Billy M. Williams

Urban Freeway Traffic Flow Prediction: Application of Seasonal Autoregressive Integrated Moving Average and Exponential Smoothing Models

The application of seasonal time series models to the single-interval traffic flow forecasting problem for urban freeways is addressed. Seasonal time series approaches have not been used in previous forecasting research. However, time series of traffic flow data are characterized by definite periodic cycles. Seasonal autoregressive integrated moving average (ARIMA) and Winters exponential smoothing models were developed and tested on data sets belonging to two sites: Telegraph Road and the Woodrow Wilson Bridge on the inner and outer loops of the Capital Beltway in northern Virginia. Data were 15-min flow rates and were the same as used in prior forecasting research by B. Smith. Direct comparisons with the Smith report findings were made and it was found that ARIMA (2, 0, 1)(0, 1, 1)96 and ARIMA (1, 0, 1)(0, 1, 1)96 were the best-fit models for the Telegraph Road and Wilson Bridge sites, respectively. Best-fit Winters exponential smoothing models were also developed for each site. The single-step forecasting results indicate that seasonal ARIMA models outperform the nearest-neighbor, neural network, and historical average models as reported by Smith.

Multivariate Vehicular Traffic Flow Prediction: Evaluation of ARIMAX Modeling

Short-term freeway traffic flow forecasting efforts to date have focused on predictions based solely on previous observations at the location of interest. This univariate prediction is useful for certain types of intelligent transportation system (ITS) forecasts, such as operational demand forecasts at system entry points. In addition, data from upstream sensors should improve forecasts at downstream locations. This motivates investigation of multivariate forecast models that include upstream sensor data. A candidate model is transfer functions with autoregressive integrated moving average errors, otherwise known as the ARIMAX model. The ARIMAX model was applied to motorway data from France that had been the subject of previous traffic flow forecasting research. The results indicate that ARIMAX models provide improved forecast performance over univariate forecast models. However, several issues must be addressed before widespread use of ARIMAX models for ITS forecasts is feasible. These issues include the increased complexity of model specification, estimation, and maintenance; model consistency; model robustness in the face of interruptions in the upstream data series; and variability in the cross-correlation between upstream and downstream observations. The last issue is critical because ARIMAX models assume constant transfer function parameters, whereas the correlation between upstream and downstream observations vary with prevailing traffic conditions, especially traffic stream speed. Therefore, further research is needed to investigate model extensions and refinements to provide a generalizable, self-tuning multivariate forecasting model that is easily implemented and that effectively models varying upstream to downstream correlations.

Traffic Management Center Use of Incident Detection Algorithms: Findings of a Nationwide Survey

The focus of this paper is the context in which the decision makers for traffic management centers (TMCs) choose whether to include and/or use automatic incident detection (AID) algorithms. A survey was conducted of TMC professionals in positions to make, influence, or provide input to decisions regarding TMC operational policies as well as decisions regarding priorities for future system enhancements. Analysis of the survey results not only provides an understanding of the reasons behind the limited implementation of AID algorithms but also allows a direct comparison between the conventional incident detection methods and the AID technology on the basis of measured and/or perceived performance. It was observed that 90% of the survey respondents feel that the current methods of incident detection are insufficient either at present (70%) or will be so in the future (20%). This finding alone motivates a need to redouble research efforts aimed at developing robust and accurate automatic detection methods. In this regard, this paper presents promising directions to overcome past AID algorithm deficiencies

Real-Time Short-Term Traffic Speed Level Forecasting and Uncertainty Quantification Using Layered Kalman Filters

Short-term traffic condition forecasting has long been argued as essential for developing proactive traffic control systems that could alleviate the growing congestion in the United States. In this field, short-term traffic condition level forecasting and short-term traffic condition uncertainty forecasting play an equally important role. Past literature showed that linear stochastic time series models are promising in modeling and hence forecasting traffic condition levels and traffic conditional variance with workable performance. On the basis of this finding, an autoregressive moving average plus generalized autoregressive conditional heteroscedasticity structure was proposed for modeling the station-by-station traffic speed series. An online algorithm based on layered Kalman filter was developed for processing this structure in real time. Empirical results based on real-world station-by-station traffic speed data showed that the proposed online algorithm can generate workable short-term traffic speed level forecasts and associated prediction confidence intervals. Future work is recommended to develop and test a proactive traffic control system in a simulated environment, to refine the uncertainty modeling through a stochastic volatility model, and to extend uncertainty modeling and forecasting to link level and network level.

Identification and Calibration of Site-Specific Stochastic Freeway Breakdown and Queue Discharge

The stochastic nature of freeway bottleneck breakdown and queue discharge is investigated through a comprehensive analysis of sensor data collected at bottleneck sites in the San Francisco Bay Area, California, and San Antonio, Texas. A new procedure was proposed to define the stochastic variation of the onset of freeway breakdown and of queue discharge capacity on the basis of time-indexed field data of speed–flow profiles. The former was developed as a function of average vehicle time headways preceding observed conditions when both speed was below and density was above locally defined congested flow thresholds. A full-year 15-min data series was used in the demonstration and testing of the procedure and yielded a high degree of statistical confidence in the resulting estimates of headway distribution parameters. The statistical analysis indicated that the probability function of freeway bottleneck prebreakdown headways followed a shifted lognormal distribution. In addition, a recursive queue discharge model was proposed for bottleneck flows under congested (queued) conditions. The proposed queue discharge model was a simple autocorrelated time series recursion that was seeded with the corresponding prebreakdown flow and dampens to the mean queue discharge rate. The proposed stochastic models are robust and accurate and represent a significant improvement in the understanding and modeling of freeway bottleneck flow. The models were implemented in the mesoscopic network model DYNASMART-P to test the effects of stochastic freeway capacity on sustained service rates and network performance.

