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In this study, we introduce and investigate a new class of split inverse problems, comprising a multidimensional parameter of evolution, which we call the multidimensional split variational inequality problem with multiple output sets. To demonstrate its applicability, we formulate the equilibrium flow of multidimensional traffic network models for an arbitrary number of locations. We define a multidimensional split Wardrop condition with multiple output sets and establish its equivalence with the formulated equilibrium flow of multidimensional traffic network models. We then establish the existence and uniqueness of equilibria for our proposed model. In addition, we propose a method for solving the introduced problem. We then validate our results using some numerical experiments. [ABSTRACT FROM AUTHOR]

Short-term traffic-flow forecasting, the process of predicting future traffic conditions based on historical and real-time observations, is an essential aspect of intelligent transportation systems. The existing well-known algorithms used for short-term traffic flow include time-series analysis-based techniques, of which the seasonal auto-regressive moving average model is one of the most precise methods used in this field. The effectiveness of short-term traffic flow in an urban transport network can be fully realised only in its multivariate form where traffic flow is predicted at multiple sites simultaneously. In this paper, this concept in explored utilising an additive seasonal vector auto-regressive moving average model to predict traffic flow in the short-term future considering the spatial dependency among multiple sites. The dynamic linear model representation of the auto-regressive moving average model is used to reduce the number of latent variables. The parameters of the model are estimated in a Bayesian inference framework employing a Markov chain Monte Carlo sampling method. The efficiency of the proposed prediction algorithm is evaluated by modelling real-time traffic-flow observations available from a certain junction in the city centre of Dublin, Ireland. [ABSTRACT FROM AUTHOR]

Predictions of fundamental traffic variables in the short-term or near-term future are vital for any successful dynamic traffic management application. Univariate short-term traffic flow prediction algorithms are popular in literature. However, to facilitate the operationalities of advanced adaptive traffic management systems, there is a necessity of developing multivariate traffic condition prediction algorithms. A new multivariate short-term traffic flow and speed prediction methodology is proposed in this paper where the traffic flow and speed observations from uncongested (or linear) and congested (or nonlinear) regimes are regime-adjusted to ensure consistent system dynamics. The prediction methodology is developed by using artificial neural networks (ANN) algorithms in conjunction with adaptive learning rules. These learning rules demonstrate significantly improved accuracy and simultaneous reduction in computation times. Additionally, the paper attempts to identify the most suitable adaptive learning rule from a chosen pool of rules. The validation of the prediction methodology is performed by using traffic data from multiple locations in the United Kingdom (U.K.). The results indicate that the proposed multivariate forecasting algorithm is effective and computationally parsimonious to simultaneously predict traffic flow and speed in freeway or highway networks. [ABSTRACT FROM AUTHOR]

The existing well-known short-term traffic forecasting algorithms require large traffic flow data sets, including information on current traffic scenarios to predict the future traffic conditions. This article proposes a random process traffic volume model that enables estimation and prediction of traffic volume at sites where such large and continuous data sets of traffic condition related information are unavailable. The proposed model is based on a combination of wavelet analysis (WA) and Bayesian hierarchical methodology (BHM). The average daily 'trend' of urban traffic flow observations can be reliably modeled using discrete WA. The remaining fluctuating parts of the traffic volume observations are modeled using BHM. This BHM modeling considers that the variance of the urban traffic flow observations from an intersection vary with the time-of-the-day. A case study has been performed at two busy junctions at the city-centre of Dublin to validate the effectiveness of the strategy. [ABSTRACT FROM AUTHOR]

The paper develops a short-term space-time traffic flow forecasting strategy integrating the empirical-based seasonal autoregressive integrated moving average (SARIMA) time-series forecasting technique with the theoretical-based first-order macroscopic traffic flow model—cell transmission model. A case study in Dublin city center which has serious traffic congestion is performed to test the effectiveness of the proposed multivariate traffic forecasting strategy. The results show that the forecasts at the junctions only deviate around 10% at a maximum from the original observations and seem to indicate that the proposed strategy is one of the effective approaches to predict the real-time traffic flow level in a congested network especially at the locations where no continuous data collection takes place. [ABSTRACT FROM AUTHOR]

The seasonal autoregressive integrated moving average (SARIMA) model is one of the popular univariate time-series models in the field of short-term traffic flow forecasting. The parameters of the SARIMA model are commonly estimated using classical (maximum likelihood estimate and/or least-squares estimate) methods. In this paper, instead of using classical inference the Bayesian method is employed to estimate the parameters of the SARIMA model considered for modeling. In Bayesian analysis the Markov chain Monte Carlo method is used to solve the posterior integration problem in high dimension. Each of the estimated parameters from the Bayesian method has a probability density function conditional to the observed traffic volumes. The forecasts from the Bayesian model can better match the traffic behavior of extreme peaks and rapid fluctuation. Similar to the estimated parameters, each forecast has a probability density curve with the maximum probable value as the point forecast. Individual probability density curves provide a time-varying prediction interval unlike the constant prediction interval from the classical inference. The time-series data used for fitting the SARIMA model are obtained from a certain junction in the city center of Dublin. [ABSTRACT FROM AUTHOR]