Discrete Dynamics in Nature and Society

Volume 2018, Article ID 7650928, 12 pages

https://doi.org/10.1155/2018/7650928

## Two-Phase Model of Multistep Forecasting of Traffic State Reliability

^{1}Dr., College of Urban Railway Transportation, Shanghai University of Engineering Science, China^{2}Prof., College of Urban Railway Transportation, Shanghai University of Engineering Science, China^{3}Prof., Faculty of Maritime and Transportation, Ningbo University, China

Correspondence should be addressed to Zhigang Liu; nc.ude.seus@10006001

Received 7 November 2017; Revised 29 January 2018; Accepted 21 May 2018; Published 9 July 2018

Academic Editor: Aura Reggiani

Copyright © 2018 Jufen Yang et al. 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

Multistep prediction of traffic state is a key technology for advanced transportation information system. The research results based on the principle of multistep prediction can provide more information about the traffic operating quality in advance. Considering that prediction error increases with the increasing numbers of multistep predictions, this research proposes the concept of dynamic predictability that is related to the characteristic of historical traffic flow data used. The traffic flow is characterized by randomness, regularity, and volatility according to the traffic flow theory. Therefore, three key indexes are firstly calculated to measure the characteristics of reliability series. Then a two-phase model is established based on wavelet neural network optimized by particle swarm optimization. The upper phase is a model to estimate the number of predictable steps, and the lower phase is the multistep prediction model of reliability. Compared with that of backpropagation neural network and support vector machine, results show that the convergence time of the wavelet neural network optimized by particle swarm optimization is the lowest, which only costs 256 and 291 seconds in both two-phase models under the same conditions. The average relative error of multistep prediction reached the lowest value, 8.91% and 12.01%, respectively, for weekday and weekend data used. Moreover, the prediction performance based on weekday is better than that of weekend. The research results lay a decision-making basis for managers in determining the key parts of road network to develop future improvement measures.

#### 1. Introduction

In recent decades, the increasing demand for road transportation has negatively affected the stability and reliability of traffic operation which caused a series of drawbacks, such as extensive waste of travel time, decreasing of environmental quality, and aggravated vehicle wear and tear. Meanwhile, the requirement for accurate prediction of traffic state is increasing. Prediction results serve not only as an important basis for traffic control and guidance but also as a decision support for travelers to adjust their travel plan.

Development of Advanced Traveler Information Systems usually divides traffic state into three states: smooth, congested, and blocked. It has oversimplified the problem since traffic state parameter is a continuous variable, e.g., flow, density, and speed. This study presents a new concept to describe traffic state. It is the traffic state reliability which is defined as the degree of actual traffic flow relative to the free flow, which assumes that the reliability of free flow is highest. In order to get the traffic flow trend in the future, the forecasting of traffic state reliability is needed to quantitatively measure the reliability of each alternative in future.

For example, there are five links A, B, C, D, and E for the travelers. The prediction result shows that links A, C, and D are in smooth state. However, the travelers do not know how to determine which is the best link among links A, C, and D. If the reliability prediction could provide the level of actual traffic flow relative to the most reliable free flow state of each link (that is, 0.9, 0.2, 0.92, 0.79, and 0.1). Obviously, the traveler will prioritize link C with the highest reliability value to travel.

Antoniou et al. [1] present an approach for local traffic state estimation and traffic state prediction; the method exploits all available (traffic and other) information and uses data-driven computational techniques. The approach is advantageous as it can flexibly incorporate additional explanatory variables. Given that previously proposed models can outperform current state-of-the-art models, integrating them into existing traffic estimation and prediction models is valuable. Current technologies, such as global position system- (GPS-) enabled cell phones, can record vehicle trajectories and have opened a new way of collecting traffic data. Hiribarren and Herrera [2] present and assess a new method to estimate traffic states on arterials based on trajectory data. The method is based on the Lighthill–Whitham–Richards theory. Preliminary analysis based on microsimulation suggested that this method yields good traffic state estimates at congested and uncongested situations. Mannini et al. [3] explore traffic state estimation on freeways in urban areas and route-based data to properly feed a second-order traffic flow model. This model is recursively corrected by an extended Kalman filter. Considering the lack of real-time information, these authors use simulation-based data to improve the traffic state estimation accuracy.

