Saif Eddin Jabari

Fangfang Zheng, Saif Eddin Jabari, Henry X. Liu et al.

This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty. It also results in smooth vehicle trajectories in a stochastic context, which is in agreement with real-world traffic dynamics and, thereby, overcoming issues with aggressive oscillation typically observed in sample paths of stochastic traffic flow models. We utilize ensemble filtering techniques for data assimilation (traffic state estimation), but derive the mean and covariance dynamics as the ensemble sizes go to infinity, thereby bypassing the need to sample from the parameter distributions while estimating the traffic states. As a result, the estimation algorithm is just a standard Kalman-Bucy algorithm, which renders the proposed approach amenable to real-time applications using recursive data. Data assimilation examples are performed and our results indicate good agreement with out-of-sample data.

Li Li, Saif Eddin Jabari

Decentralized intersection control techniques have received attention in the literature as tools that address scalability issues of network intersection control. Chief among these techniques are backpressure (BP) control algorithms, which were originally developed of for large wireless networks. In addition to being light-weight computationally, they come with guarantees of performance at the network level, specifically network-wide stability. The dynamics in backpressure control are represented using networks of point queues and this also applies to all of the applications to traffic control. As such, BP in traffic fail to capture the spatial distribution of vehicles along the intersection links and, consequently, spill-back dynamics. This paper derives a position weighted backpressure (PWBP) control policy for network traffic applying continuum modeling principles of traffic dynamics and thus capture the spatial distribution of vehicles along network roads and spill-back dynamics. PWBP inherits the computational advantages of traditional BP. To prove stability of PWBP, (i) a Lyapunov functional that captures the spatial distribution of vehicles is developed; (ii) the capacity region of the network is formally defined in the context of macroscopic network traffic; and (iii) it is proved, when exogenous arrival rates are within the capacity region, that PWBP control is network stabilizing. We conduct comparisons against a real-world adaptive control implementation for an isolated intersection. Comparisons are also performed against other BP approaches in addition to optimized fixed timing control at the network level. These experiments demonstrate the superiority of PWBP over the other control policies in terms of capacity region, network-wide delay, congestion propagation speed, recoverability from heavy congestion (outside of the capacity region), and response to incidents.

Yue Wang, Wenqing Li, Esha Sarkar et al.

Backdoor attacks impose a new threat in Deep Neural Networks (DNNs), where a backdoor is inserted into the neural network by poisoning the training dataset, misclassifying inputs that contain the adversary trigger. The major challenge for defending against these attacks is that only the attacker knows the secret trigger and the target class. The problem is further exacerbated by the recent introduction of "Hidden Triggers", where the triggers are carefully fused into the input, bypassing detection by human inspection and causing backdoor identification through anomaly detection to fail. To defend against such imperceptible attacks, in this work we systematically analyze how representations, i.e., the set of neuron activations for a given DNN when using the training data as inputs, are affected by backdoor attacks. We propose PiDAn, an algorithm based on coherence optimization purifying the poisoned data. Our analysis shows that representations of poisoned data and authentic data in the target class are still embedded in different linear subspaces, which implies that they show different coherence with some latent spaces. Based on this observation, the proposed PiDAn algorithm learns a sample-wise weight vector to maximize the projected coherence of weighted samples, where we demonstrate that the learned weight vector has a natural "grouping effect" and is distinguishable between authentic data and poisoned data. This enables the systematic detection and mitigation of backdoor attacks. Based on our theoretical analysis and experimental results, we demonstrate the effectiveness of PiDAn in defending against backdoor attacks that use different settings of poisoned samples on GTSRB and ILSVRC2012 datasets. Our PiDAn algorithm can detect more than 90% infected classes and identify 95% poisoned samples.

