each iteration's population size be n, after the algorithm completes the selection operation in the iteration process, the remaining individuals are sorted by fitness value, and the fitness threshold condition f t is set to further divide the population into a high fitness population A and a low fitness population B. e threshold condition f t f t is defined as follows: (19) where f i represents the individual's fitness value for the population crossover operation, the probability p of one parent's fitness relative to the overall fitness of both parents is calculated and used to determine the position of the gene breakpoint c break . ...
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... The system shows that correlating speed violations with high tickets helps in regulating users' behavior. However, providing these sensors on all the network's streets is a costly and not practical task [7]. Therefore, users tend to locate the roads in which the sensors are installed to avoid being charged without any tangible change in their driving habits. ...
... In [31,32], the bi-level optimization is used by which the equilibrium between the estimating O/D flows and users' route choice model is ensured in the final solution. Recently, Owais et al. [7] deployed the deep neural network for the flow estimation using innovative learning architecture based on Stacked sparse Auto-Encoders (SAEs) to attain meaningful patterns between the sensors data and the network structure. ...
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... However, in the real-world, each link travel time is variant and hard to predict. It depends on the level of traffic on it, so the algorithm fails to find the optimum path until the traffic is observed on all links in real-time which unpractical premise [9][10][11]. The traffic is also stochastic with time causing travel time uncertainty turning the TN to what is called Stochastic Transportation Network (STN). ...
... It also has a non-path based solution algorithm which makes it a non-biased method to evaluate the generated paths. DUE is formulated as follows: (11) s.t (12) (1 3) (14) To solve this set of equations for any time slot , the convex combination method is adapted as follows: ...
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... In addition, Shao et al. (2021) used the same concept while minimizing the error propagation of accumulated counting measurements for each link inference. Interestingly, Owais et al. (2020c) obtained similar results to these link flow inference methods with fewer sensors via deep learning neural networks. The proposed technique can learn the latent relationships among a network's flow elements to accurately predict missing link data (Moussa & Owais, 2020. ...
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... While loop detectors are installed to collect link flow data, the observation points are often limited to a subset of links and there are still a large proportion of links that do not have direct observations. Thus, unobserved link flows need to be estimated based on available data and this is referred to as the link flow estimation problem in the transportation literature (Abadi et al. 2015;Brunauer et al., 2017;Lederman and Wynter, 2011;Owais et al. 2020;Van Oijen et al. 2020). ...
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... The performance of such models is outstanding in many aspects Owais 2020, 2021). At present, the DL techniques in urban traffic flow research mainly include traditional neural networks applicable to gridded traffic flows and graph neural networks (GNNs) applicable to networked flows (Bui, Cho, and Yi 2021;Owais, Moussa, and Hussain 2020;Xiong et al. 2020). In contrast to gridding urban traffic as a feature image, the networked approach considers the traffic flow only at node locations. ...
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... (3) e adjustment of the support stiffness or sleeper spacing leads to fluctuations in the corrugation wavelength and its growth rate, while reducing the support stiffness and the sleeper spacing can suppress the formation of rail corrugation. e above studies coincide well with the conclusions obtained in existing studies and are of great significance to the prevention and maintenance of corrugated wear, while the real-time detection of rail corrugation based on deep learning network [67,68] will be investigated in the future research. ...
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... Most of the line design techniques depend on the demand information, which adds more complexity to the problem. As the conventional transportation problem, the transit O/D estimation could be based on the well-known step planning models (i.e., trip generation, trip distribution, modal choice, and traffic assignment) [44][45][46][47]. For the actual size networks as our case, the four models are unlikely to give accurate results due to the high level of uncertainty at the operational stage [48,49]. ...