In recent years, traffic data are currently collected through various sensors, including loop detectors, probe vehicles, cell phones, Bluetooth devices, video cameras, remote sensing applications, and public transport smart cards. Nantes et al. [4] develop a new model-based methodology for real-time traffic state estimation in urban corridors from multiple sources, particularly from loop detectors and partial observations from Bluetooth and GPS devices. Zheng and Su [5] develop a novel algorithm based on compressed sensing theory to recover traffic data with Gaussian measurement noise, missing partial data, and corrupted noise using information recovered from noisy traffic data and traffic state estimation. These authors extend traffic state estimation method to handle traffic state variables of high dimensions.

Traffic state estimation is a key problem with considerable implication for modern traffic management. Kong et al. [6] propose a novel approach to efficiently estimate and predict urban traffic congestion using floating car trajectory data. An innovative traffic flow prediction method using particle swarm optimization is used to calculate the traffic flow parameters for predicting traffic congestion. Then, a congestion state fuzzy division module is applied to convert the predicted flow parameters to the cognitive congestion state of citizens.

Travelers should be able to select the best path to avoid traffic congestion. However, if travelers also avoid the link with high variability, then travelers will enjoy additional benefits, that is, the “reliability benefits.” To date, traffic reliability has introduced the idea of reliability into traffic research and is an important field of traffic problems analysis. Considerable research has been conducted on traffic reliability, covering from theory to practice and from model to algorithm. Frameworks for reliability analysis have also been developed.

Wang et al. [7] comprehensively review the literature on traffic reliability. Basic definitions, theory, and methods are depicted accompanied with the application of traffic optimization. These authors also discuss the future development of traffic reliability research. Xiao et al. [8, 9] consider the influence of travel time variability on the congestion profile in the presence of endogenous congestion and the role of scheduling preferences. The results show that the cost of travel time variability is the same in exogenous or endogenous congestion for two classes of preferences: linear at work and constant-exponential marginal utility of time. He et al. [10] introduce road segment and network congestion indexes to, respectively, measure the congestion levels of urban road segment and network. He also carries out a traffic congestion analysis for Beijing expressway network, based on the speed performance data.

Probabilistic forecasting of reliability can be used for risk-averse routing. Bezuglov and Comert [11] have studied the possible applications and accuracy levels of three gray system theory models for short-term traffic speed and travel time predictions. Gray models consistently demonstrate low prediction errors over all time series, thereby successfully improving the accuracy by approximately 50% on average in root-mean-squared errors and mean absolute percent errors. Traffic parameters can vary due to several factors, such as weather, accidents, and driving characteristics. Comert et al. [12] develop a model to predict traffic speed under abrupt change. The developed model is tested from 1-step to 45-step forecasts. The accuracy of predictions is improved until the 15-step forecast compared with nonadaptive and mean adaptive models. Although the developed model is not retrained on different data sets, the method provides better results than or close results to nonadaptive and adaptive models that are retrained on the corresponding data set. Chen and Rakha [13] develop an agent-based modeling approach to predict multistep ahead experienced travel time using real-time and historical spatiotemporal traffic data. The results show that the agent-based modeling approach produced the least prediction errors compared with other state-of-the-practice and state-of-the-art methods (such as instantaneous travel time, historical average, and k-nearest neighbor). The fast algorithm computation allows the proposed approach to be implemented in real-time applications in traffic management centers.

Papathanasopoulou et al. [14] develop a methodology to realize online calibration of microscopic traffic simulation models for dynamic multistep prediction of traffic measures. The application leads to less than 10% error in speed prediction even for 10 steps into the future in all considered data sets. Rajabzadeh et al. [15] provide a two-step approach based on stochastic differential equations to improve short-term prediction. At the first step, a Hull–White model is applied to obtain a baseline prediction model from previous days. Then, the extended Vasicek model is employed to model the difference between observations and baseline predictions (residuals) during an individual day. The results show that the proposed model can accurately input the missing data in traffic data set.