Bilal Thonnam Thodi, Sai Venkata Ramana Ambadipudi, Saif Eddin Jabari

Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial differential equations with applications in macroscopic traffic flow models. In this framework, an operator is trained to map heterogeneous and sparse traffic input data to the complete macroscopic traffic state in a supervised learning setting. We chose a physics-informed Fourier neural operator ($π$-FNO) as the operator, where an additional physics loss based on a discrete conservation law regularizes the problem during training to improve the shock predictions. We also propose to use training data generated from random piecewise constant input data to systematically capture the shock and rarefied solutions. From experiments using the LWR traffic flow model, we found superior accuracy in predicting the density dynamics of a ring-road network and urban signalized road. We also found that the operator can be trained using simple traffic density dynamics, e.g., consisting of $2-3$ vehicle queues and $1-2$ traffic signal cycles, and it can predict density dynamics for heterogeneous vehicle queue distributions and multiple traffic signal cycles $(\geq 2)$ with an acceptable error. The extrapolation error grew sub-linearly with input complexity for a proper choice of the model architecture and training data. Adding a physics regularizer aided in learning long-term traffic density dynamics, especially for problems with periodic boundary data.

Bilal Thonnam Thodi, Sai Venkata Ramana Ambadipudi, Saif Eddin Jabari

We study learning weak solutions to nonlinear hyperbolic partial differential equations (H-PDE), which have been difficult to learn due to discontinuities in their solutions. We use a physics-informed variant of the Fourier Neural Operator ($π$-FNO) to learn the weak solutions. We empirically quantify the generalization/out-of-sample error of the $π$-FNO solver as a function of input complexity, i.e., the distributions of initial and boundary conditions. Our testing results show that $π$-FNO generalizes well to unseen initial and boundary conditions. We find that the generalization error grows linearly with input complexity. Further, adding a physics-informed regularizer improved the prediction of discontinuities in the solution. We use the Lighthill-Witham-Richards (LWR) traffic flow model as a guiding example to illustrate the results.

Yue Wang, Wending Li, Michail Maniatakos et al.

Deep Reinforcement Learning (DRL) enhances the efficiency of Autonomous Vehicles (AV), but also makes them susceptible to backdoor attacks that can result in traffic congestion or collisions. Backdoor functionality is typically incorporated by contaminating training datasets with covert malicious data to maintain high precision on genuine inputs while inducing the desired (malicious) outputs for specific inputs chosen by adversaries. Current defenses against backdoors mainly focus on image classification using image-based features, which cannot be readily transferred to the regression task of DRL-based AV controllers since the inputs are continuous sensor data, i.e., the combinations of velocity and distance of AV and its surrounding vehicles. Our proposed method adds well-designed noise to the input to neutralize backdoors. The approach involves learning an optimal smoothing (noise) distribution to preserve the normal functionality of genuine inputs while neutralizing backdoors. By doing so, the resulting model is expected to be more resilient against backdoor attacks while maintaining high accuracy on genuine inputs. The effectiveness of the proposed method is verified on a simulated traffic system based on a microscopic traffic simulator, where experimental results showcase that the smoothed traffic controller can neutralize all trigger samples and maintain the performance of relieving traffic congestion

Chuhan Yang, Sai Venkata Ramana Ambadipudi, Saif Eddin Jabari

The adaptive smoothing method (ASM) is a standard data-driven technique used in traffic state estimation. The ASM has free parameters which, in practice, are chosen to be some generally acceptable values based on intuition. However, we note that the heuristically chosen values often result in un-physical predictions by the ASM. In this work, we propose a neural network based on the ASM which tunes those parameters automatically by learning from sparse data from road sensors. We refer to it as the adaptive smoothing neural network (ASNN). We also propose a modified ASNN (MASNN), which makes it a strong learner by using ensemble averaging. The ASNN and MASNN are trained and tested two real-world datasets. Our experiments reveal that the ASNN and the MASNN outperform the conventional ASM.

Chuhan Yang, Fares B. Mehouachi, Monica Menendez et al.