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The overall purpose of this study is to enhance existing transit systems by planning a new underground metro network. The design of a new metro network in the existing cities is a complex problem. Therefore, in this research, the study idea arises from the prerequisites to get out of conventional metro network design to develop a future scheme for forecasting an optimal metro network for these existing cities. Two models are proposed to design metro transit networks based on an optimal cost-benefit ratio. Model 1 presents a grid metro network, and Model 2 presents the ring-radial metro network. The proposed methodology introduces a non-demand criterion for transit system design. The new network design aims to increase the overall transit system connectivity by minimizing passenger transfers through the transit network between origin and destination. An existing square city is presented as a case study for both models. It includes twenty-five traffic analysis zones, and thirty-six new metro stations are selected at the existing street intersection. TransCAD software is used as a base for stations and the metro network lines to coordinate all these data. A passenger transfer counting algorithm is then proposed to determine the number of needed transfers between stations from each origin to each destination. Thus, a passenger Origin/Destination transfer matrix is created via the NetBeans program to help in determining the number of transfers required to complete the trips on both proposed networks. Results show that Model 2 achieves the maximum cost-benefit ratio (CBR) of the transit network that increases 41% more than CBR of Model 1. Therefore, it is found that the ring radial network is a more optimal network to existing square cities than the grid network according to overall network connectivity.
... Most of the line design techniques depend on the demand information, which adds more complexity to the problem. As the conventional transportation problem, the transit O/D estimation could be based on the well-known step planning models (i.e., trip generation, trip distribution, modal choice, and traffic assignment) [49][50][51][52]. For the actual size networks as our case, the four models are unlikely to give accurate results due to the high level of uncertainty at the operational stage [53,54]. ...
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Traffic congestion is known as the most significant problem in developing countries in recent years. This study investigates the integration of bus and metro systems by proposing new ring lines. Study methodology presents a practical scheme of multiple subway line design to obviate the difficulty of dealing with large-scale networks that always suffer from severely combinatorial problems, which represent a hindrance to many theoretical design algorithms. The new lines are aimed to increase the connection between the transit modes and consequently increasing the overall transit network efficiency. In design strategic phase, a mathematical formulation is derived to minimize passenger transfer number (PTN) among public transportation facilities. A real case network of the Greater Cairo city is used to validate the presented methodology. After testing many solutions using the brute force technique, two subway lines are recommended with their station structure to increase the overall network connectivity by more than 70%.
... Furthermore, it would be helpful to propose a nondemand-based criterion for analyzing demand-coverage imbalances in existing transit networks. This would allow for determination of unsatisfied demand centers, and facilitate direct planning in scenarios concerning sizeable scale networks with unreliable demand information (Owais, Moussa, & Hussain, 2020). Reducing the potential number of transfers from one mode to another could reflect positively on passengers, and increase their confidence in public transport (Owais & Osman, 2018). ...
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Connectivity is a significant problem in large-scale transit networks because the number of transfers required to conduct a trip is considered a discomfort by transit users. This paper presents a practical solution for an underground metro line planning problem by integrating existing bus and metro networks into a single connected transit network. The proposed method aims to obviate the usual combinatorial complexity when solving a transit route design problem. It aims to increase the overall transit system connectivity by selecting a consistent and non-demand-oriented criterion for the design. The metro lines are designed by minimizing passenger transfers through the transit network according to predefined demand node pairs. The design scheme offers a set of ring route alternatives for a sizeable case study in Greater Cairo. The case study selected sixteen traffic analysis zones, an existing metro network consisting of three main lines (113.6 km long), and twelve main bus lines (487.7 km long) for analysis. TransCAD software was used as the basis for coordinating the stations and lines of both the bus and metro systems. Subsequently, a passenger transfer counting algorithm was implemented to determine the number of transfers required between stations from each origin to each destination. A passenger origin-destination transfer matrix was created using the NetBeans integrated development environment to help determine the number of transfers required to complete trips on the transit network before and after proposing the new line. Based on the evaluation, the ring lines were highly efficient at significantly decreasing passenger transfers between stations with the minimum construction cost. This study will be of value during the strategic stages of the transit line design and will assist in rapidly generating initial solutions when certain demand information is unavailable.
... One of the fastest-growing methods in the field of ML, which has gained popularity in the last years due to its outstanding results in numerous engineering application domains, is deep learning architecture (DL) [70,71]. DL architecture is an artificial neural network that contains multiple layers (deep networks) between input and output layers [72]. Multiple layers allow the architecture to progressively extract high-level features from the raw input data [73,74]. ...