In summary, most studies focus on traffic state estimation and travel time reliability, which mainly emphasize the traffic quality but not the reliability of traffic quality. Advanced Traveler Information System is one of the functional areas of Intelligent Transportation Systems and aims to provide forecasted traffic information for travelers to make better decisions. There are two methods to forecast the traffic data. One is one-step prediction, which predicts the reliability in the next one step. The other is fixed multistep prediction, in which the number of prediction steps is fixed. The results of fixed multistep prediction show that it easily leads to large prediction errors and the prediction errors gradually linearly increase with the number of multisteps [14]. For example, fixed multistep prediction can obtain the reliability in the next 10 days or even 30 days; however, the prediction error may be 10% in the next 10 days and 40% in the next 30 days. If an acceptable prediction errors is less than 20% for travelers (it can be obtained through investigation), do you want an accurate 10-day forecast or an inaccurate 30-day forecast? How to determine the number of predictable steps, which can not only guarantee exceeding the acceptable prediction errors but also provide as much future reliability data as possible. If there is a certain number* S* of steps to guarantee it, the number* S* of predictable steps is defined as the dynamic predictability.

The proposed concept of dynamic predictability needs to find the number* S* of predictable steps. After determining the number of predictable steps, the multistep prediction limited to the number of predictable steps will be performed. The realization of this theoretical principle is described in the following. Firstly, the traffic state reliability is defined, and the multistep forecasting theory and basic conditions are put forward in Section 2. Section 3 describes a two-phase model which determines the number of predictable steps in the upper-phase model and performs multistep prediction in the lower-phase model. Based on this, Section 4 verifies the validity and accuracy of the proposed method by applying actual traffic data. Section 5 summarizes the research conclusions.

#### 2. Methodology

The definition of traffic state reliability (TSR) is the basis for setting a method to measure reliable level of traffic state. What is the relationship between past and present reliability and the future reliability? It is the discussion focus of this part.

##### 2.1. Traffic State Reliability Calculation

For a link, intersection, or road network, TSR is defined as the degree of actual traffic flow state relative to the most reliable free flow state, which assumes that the reliability of free flow state is highest. It uses the TSR index to quantify evaluation, which is the ratio between actual speed and free flow speed in this research. TRS is classified to be equal to 1, when the actual speed is larger than or equal to the free flow speed and equal to (see (1)) when the actual speed is less than the free flow speed. Therefore, TSR value is distributed from 0 to 1 and is calculated as where is the TSR of link or direction link* p* at the period* t*; is the average travel speed of link or direction link* p* at the period* t*; is the free flow speed of link or direction link* p*.

##### 2.2. Multistep Prediction Principle

One-step prediction [11] means predicting the reliability index in the next one step based on current and past reliability index series. Multistep prediction [12] means predicting the reliability index in the next several steps. The reliability series of Monday consists of TSR of the continuously (t-n+1)th Monday, , (t-1)th Monday, ,* t*th Monday, also for all the other days of the week. The prediction principle of future* S*th series of reliability iswhere , , and* t* is the current time interval; represents the predictive value of reliability in the next* (**)*th interval; represents the predictive function;* n* is the number of time intervals.

The above method can be used to offline predict the reliability of the next S steps by a kind of prediction method. The prediction results show that the average prediction errors gradually linearly increase with the number of steps. The graph shows the relationship between the average prediction errors and the number S of steps is seen in Figure 1 (Data Source in Section 4.1). The acceptable prediction errors investigated are less than 20% for travelers. Ultimately, the error 20% is the error threshold; the number* S* of steps corresponding to error 20% is the dynamic predictability. The prediction error is related to the characteristic of historical traffic flow data used. Traffic flow is characterized by randomness, regularity, and volatility according to traffic flow theory [8, 9]. Therefore, three key indexes should be first calculated to measure the characteristics of reliability series. Then, a model should be constructed to associate the key index with the dynamic predictability.