Predicting traffic flow in data-scarce cities is challenging due to limited historical data. To address this, we leverage transfer learning by identifying periodic patterns common to data-rich cities using a customized variant of Dynamic Mode Decomposition (DMD): constrained Hankelized DMD (TrHDMD). This method uncovers common eigenmodes (urban heartbeats) in traffic patterns and transfers them to data-scarce cities, significantly enhancing prediction performance. TrHDMD reduces the need for extensive training datasets by utilizing prior knowledge from other cities. By applying Koopman operator theory to multi-city loop detector data, we identify stable, interpretable, and time-invariant traffic modes. Injecting ``urban heartbeats'' into forecasting tasks improves prediction accuracy and has the potential to enhance traffic management strategies for cities with varying data infrastructures. Our work introduces cross-city knowledge transfer via shared Koopman eigenmodes, offering actionable insights and reliable forecasts for data-scarce urban environments.

Wenqing Li, Yue Wang, Muhammad Shafique et al.

Recent studies reveal that Autonomous Vehicles (AVs) can be manipulated by hidden backdoors, causing them to perform harmful actions when activated by physical triggers. However, it is still unclear how these triggers can be activated while adhering to traffic principles. Understanding this vulnerability in a dynamic traffic environment is crucial. This work addresses this gap by presenting physical trigger activation as a reachability problem of controlled dynamic system. Our technique identifies security-critical areas in traffic systems where trigger conditions for accidents can be reached, and provides intended trajectories for how those conditions can be reached. Testing on typical traffic scenarios showed the system can be successfully driven to trigger conditions with near 100% activation rate. Our method benefits from identifying AV vulnerability and enabling effective safety strategies.

Nishant Suresh Aswani, Saif Eddin Jabari, Muhammad Shafique

The strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable. We draw from a dynamical systems view of neural networks, offering a fresh perspective by using Koopman operator theory and its connections with dynamic mode decomposition (DMD). Together, they offer a framework for linearizing dynamical systems by embedding the system into an appropriate observable space. By reframing a neural network as a dynamical system, we demonstrate that we can replace the nonlinear layer in a pretrained multi-layer perceptron (MLP) with a finite-dimensional linear operator. In addition, we analyze the eigenvalues of DMD and the right singular vectors of SVD, to present evidence that time-delayed coordinates provide a straightforward and highly effective observable space for Koopman theory to linearize a network layer. Consequently, we replace layers of an MLP trained on the Yin-Yang dataset with predictions from a DMD model, achieving a mdoel accuracy of up to 97.3%, compared to the original 98.4%. In addition, we replace layers in an MLP trained on the MNIST dataset, achieving up to 95.8%, compared to the original 97.2% on the test set.

Nishant Suresh Aswani, Saif Eddin Jabari

Recent work has shown that contiguous vision transformer (ViT) blocks (a) can be replaced by a linear map and (b) organize into recurrent phases of computation. We ask whether these observations coincide: does ViT depth implement approximately \textit{autonomous linear} dynamics, admitting a single operator $K$ applied recurrently across a contiguous span? We test this using Dynamic Mode Decomposition (DMD), which fits $K$ from selected, consecutive hidden-state pairs and predicts $p$ steps ahead via $K^p$. On four pretrained DINO ViTs, we study the regularization, rank, and calibration budget required for stable fitting. For short spans ($p \leq 4$), $K^p$ tracks an unconstrained endpoint map to within $0.02$ cosine similarity on DINOv3-H/16+, while also recovering intermediate activations at each skipped block. At early cut starts, the fitted operators compress to rank $\ll d$ with minimal calibration data, and across tokens, \texttt{cls} is most amenable to linearization; both properties decay monotonically with depth. Yet this local fidelity does not transfer downstream. At the final hidden state, after propagating through the remaining blocks, an identity baseline becomes competitive.

Prajwal Chauhan, Salah Eddine Choutri, Mohamed Ghattassi et al.