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... Past decades have been dedicated to traffic simulation models and algorithms since demand simulation is essential for the analysis of urban transportation systems [45][46][47]. Specialized engineering in simulation can study the formation and dissipation of congestion on roadways, assess the impacts of control strategies, and compare alternative geometric configurations. A superior list of methods and guidelines for supporting the use, calibration, and validation of traffic simulators are found in [48]. ...
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In this study, we consider the bi-objective traffic counting location problem for the purpose of origin-destination (O-D) trip table estimation. The problem is to determine the number and locations of counting stations that would best cover the network. The maximal coverage and minimal resource utilization criteria, which are generally conflicting, are simultaneously considered in a multi-objective manner to reveal the tradeoff between the quality and cost of coverage. A distance-based genetic algorithm (GA) is used to solve the proposed bi-objective traffic counting location problem by explicitly generating the non-dominated solutions. Numerical results are provided to demonstrate the feasibility of the proposed model. The primary results indicate that the distance-based GA can produce the set of non-dominated solutions from which the decision makers can examine the tradeoff between the quality and cost of coverage and make a proper selection without the need to repeatedly solve the maximal covering problem with different levels of resource.
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Sensors are used to monitor traffic in networks. For example, in transportation networks, they may be used to measure traffic volumes on given arcs and paths of the network. This paper refers to an active sensor when it reads identifications of vehicles, including their routes in the network, that the vehicles actively provide when they use the network. On the other hand, the conventional inductance loop detectors are passive sensors that mostly count vehicles at points in a network to obtain traffic volumes (e.g., vehicles per hour) on a lane or road of the network. This paper introduces a new set of network location problems that determine where to locate active sensors in order to monitor or manage particular classes of identified traffic streams. In particular, it focuses on the development of two generic locational decision models for active sensors, which seek to answer these questions: (1) “How many and where should such sensors be located to obtain sufficient information on flow volumes on specified paths?”, and (2) “Given that the traffic management planners have already located count detectors on some network arcs, how many and where should active sensors be located to get the maximum information on flow volumes on specified paths?” The problem is formulated and analyzed for three different scenarios depending on whether there are already count detectors on arcs and if so, whether all the arcs or a fraction of them have them. Location of an active sensor results in a set of linear equations in path flow variables, whose solution provide the path flows. The general problem, which is related to the set-covering problem, is shown to be NP-Hard, but special cases are devised, where an arc may carry only two routes, that are shown to be polynomially solvable. New graph theoretic models and theorems are obtained for the latter cases, including the introduction of the generalized edge-covering by nodes problem on the path intersection graph for these special cases. An exact algorithm for the special cases and an approximate one for the general case are presented.
Conference Paper
Successful traffic speed prediction is of great importance for the benefits of both road users and traffic management agencies. To solve the problem, traffic scientists have developed a number of time-series speed prediction approaches, including traditional statistical models and machine learning techniques. However, existing methods are still unsatisfying due to the difficulty to reflect the stochastic traffic flow characteristics. Recently, various deep learning models have been introduced to the prediction field. In this paper, a deep learning method, the Deep Belief Network (DBN) model, is proposed for short-term traffic speed information prediction. The DBN model is trained in a greedy unsupervised method and fine-tuned by labeled data. Based on traffic speed data collected from one arterial in Beijing, China, the model is trained and tested for different prediction time horizons. From experiment analysis, it is concluded that the DBN can outperform Back Propagation Neural Network (BPNN) and Auto-Regressive Integrated Moving Average (ARIMA) for all time horizons. The advantages of DBN indicate that deep learning is promising in traffic research area.