Systematic Approach for Validating Traffic Simulation Models

Modeling processes and model testing processes are discussed as parts of the model life cycle, and the tasks of these processes and their relations are highlighted. Of particular interest is the model validation process, which ensures that the model closely simulates what the real system does. A collection of validation techniques is presented to facilitate a systematic check of model performance from various perspectives. Under the qualitative category, a few graphical techniques are presented to help a visual examination of the differences between the simulation and the observation. Under the quantitative category, several statistical measures are discussed to quantify the goodness of fit; to achieve a higher level of confidence about model performance, a simultaneous statistical inference technique is proposed that tests both model accuracy and precision. As an illustrative example, these validation techniques are comprehensively applied to test an enhanced macroscopic simulation model, KWaves, in a systematic manner.

Traveler Information Delivery Mechanisms: Impact on Consumer Behavior

Advanced traveler information systems (ATISs) help individuals make informed travel decisions. Current ATIS applications encompass a variety of delivery mechanisms, including the Internet, telephone, television, radio, variable message signs, and in-vehicle navigation devices to support decisions about destinations, travel mode, departure time, routes, parking, and trip cancellation. It is important for researchers and practitioners to review the status of ATIS technologies and to understand travelers’ access and response to current ATIS deployment. Focusing on largely public-sector delivery mechanisms, this study answers two fundamental questions: whether accessing more information sources is associated with a higher likelihood of travel decision adjustments and which technologies are more likely to elicit substantive adjustments to routine travel. These questions are answered by using a comprehensive and recent behavioral data set, collected in the Research Triangle area of North Carolina. The study generates useful knowledge about how to operate existing traveler information systems more efficiently and how to improve them in the future.

Adaptive Seasonal Time Series Models for Forecasting Short-Term Traffic Flow

Conventionally, most traffic forecasting models have been applied in a static framework in which new observations are not used to update model parameters automatically. The need to perform periodic parameter reestimation at each forecast location is a major disadvantage of such models. From a practical standpoint, the usefulness of any model depends not only on its accuracy but also on its ease of implementation and maintenance. This paper presents an adaptive parameter estimation methodology for univariate traffic condition forecasting through use of three well-known filtering techniques: the Kalman filter, recursive least squares, and least mean squares. Results show that forecasts obtained from recursive adaptive filtering methods are comparable with those from maximum likelihood estimated models. The adaptive methods deliver this performance at a significantly lower computational cost. As recursive, self-tuning predictors, the adaptive filters offer plug-and-play capability ideal for implementation in real-time management and control systems. The investigation presented in this paper also demonstrates the robustness and stability of the seasonal time series model underlying the adaptive filtering techniques.

Data Collection Time Intervals for Stochastic Short-Term Traffic Flow Forecasting

The specification of time intervals for data collection is a fundamental determinant of the nature and utility of the resulting traffic condition data streams. In the context of short-term traffic flow forecasting, the establishment of the data collection time interval should play a key role in determining the corresponding appropriate forecasting approach. The data collection time interval provides the forecasting horizon for one-step-ahead forecasting. Nevertheless, the need for more rigorous understanding of the effects of data collection time interval specification within the context of short-term traffic flow forecasting is not well recognized. By contrast, it has been common practice in previous research to select the data collection time interval and forecasting approach without explicit consideration of time interval effects or systematic evaluation of available forecasting methods. A stochastic seasonal autoregressive integrated moving average plus generalized autoregressive conditional heteroscedasticity (SARIMA+GARCH) structure proposed in previous work holds promise in providing accurate point forecasts and reasonable forecasting confidence intervals. In this paper, a spectrum of data collection time intervals is tested with an online forecasting algorithm developed based on the SARIMA+GARCH structure to determine the applicable data collection time intervals for this structure. In this test, both the forecast accuracy and the validity of the forecasting confidence intervals are investigated. This work serves as an important step toward establishing a short-term traffic condition forecasting framework that identifies appropriate forecasting approaches for candidate data collection time intervals based on the functional requirements of specific applications.

The Network Kinematic Waves Model: A Simplified Approach to Network Traffic

Flow of traffic on freeways and limited access highways can be represented as a series of kinemetic waves. Solutions to these systems of equations become problematic under congested traffic flow conditions, and under complicated (real-world) networks. A simplified theory of kinematics waves (KWaves) was previously proposed. Simplifying elements includes translation of the problem to moving coordinate system, adoption of triangular speed-density relationships, and adoption of restrictive constraints at the on- and off-ramps. However, these simplifying assumptions preclude application of this technique to most practical situations. By directly addressing the limitations of the original theory, this article proposes a simplified Kwaves model for network traffic (N-KWaves). Several key constraints of the original theory are relaxed. For example, the original merge model, which gives full priority to on-ramp traffic, is relaxed and replaced with a capacity-based weighted queuing (CBWFQ) merge model. The original diverge model, which blocks upstream traffic as a whole when a downstream queue exceeds the diverge, is also relaxed and replaced with a contribution-based weighted splitting (CBWS) diverge model. Based on the above, the original theory is reformulated and extended to address network traffic. Central to the N-KWaves model is a five-step computational procedure based on a generic building block. It is assumed that a freeway network can be represented by the combination of some special cases of the generic building block. An empirical field study showed satisfactory results. The N-KWaves model is best suited for modeling traffic operation in a regional freeway network and has a strong connection to Intelligent Transportation Systems (ITS).