This paper investigates the limitations of neural operators in learning solutions for a Hughes model, a first-order hyperbolic conservation law system for crowd dynamics. The model couples a Fokker-Planck equation representing pedestrian density with a Hamilton-Jacobi-type (eikonal) equation. This Hughes model belongs to the class of nonlinear hyperbolic systems that often exhibit complex solution structures, including shocks and discontinuities. In this study, we assess the performance of three state-of-the-art neural operators (Fourier Neural Operator, Wavelet Neural Operator, and Multiwavelet Neural Operator) in various challenging scenarios. Specifically, we consider (1) discontinuous and Gaussian initial conditions and (2) diverse boundary conditions, while also examining the impact of different numerical schemes. Our results show that these neural operators perform well in easy scenarios with fewer discontinuities in the initial condition, yet they struggle in complex scenarios with multiple initial discontinuities and dynamic boundary conditions, even when trained specifically on such complex samples. The predicted solutions often appear smoother, resulting in a reduction in total variation and a loss of important physical features. This smoothing behavior is similar to issues discussed by Daganzo (1995), where models that introduce artificial diffusion were shown to miss essential features such as shock waves in hyperbolic systems. These results suggest that current neural operator architectures may introduce unintended regularization effects that limit their ability to capture transport dynamics governed by discontinuities. They also raise concerns about generalizing these methods to traffic applications where shock preservation is essential.

Fares B. Mehouachi, Saif Eddin Jabari

Adversarial training is a cornerstone of robust deep learning, but fast methods like the Fast Gradient Sign Method (FGSM) often suffer from Catastrophic Overfitting (CO), where models become robust to single-step attacks but fail against multi-step variants. While existing solutions rely on noise injection, regularization, or gradient clipping, we propose a novel solution that purely controls the $l^p$ training norm to mitigate CO. Our study is motivated by the empirical observation that CO is more prevalent under the $l^{\infty}$ norm than the $l^2$ norm. Leveraging this insight, we develop a framework for generalized $l^p$ attack as a fixed point problem and craft $l^p$-FGSM attacks to understand the transition mechanics from $l^2$ to $l^{\infty}$. This leads to our core insight: CO emerges when highly concentrated gradients where information localizes in few dimensions interact with aggressive norm constraints. By quantifying gradient concentration through Participation Ratio and entropy measures, we develop an adaptive $l^p$-FGSM that automatically tunes the training norm based on gradient information. Extensive experiments demonstrate that this approach achieves strong robustness without requiring additional regularization or noise injection, providing a novel and theoretically-principled pathway to mitigate the CO problem.

Salah Eddine Choutri, Prajwal Chauhan, Othmane Mazhar et al.

The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural Operators, MCNO makes no spectral or translation-invariance assumptions. The kernel is represented as a learnable tensor over a fixed set of randomly sampled points. This design enables generalization across multiple grid resolutions without relying on fixed global basis functions or repeated sampling during training. Experiments on standard 1D PDE benchmarks show that MCNO achieves competitive accuracy with low computational cost, providing a simple and practical alternative to spectral and graph-based neural operators.

Salah Eddine Choutri, Prajwal Chauhan, Othmane Mazhar et al.

The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral operator using a Monte Carlo-type approach. Unlike Fourier Neural Operators (FNOs), which rely on spectral representations and assume translation-invariant kernels, MCNO makes no such assumptions. The kernel is represented as a learnable tensor over sampled input-output pairs, and sampling is performed once, uniformly at random from a discretized grid. This design enables generalization across multiple grid resolutions without relying on fixed global basis functions or repeated sampling during training, while an interpolation step maps between arbitrary input and output grids to further enhance flexibility. Experiments on standard 1D PDE benchmarks show that MCNO achieves competitive accuracy with efficient computational cost. We also provide a theoretical analysis proving that the Monte Carlo estimator yields a bounded bias and variance under mild regularity assumptions. This result holds in any spatial dimension, suggesting that MCNO may extend naturally beyond one-dimensional problems. More broadly, this work explores how Monte Carlo-type integration can be incorporated into neural operator frameworks for continuous-domain PDEs, providing a theoretically supported alternative to spectral methods (such as FNO) and to graph-based Monte Carlo approaches (such as the Graph Kernel Neural Operator, GNO).

Fares B. Mehouachi, Saif Eddin Jabari

We introduce FlowMixer, a neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns. At its core, FlowMixer incorporates non-negative matrix mixing layers within a reversible mapping framework-applying transforms before mixing and their inverses afterward. This shape-preserving design enables a Kronecker-Koopman eigenmode framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. Extensive experiments across diverse domains demonstrate FlowMixer's robust long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. These results suggest that architectural constraints can simultaneously enhance predictive performance and mathematical interpretability in neural forecasting systems.