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Global optimization of the energy consumption of dual power source vehicles such as hybrid electric vehicles, plug-in hybrid electric vehicles, and plug in fuel cell electric vehicles requires knowledge of the complete route characteristics at the beginning of the trip. One of the main characteristics is the vehicle speed profile across the route. The profile will translate directly into energy requirements for a given vehicle. However, the vehicle speed that a given driver chooses will vary from driver to driver and from time to time, and may be slower, equal to, or faster than the average traffic flow. If the specific driver speed profile can be predicted, the energy usage can be optimized across the route chosen. The purpose of this paper is to research the application of Deep Learning techniques to this problem to identify at the beginning of a drive cycle the driver specific vehicle speed profile for an individual driver repeated drive cycle, which can be used in an optimization algorithm to minimize the amount of fossil fuel energy used during the trip.
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The traditional approach to origin-destination (OD) estimation based on data surveys is highly expensive. Therefore, researchers have attempted to develop reasonable low-cost approaches to estimating the OD vector, such as OD estimation based on traffic sensor data. In this estimation approach, the location problem for the sensors is critical. One type of sensor that can be used for this purpose, on which this paper focuses, is vehicle identification sensors. The information collected by these sensors that can be employed for OD estimation is discussed in this paper. We use data gathered by vehicle identification sensors that include an ID for each vehicle and the time at which the sensor detected it. Based on these data, the subset of sensors that detected a given vehicle and the order in which they detected it are available. In this paper, four location models are proposed, all of which consider the order of the sensors. The first model always yields the minimum number of sensors to ensure the uniqueness of path flows. The second model yields the maximum number of uniquely observed paths given a budget constraint on the sensors. The third model always yields the minimum number of sensors to ensure the uniqueness of OD flows. Finally, the fourth model yields the maximum number of uniquely observed OD flows given a budget constraint on the sensors. For several numerical examples, these four models were solved using the GAMS software. These numerical examples include several medium-sized examples, including an example of a real-world large-scale transportation network in Mashhad.
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The link observability problem is to identify the minimum set of links to be installed with sensors that allow the full determination of flows on all the unobserved links. Inevitably, the observed link flows are subject to measurement errors, which will accumulate and propagate in the inference of the unobserved link flows, leading to uncertainty in the inference process. In this paper, we develop a robust network sensor location model for complete link flow observability, while considering the propagation of measurement errors in the link flow inference. Our model development relies on two observations: (1) multiple sensor location schemes exist for the complete inference of the unobserved link flows, and different schemes can have different accumulated variances of the inferred flows as propagated from the measurement errors. (2) Fewer unobserved links involved in the nodal flow conservation equations will have a lower chance of accumulating measurement errors, and hence a lower uncertainty in the inferred link flows. These observations motivate a new way to formulate the sensor location problem. Mathematically, we formulate the problem as min–max and min–sum binary integer linear programs. The objective function minimizes the largest or cumulative number of unobserved links connected to each node, which reduces the chance of incurring higher variances in the inference process. Computationally, the resultant binary integer linear program permits the use of a number of commercial software packages for its globally optimal solution. Furthermore, considering the non-uniqueness of the minimum set of observed links for complete link flow observability, the optimization programs also consider a secondary criterion for selecting the sensor location scheme with the minimum accumulated uncertainty of the complete link flow inference.
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Many past researchers have ignored the multi-objective nature of the transit route network design problem (TrNDP), recognizing user or operator cost as their sole objective. The main purpose of this study is to identify the inherent conflict among TrNDP objectives in the design process. The conventional scheme for transit route design is addressed. A route constructive genetic algorithm is proposed to produce a vast pool of candidate routes that reflect the objectives of design, and then, a set covering problem (SCP) is formulated for the selection stage. A heuristic algorithm based on a randomized priority search is implemented for the SCP to produce a set of nondominated solutions that achieve different tradeoffs among the identified objectives. The solution methodology has been tested using Mandl's benchmark network problem. The test results showed that the methodology developed in this research not only outperforms solutions previously identified in the literature in terms of strategic and tactical terms of design, but it is also able to produce Pareto (or near Pareto) optimal solutions. A real-scale network of Rivera was also tested to prove the proposed methodology's reliability for larger-scale transit networks. Although many efficient meta-heuristics have been presented so far for the TrNDP, the presented one may take the lead because it does not require any weight coefficient calibration to address the multi-objective nature of the problem.
