Neural Network Based Traffic Flow Model for Urban Arterial Travel Time Prediction

Many research efforts on travel time prediction focus predominantly on freeways, while limited work has been done on urban arterials. Among the latter, data driven models, particularly neural networks, have demonstrated promising performance. In most cases, the inputs from spatially separated sources (volumes/speeds collected by loop detectors from different locations) are combined in one single input vector. As a consequence, as the length of the route of interest increases, more and more input variables are inserted into the input vector. This results in a significant increase of parameters of the neural network. A larger parameter space yields more difficulty in training neural networks to not only fit the particular data used for training, but also generalize well to ‘unseen’ data. This paper provides a neural network based traffic flow model to address the problem of urban arterial travel time prediction. A single segment model based on the Recurrent Neural Network is used for modeling traffic flow on one single signalized link. To model a longer arterial, several separate segment models can be assembled together. This reduces significantly the amount of parameters of the neural network, which make it simpler and easier to be implemented in practice. An urban arterial in the Netherlands has been selected as test bed. Both empirical data and simulation data have been used to evaluate this model. The results indicate that this proposed model is capable of dealing with complex nonlinear urban arterial travel time predictions with satisfying accuracy and effectiveness. Hao Liu, Hans van Lint, Henk van Zuylen 2 INTRODUCTION Accurate and timely prediction of travel time is a critical component for many advanced traveler information and advanced traffic management systems. Many research efforts on travel time prediction focus predominantly on freeways, while limited work has been done on urban streets. Since the characteristics and resulting traffic behavior on freeways and urban streets are quite different, approaches that address freeway travel time prediction are not easily translated to urban environments. Artificial neural networks have been shown to be a promising solution to predict traffic variables on urban arterials. Since delays play an important role in travel time on urban arterials, several promising neural network models have been proposed on queue prediction (delays can be derived from queues), for example (1,2). However, training these neural network models require direct measurements of queue lengths, which are not easily obtained from sensors in practice. This is why these models were tested with simulation data. Thus, these models still need to be adjusted or improved if only conventional loop detector data are available. This paper presents a neural network based traffic flow model to address the problem of travel time prediction on urban arterials. An urban arterial is subdivided into several segments/links. A general segment neural network model is proposed to predict travel time on a basic segment of urban arterials. Modeling traffic along a signalized urban arterial can be conducted by assembling basic segment models for each segment along the route. To train this scalable neural network, two types of data are needed: volumes (input) and travel times (output). This data requirement is applicable for real-life systems. Two data sets, respectively data set A and B, have been used to assess this proposed approach. Data set A is synthetic data set obtained from a traffic micro-simulation tool, VISSIM (3). Synthetic data are suitable, from conceptual point of view, for evaluating performance of this proposed model with 100% correct and reliable simulation data. Data set B is empirical data set drawn from a real urban arterial, Kruithuisweg, in the Netherlands. Results obtained from test on empirical data demonstrate the applicability in practice. The rest of this paper is organized as follows: The next section summarizes related literature regarding travel time prediction on urban arterials. In the section thereafter, a discussion of why we choose data-driven approach instead of model-based approach is carefully elaborated. Next, the design of proposed model based on neural network for a segment of urban arterial is addressed, including a discussion how to extend the basic general model to whole route of urban arterial. The last sections evaluate the performance of the proposed models and offer conclusions and directions for future research. THE STATE OF THE ART From literature two main approaches to travel time prediction can be identified: model-based approaches and data-driven approaches. Note that most approaches used for urban environments are data-driven approaches. Here we give a short review of these data-driven models. A comprehensive literature review has been done to summarize previous research efforts aiming at the development of models for estimating travel time from detector output under various traffic and road conditions (4). The authors found the following limitations of previous research: a) most existing models are link-specific and site-dependent so that these limit the applicability and transferability of the models; b) none of the existing models account for the differences in travel times due to movement type; c) field validation is generally missing, although simulation results showed promising. Although non-parameterized methods, such as the k-Nearest Neighbor (k-NN) method (5-7) show the capability to estimate travel time. The basic concept of k-NN is to match the Hao Liu, Hans van Lint, Henk van Zuylen 3 present measurement (e.g. flow, speed, occupancy) with a similar historical pattern. It implicitly acts as an instantaneous model, which assumes traffic condition remaining stationary in the future. Moreover, the choice of temporal window and spatial scope for feature vector require a priori knowledge. For the key parameter k the value of k might be specific for different traffic situations. It is an intensive task to find out appropriate value of k. Lin proposed a Markov Chain model, splitting the delay experienced by drivers at each intersection along arterial roads into two distinctive states, a state of zero-delay and a state of nominal delay (8). This is coupled with a one-step transition matrix that relates the delay of a through vehicle at an intersection to its delay status at the adjacent upstream intersection. However, the effort needed for a detailed calibration of the transition matrix is extremely time-consuming and tedious. Also, it is quite difficult to use empirical data (e.g. loop detector data) to calibrate this model. In (9) Liu reviews previous neural network models by categorizing them into two main branches: enhancement of input layers and the use of a new structure of neural networks. All of these models are regarded as data-driven approaches, which are different from model-based approaches, without physical meaning of transportation systems. To build up neural network models that are able to describe traffic flow, neural network arterial models in (1, 2) have been developed. However, training these neural network models require direct measurements of queue