Nishant Suresh Aswani, Saif Eddin Jabari

This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers, treating these representations as states in a dynamical system. Our approach learns a surrogate model that predicts how neural representations transform from input to output, with two key advantages. First, by way of lifting the original states via an autoencoder, it operates in a linear space, making editing the dynamics straightforward. Second, it preserves the topologies of the original representations by regularizing the autoencoding objective. We demonstrate that these surrogate models naturally replicate the progressive topological simplification observed in neural networks. As a practical application, we show how our approach enables targeted class unlearning in the Yin-Yang and MNIST classification tasks.

Bilal Thonnam Thodi, Zaid Saeed Khan, Saif Eddin Jabari et al.

Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the macroscopic traffic speed dynamics from these space-time visualizations, and demonstrate its application in the framework of traffic state estimation. Compared to existing estimation approaches, our approach allows a finer estimation resolution, eliminates the dependence on the initial conditions, and is agnostic to external factors such as traffic demand, road inhomogeneities and driving behaviors. Our model respects causality in traffic dynamics, which improves the robustness of estimation. We present the high-resolution traffic speed fields estimated for several freeway sections using the data obtained from the Next Generation Simulation Program (NGSIM) and German Highway (HighD) datasets. We further demonstrate the quality and utility of the estimation by inferring vehicle trajectories from the estimated speed fields, and discuss the benefits of deep neural network models in approximating the traffic dynamics.

Bilal Thonnam Thodi, Zaid Saeed Khan, Saif Eddin Jabari et al.

We propose a kinematic wave-based Deep Convolutional Neural Network (Deep CNN) to estimate high-resolution traffic speed fields from sparse probe vehicle trajectories. We introduce two key approaches that allow us to incorporate kinematic wave theory principles to improve the robustness of existing learning-based estimation methods. First, we propose an anisotropic traffic kernel for the Deep CNN. The anisotropic kernel explicitly accounts for space-time correlations in macroscopic traffic and effectively reduces the number of trainable parameters in the Deep CNN model. Second, we propose to use simulated data for training the Deep CNN. Using a targeted simulated data for training provides an implicit way to impose desirable traffic physical features on the learning model. In the experiments, we highlight the benefits of using anisotropic kernels and evaluate the transferability of the trained model to real-world traffic using the Next Generation Simulation (NGSIM) and the German Highway Drone (HighD) datasets. The results demonstrate that anisotropic kernels significantly reduce model complexity and model over-fitting, and improve the physical correctness of the estimated speed fields. We find that model complexity scales linearly with problem size for anisotropic kernels compared to quadratic scaling for isotropic kernels. Furthermore, evaluation on real-world datasets shows acceptable performance, which establishes that simulation-based training is a viable surrogate to learning from real-world data. Finally, a comparison with standard estimation techniques shows the superior estimation accuracy of the proposed method.

Wenqing Li, Chuhan Yang, Saif Eddin Jabari

This paper develops a data-driven toolkit for traffic forecasting using high-resolution (a.k.a. event-based) traffic data. This is the raw data obtained from fixed sensors in urban roads. Time series of such raw data exhibit heavy fluctuations from one time step to the next (typically on the order of 0.1-1 second). Short-term forecasts (10-30 seconds into the future) of traffic conditions are critical for traffic operations applications (e.g., adaptive signal control). But traffic forecasting tools in the literature deal predominantly with 3-5 minute aggregated data, where the typical signal cycle is on the order of 2 minutes. This renders such forecasts useless at the operations level. To this end, we model the traffic forecasting problem as a matrix completion problem, where the forecasting inputs are mapped to a higher dimensional space using kernels. The formulation allows us to capture both nonlinear dependencies between forecasting inputs and outputs but also allows us to capture dependencies among the inputs. These dependencies correspond to correlations between different locations in the network. We further employ adaptive boosting to enhance the training accuracy and capture historical patterns in the data. The performance of the proposed methods is verified using high-resolution data obtained from a real-world traffic network in Abu Dhabi, UAE. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.