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Accurate and timely traffic flow information is important for the successful deployment of intelligent transportation systems. Over the last few years, traffic data have been exploding, and we have truly entered the era of big data for transportation. Existing traffic flow prediction methods mainly use shallow traffic prediction models and are still unsatisfying for many real-world applications. This situation inspires us to rethink the traffic flow prediction problem based on deep architecture models with big traffic data. In this paper, a novel deep-learning-based traffic flow prediction method is proposed, which considers the spatial and temporal correlations inherently. A stacked autoencoder model is used to learn generic traffic flow features, and it is trained in a greedy layerwise fashion. To the best of our knowledge, this is the first time that a deep architecture model is applied using autoencoders as building blocks to represent traffic flow features for prediction. Moreover, experiments demonstrate that the proposed method for traffic flow prediction has superior performance.
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Traffic sensors serve an important function in obtaining traffic information. In this paper, a novel traffic sensor location approach is proposed to determine the maximum number of traffic flows by considering the time-spatial correlation. The problem is formulated as three 0-1 programming models to maximise the number of obtained flows under different cases. To solve these novel sensor location problems, an ant colony optimisation algorithm with a local search procedure is designed. Numerical experiments are conducted in both a simulated network and in the Sioux-Falls network. Results demonstrate the effectiveness and robustness of the proposed algorithm, which is believed to possess potential applicability in real surveillance network design.
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Path-differentiated congestion pricing is a tolling scheme that imposes tolls on paths instead of individual links. One way to implement this scheme is to deploy automated vehicle identification sensors, such as toll tag readers or license plate scanners, on roads in a network. These sensors collect vehicles’ location information to identify their paths and charge them accordingly. In this paper, we investigate how to optimally locate these sensors for the purpose of implementing path-differentiated pricing. We consider three relevant problems. The first is to locate a minimum number of sensors to implement a given path-differentiated scheme. The second is to design an optimal path-differentiated pricing scheme for a given set of sensors. The last problem is to find a path differentiated scheme to induce a given target link-flow distribution while requiring a minimum number of sensors.
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In this paper, we deal with the observability problem in traffic networks and the optimal location of counting and scanning devices. After explaining what we mean by observability, the problems of what to observe, how to observe traffic data and how to incorporate prior or obsolete information together with the cases of genuine and pseudo-samples of flow data are discussed. Plate scanning information is dealt with and the flow amount of information measure of information corresponding to a subset of scanned links is analysed. Some pivoting and matrix techniques are given for solving the most common problems of observability of traffic flows in a network. Finally, the problem of optimal location of counters and plate scanning cameras is analysed and several examples are given.
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With the advent of intelligent transportation systems, transportation networks have a considerable amount of traffic detectors, and large amounts of streaming data are available to manage and plan a multi-modal network and provide real-time traffic information to travelers. The related problem of optimally locating sensors on the network to estimate flows has been the object of growing interest in the past few years. Available sensors use various technologies and measure different aspects of traffic flows. This paper classifies sensor location problems in the literature in two categories: the sensor location flow-observability problem and the sensor location flow-estimation problem. This paper reviews the existing contributions for the latter of the two problem types and presents a unifying bilevel optimization framework in which the upper level addresses the location decisions and the lower level addresses the estimation variables. Several directions for future research are discussed.
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Traffic flow prediction is a fundamental problem in transportation modeling and management. Many existing approaches fail to provide favorable results due to being: 1) shallow in architecture; 2) hand engineered in features; and 3) separate in learning. In this paper we propose a deep architecture that consists of two parts, i.e., a deep belief network (DBN) at the bottom and a multitask regression layer at the top. A DBN is employed here for unsupervised feature learning. It can learn effective features for traffic flow prediction in an unsupervised fashion, which has been examined and found to be effective for many areas such as image and audio classification. To the best of our knowledge, this is the first paper that applies the deep learning approach to transportation research. To incorporate multitask learning (MTL) in our deep architecture, a multitask regression layer is used above the DBN for supervised prediction. We further investigate homogeneous MTL and heterogeneous MTL for traffic flow prediction. To take full advantage of weight sharing in our deep architecture, we propose a grouping method based on the weights in the top layer to make MTL more effective. Experiments on transportation data sets show good performance of our deep architecture. Abundant experiments show that our approach achieved close to 5% improvements over the state of the art. It is also presented that MTL can improve the generalization performance of shared tasks. These positive results demonstrate that deep learning and MTL are promising in transportation research.