lengths, which are difficult to be measured in real world. Thus, these models still need to be adjusted or improved if no innovative measurement equipment can collect queues in real-life, although they showed promising performance on simulation data. MOTIVATION OF RESEARCH APPROACHES Insight into the limitations of model-based approaches is our motivation to choose a datadriven approach. The classic Lighthill, Whitham and Richards macroscopic traffic model (10) and analytical delay models are possible model-based approaches dealing with specific urban traffic problems. However, they are not suitable for our purpose. The following explains more details about the reasons. The classic Lighthill, Whitham and Richards macroscopic traffic model is capable of describing traffic flow analogously to fluid behavior. Built upon the model of Lighthill and Whitham, several models have been proposed as modifications or extensions in an attempt to overcome inherent limitations in this pioneer model (11-13). However, these models aim at dealing with traffic flow on freeways. The main assumption in both 1 and 2 order macroscopic models is that on segments (typically in the order of 100-500 meters) traffic flows are assumed to be homogeneous. Since urban traffic is interrupted by (controlled or uncontrolled) intersections, deceleration and acceleration behavior may seriously violate those assumptions in both free-flow and congested conditions. Secondly, several analytical delay models have been developed. These calculate travel time as the sum of link free-flow travel time and the sum of delays encountered at intersections. For instance, the models in 2000 HCM, the 1995 Canadian Capacity Guide, and the 1981 Australian Capacity Guide have been widely accepted to derive delays. However, these models implicitly assume that the mean flow rate is constant for the whole analysis period of, to say, 15 minutes or even longer. This assumption is less applicable for real-time delay prediction with dynamic traffic flow. As Viti and van Zuylen showed the variation in flow rates can give highly significant variations in queue length and delays (14). The queuing models for controlled intersections in literature are not suited for traffic flows that vary between cycles, so the alternatives are to use dynamic models to predict travel times or to develop a heuristic travel time model. Hao Liu, Hans van Lint, Henk van Zuylen 4 METHODOLOGY In general, to model traffic flow on road stretches, particularly at network level, one basic element of these stretches is defined as segment/ link. Modeling traffic along a signalized urban arterial can be conducted by assembling each basic segment model together. Appropriate Structure of Neural networks Travel times are the results of complex nonlinear and spatiotemporal dynamics of traffic flow. To capture the dynamic processes, two main concerns for neural networks are: input settings and the structure of neural network. For standard feed-forward neural networks (FNN) the input vector consists of spatially separated inputs at the same time instant, and the output vector corresponds as the same time instant as the input vector. The FNNs do not take into account of temporal relationship between inputs and outputs. To solve the limitation, the so-called time-delayed neural networks (TDNN) are presented to account for input time series with fixed time lags. However, the input selection of temporal dimension (time lag) results in a trade off between model complexity and model generality. In practice, it is quite time-consuming to determine the suitable length of time lags for different spatial inputs. To avoid involving in the selection of input settings, recurrent neural networks (RNN) offer a structure, which allows the analyst to present inputs of consecutive time instants sequentially, while a feedback (memory) mechanism in the model itself takes into account the temporal dynamics. A context layer is connected with hidden layer to store the internal states. The advantage of this context layer is that the selection of input time window (range) is not required. However, if all the spatially separated inputs are augmented in a single input vector, this increases the number of parameters and, hence, may also lead to overly complex models. For instance, let assume a route with 3 segments, each segment has 3 input variables, and each segment requires 5 hidden neurons. Thus, the total number of weight parameters of a RNN model with one single input vector is 375(3×3×3×5+3×5×3×5+3×5×1), while that for a RNN model with 3 basic segment input vectors is 135(3×3×5+3×5×5+3×5×1). Also, the site-specific configuration of neural networks with one single input vector makes transferability to other routes cumbersome. Therefore, this paper will present a generic model, which can describe traffic dynamics within a basic spatial segment, which can be concatenated to predict travel time along a route. The ensuing section presents the basic concept of this paper: modeling traffic dynamics in a basic segment of urban arterials and extending it to an urban street by incorporating with flow prediction. Basic Segment of Urban Streets Along urban streets, vehicles decelerate while approaching stop-lines, stop when traffic lights are in red phase, and accelerate when traffic lights turn green. Due to the heterogeneous and non-stationary nature of urban traffic, local speed measurements (e.g. from inductive loops) provide limited information. For example, Pueboobpaphan shows that homogeneity in most cases doesn’t hold for an urban street with a length in the order of 200m, or even shorter (15). This implies that in an urban environment, local speed measurements are not appropriate to represent section traffic states. The basic segment of urban streets is defined as a link in figure 1(a). Figure 1(b) depicts a typical intersection with four branches, which can be assembled with eight basic segments. Note that no consideration has been taken into the traffic behavior when vehicles travel the inner space of the intersection. Hao Liu, Hans van Lint, Henk van Zuylen 5 Modeling Traffic on a Single Signalized Segment Using Recurrent Neural Network As stated above, there are two key issues of modeling traffic using neural networks: a) selection of a suitable type of neural networks; b) determination of input and output pairs. For the first issue, we propose to use recurrent neural networks (RNN). Elman gives insight in how the RNN manages to represent spatiotemporal patterns in a very efficient distributed manner through its weights (16). The basic idea is to add a context layer as shortterm memory, which stores the previous internal states, in order to learn complex spatiotemporal patterns. Such a RNN mathematically resembles a non-linear discrete statespace model, which in essence operates in the same manner as for example macroscopic traffic models mentioned above. Like these a RNN has a common structure in which current states are functions of previous states and the inputs in the previous time period. Van Lint showed that a particular form of RNN, a state space neural network (SSNN), is suitable to capture the complex spatiotemporal traffic dynamics, and applicable for freeway travel time prediction (17). In Flow A(k) Out Flow D(k)