Yue Wang, Esha Sarkar, Wenqing Li et al.

Recent work has shown that the introduction of autonomous vehicles (AVs) in traffic could help reduce traffic jams. Deep reinforcement learning methods demonstrate good performance in complex control problems, including autonomous vehicle control, and have been used in state-of-the-art AV controllers. However, deep neural networks (DNNs) render automated driving vulnerable to machine learning-based attacks. In this work, we explore the backdooring/trojanning of DRL-based AV controllers. We develop a trigger design methodology that is based on well-established principles of traffic physics. The malicious actions include vehicle deceleration and acceleration to cause stop-and-go traffic waves to emerge (congestion attacks) or AV acceleration resulting in the AV crashing into the vehicle in front (insurance attack). We test our attack on single-lane and two-lane circuits. Our experimental results show that the backdoored model does not compromise normal operation performance, with the maximum decrease in cumulative rewards being 1%. Still, it can be maliciously activated to cause a crash or congestion when the corresponding triggers appear.

Ouafa Benkraouda, Bilal Thonnam Thodi, Hwasoo Yeo et al.

We propose a statistical learning-based traffic speed estimation method that uses sparse vehicle trajectory information. Using a convolutional encoder-decoder based architecture, we show that a well trained neural network can learn spatio-temporal traffic speed dynamics from time-space diagrams. We demonstrate this for a homogeneous road section using simulated vehicle trajectories and then validate it using real-world data from NGSIM. Our results show that with probe vehicle penetration levels as low as 5\%, the proposed estimation method can provide a sound reconstruction of macroscopic traffic speeds and reproduce realistic shockwave patterns, implying applicability in a variety of traffic conditions. We further discuss the model's reconstruction mechanisms and confirm its ability to differentiate various traffic behaviors such as congested and free-flow traffic states, transition dynamics, and shockwave propagation.

Wenqing Li, Chuhan Yang, Saif Eddin Jabari

This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than 5 minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we employ a block-coordinate descent algorithm and demonstrate that the algorithm converges in sub-linear time to a block coordinate-wise optimizer. This allows us to capitalize on the "bigness" of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter utilizes past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic dataset from Abu Dhabi, UAE. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.

Saif Eddin Jabari, Deepthi Mary Dilip, DianChao Lin et al.

This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable learning of traffic dynamics from limited Lagrangian measurements using an efficient message passing technique. The approach ensures that estimated speeds and traffic densities are non-negative with probability one. The estimation technique is tested using vehicle trajectory datasets generated using an independent microscopic traffic simulator and is shown to efficiently reproduce traffic conditions with probe vehicle penetration levels as little as 10\%. The proposed algorithm is also compared with state-of-the-art traffic state estimation techniques developed for the same purpose and it is shown that the proposed approach can outperform the state-of-the-art techniques in terms reconstruction accuracy.

Saif Eddin Jabari, Nikolaos M. Freris, Deepthi Mary Dilip

We address two shortcomings in online travel time estimation methods for congested urban traffic. The first shortcoming is related to the determination of the number of mixture modes, which can change dynamically, within day and from day to day. The second shortcoming is the wide-spread use of Gaussian probability densities as mixture components. Gaussian densities fail to capture the positive skew in travel time distributions and, consequently, large numbers of mixture components are needed for reasonable fitting accuracy when applied as mixture components. They also assign positive probabilities to negative travel times. To address these issues, this paper derives a mixture distribution with Gamma component densities, which are asymmetric and supported on the positive numbers. We use sparse estimation techniques to ensure parsimonious models and propose a generalization of Gamma mixture densities using Mittag-Leffler functions, which provides enhanced fitting flexibility and improved parsimony. In order to accommodate within-day variability and allow for online implementation of the proposed methodology (i.e., fast computations on streaming travel time data), we introduce a recursive algorithm which efficiently updates the fitted distribution whenever new data become available. Experimental results using real-world travel time data illustrate the efficacy of the proposed methods.