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Deep learning is currently an extremely active research area in machine learning and pattern recognition society. It has gained huge successes in a broad area of applications such as speech recognition, computer vision, and natural language processing. With the sheer size of data available today, big data brings big opportunities and transformative potential for various sectors; on the other hand, it also presents unprecedented challenges to harnessing data and information. As the data keeps getting bigger, deep learning is coming to play a key role in providing big data predictive analytics solutions. In this paper, we provide a brief overview of deep learning, and highlight current research efforts and the challenges to big data, as well as the future trends.
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In recent years, deep neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarises relevant work, much of it from the previous millennium. Shallow and deep learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.
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Recently, a new methodology (“synergistic sensor location”) has been introduced to efficiently determine all link flows in a road network by using only a subset of the link flow measurements. In this paper, we generalize this previous work by solving the following problem: Suppose that one is only interested in a subset of the link flows, and that certain link flows are known a priori. At a minimum, what link flows are needed to be able to uniquely determine the desired link flows? An algorithm is presented that does not require the need for path enumeration.
Article
The problem of optimally locating sensors on a traffic network to measure flows has been object of growing interest in the past few years, due to its relevance in transportation systems. Different locations of sensors on the network can allow, indeed, the collection of data whose usage can be useful for traffic management and control purposes. Many different models have been proposed in the literature as well as corresponding solution approaches. The proposed existing models differ according to different criteria: (i) sensor types to be located on the network (e.g., counting sensors, image sensors, Automatic Vehicle Identification (AVI) readers), (ii) available a-priori information, and (iii) flows of interest (e.g., OD flows, route flows, link flows). The purpose of this paper is to review the existing contributions and to give a unifying picture of these models by categorizing them into two main problems: the Sensor Location Flow-Observability Problem and the Sensor Location Flow-Estimation Problem. For both the problems, we will describe the corresponding computational complexity and the existing results. After describing various models and identifying their advantages and limitations, we conclude with several promising directions for future research and discuss other classes of location problems that address different objectives than the ones reviewed in the paper.
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Sensors are becoming increasingly critical elements in contemporary transportation systems, gathering essential (real-time) traffic information for the planning, management and control of these complex systems. In a recent paper, Hu, Peeta and Chu introduced the interesting problem of determining the smallest subset of links in a traffic network for counting sensor installation, in such a way that it becomes possible to infer the flows on all remaining links. The problem is particularly elegant because of its limited number of assumptions. Unfortunately, path enumeration was required, which – as recognized by the authors – is infeasible for large-scale networks without further simplifying assumptions (that would destroy the assumption-free nature of the problem). In this paper, we present a reformulation of this link observability problem, requiring only node enumeration. Using this node-based approach, we prove a conjecture made by Hu, Peeta and Chu by deriving an explicit relationship between the number of nodes and links in a transportation network, and the minimum number of sensors to install in order to be able to infer all link flows. In addition, we demonstrate how the proposed method can be employed for road networks that already have sensors installed on them. Numerical examples are presented throughout.
Article
Estimating origin-destination trip matrices from link traffic counts has been a subject of substantial research. It is well known that the accuracy of the resulting estimated origin-destination (O-D) matrix largely depends on the employed estimation approach itself, errors of the input data, and an appropriate set of links from which flow information should be collected. Previous studies have overwhelmingly focused on the development of various estimation models, while paying very limited attention to the traffic counting location and error bound issues. Recognizing their interdependence, this study makes a joint investigation of the traffic counting location, estimation method, and error bound in an integrated manner, while taking into account the effects of various route choice assumptions made in the traffic assignment models and the levels of traffic congestion on the network. A few useful properties of the counting location rules and error bound measures for the O-D matrix estimation problem are demonstrated theoretically and numerically.
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Origin-destination (O-D) trip matrix estimation from traffic count surveys is regarded as the most economical and effective methodology in road network analysis for transport planning and traffic management. Despite the numerous mathematical estimation techniques previously developed, the fundamental procedure of selecting count locations itself is a prime determinant in the quality of the ultimate estimation and deserves more in-depth exploration. In this paper, some existing methods being adopted in practice are reviewed. Two basic rules are established based on previous works and are formulated in a linear programming model to determine the best survey locations for O-D estimation. However, technical problems will be incurred when applied to a large network with huge number of variables involved. The proposed maximal O-D selection method is proved to provide results with a comparable level of reliability, and a sensitivity test is conducted with different objective functions to verify this proposed strategic algorithm. This paper examines the efficiency of additional link counts for O-D estimation and recommends an efficient data collection method. The models and algorithms are illustrated with numerical examples.
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The focus of this paper is on a certain class of equilibrium traffic assignment problems characterized by a path formulation of the associated mathematical programs. In such cases the equilibration iterations would require path enumeration, and are therefore prohibitively expensive. In this paper we prove that a predetermined sequence of step sizes (in a descent direction) would guarantee, under certain regularity conditions, convergence to the equilibrium solution. This algorithm was suggested in the literature without a proof of convergence, which we give here.
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The widely used BPR volume-delay functions have some inherent drawbacks. A set of conditions is developed which a “well behaved” volume delay function should satisfy. This leads to the definition of a new class of functions named conical volume-delay functions, due to their geometrical interpretation as hyperbolic conical sections. It is shown that these functions satisfy all conditions set forth and, thus, constitute a viable alternative to the BPR type functions.
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Several route choice models are reviewed in the context of the stochastic user equilibrium problem. The traffic assignment problem has been extensively studied in the literature. Several models were developed focusing mainly on the solution of the link flow pattern for congested urban areas. The behavioural assumption governing route choice, which is the essential part of any traffic assignment model, received relatively much less attention. The core of any traffic assignment method is the route choice model. In the wellknown deterministic case, a simple choice model is assumed in which drivers choose their best route. The assumption of perfect knowledge of travel costs has been long considered inadequate to explain travel behaviour. Consequently, probabilistic route choice models were developed in which drivers were assumed to minimize their perceived costs given a set of routes. The objective of the paper is to review the different route choice models used to solve the traffic assignment problem. Focus is on the different model structures. The paper connects some of the route choice models proposed long ago, such as the logit and probit models, with recently developed models. It discusses several extensions to the simple logit model, as well as the choice set generation problem and the incorporation of the models in the assignment problem.
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This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. The paper also discusses the weaknesses of existing stochastic-network-loading techniques (with special attention paid to Dial's multipath method) and compares them to the suggested approach. The discussion is supported by several numerical examples on small contrived networks. The paper concludes with the discussion of two techniques that can be used to approximate the link flows resulting from the proposed model in large networks.
Conference Paper
We present a method for estimating the KL divergence between continuous densities and we prove it converges almost surely. Divergence estimation is typically solved estimating the densities first. Our main result shows this intermediate step is unnecessary and that the divergence can be either estimated using the empirical cdf or k-nearest-neighbour density estimation, which does not converge to the true measure for finite k. The convergence proof is based on describing the statistics of our estimator using waiting-times distributions, as the exponential or Erlang. We illustrate the proposed estimators and show how they compare to existing methods based on density estimation, and we also outline how our divergence estimators can be used for solving the two-sample problem.
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The increasing need for mobility has brought about significant changes in transportation infrastructures. Inefficiencies cause enormous losses of time, decrease in the level of safety for both vehicles and pedestrians, high pollution, degradation of quality of life, and huge waste of nonrenewable fossil energy.The scope of this article is to introduce novel functionality for providing knowledge to vehicles, thus jointly managing traffic and safety. This will be achieved through the design of the proposed functionality, which, at a high level, will comprise (1) sensor networks formed by vehicles of a certain vicinity that exchange traffic-related information, (2) cognitive management functionality placed inside the vehicles for inferring knowledge and experience, and (3) cognitive management functionality in the overall transportation infrastructure. The goal of the aforementioned three main components shall be to issue directives to the drivers and the overall transportation infrastructure valuable in context handling.
Article
Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the literature, most studies to develop such strategies typically assume the availability of measured link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, the assumption of installed sensors on all links is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the path flows are static. A “basis link” method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its “basis” in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.
Article
This paper describes the validation of a route choice simulator known as VLADIMIR (Variable Legend Assessment Device for Interactive Measurement of Individual Route choice). VLADIMIR is an interactive computer-based tool designed to study drivers’ route choice behaviour. It has been extensively used to obtain data on route choice in the presence of information sources such as Variable Message Signs or In-Car Navigation devices. The simulator uses a sequence of digitized photographs to portray a real network with junctions, links, landmarks and road signs. Subject drivers are invited to make journeys between specified origins and destinations under a range of travel scenarios, during which the simulator automatically records their route choices. This paper describes validation experiments carried out during the period Summer 1994 to Autumn 1995 and reports on the results obtained. Each experiment involved a comparison of routes selected in real life with those driven under simulated conditions in VLADIMIR. The analysis included investigation of the subjects’ own assessment of the realism of the VLADIMIR routes they had chosen, a comparison of models based on the real life routes with models based on VLADIMIR routes, and a statistical comparison of the two sets of routes. After an extensive series of data collection exercises and analyses, we have concluded that a well designed simulator is able to replicate real life route choices with a very high degree of detail and accuracy. Not only was VLADIMIR able to precisely replicate the route choices of drivers who were familiar with the network but it also appears capable of representing the kind of errors made and route choice strategies adopted by less familiar drivers. Furthermore, evidence is presented to suggest that it can accurately replicate route choice responses to roadside VMS information.
Article
There has been substantial interest in development and application of methodology for estimating origin–destination (O–D) trip matrices from traffic counts. Generally, the quality of an estimated O–D matrix depends much on the reliability of the input data, and the number and locations of traffic counting points in the road network. The former has been investigated extensively, while the latter has received very limited attention. This paper addresses the problem of how to determine the optimal number and locations of traffic counting points in a road network for a given prior O–D distribution pattern. Four location rules: O–D covering rule, maximal flow fraction rule, maximal flow-intercepting rule and link independence rule are proposed, and integer linear programming models and heuristic algorithms are developed to determine the counting links satisfying these rules. The models and algorithms are illustrated with numerical examples.
Article
The paper proposes an efficient algorithm for determining the stochastic user equilibrium solution for logit-based loading. The commonly used Method of Successive Averages typically has a very slow convergence rate. The new algorithm described here uses Williams’ result [ Williams, (1977)On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning9A(3), 285–344] which enables the expected value of the perceived travel costs Srs to be readily calculated for any flow vector x. This enables the value of the Sheffi and Powell, 1982objective function [Sheffi, Y. and Powell, W. B. (1982) An algorithm for the equilibrium assignment problem with random link times. Networks12(2), 191–207], and its gradient in any specified search direction, to be calculated. It is then shown how, at each iteration, an optimal step length along the search direction can be easily estimated, rather than using the pre-set step lengths, thus giving much faster convergence. The basic algorithm uses the standard search direction (towards the auxiliary solution). In addition the performance of two further versions of the algorithm are investigated, both of which use an optimal step length but alternative search directions, based on the Davidon–Fletcher–Powell function minimisation method. The first is an unconstrained and the second a constrained version. Comparisons are made of all three versions of the algorithm, using a number of test networks ranging from a simple three-link network to one with almost 3000 links. It is found that for all but the smallest network the version using the standard search direction gives the fastest rate of convergence. Extensions to allow for multiple user classes and elastic demand are also possible.