Related papers: Properties of the LWR model with time delay
In this paper, we develop a mechanical system inspired microscopic traffic model to characterize the longitudinal interaction dynamics among a chain of vehicles. In particular, we extend our prior work on mass-spring-damper-clutch based…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
In this paper, we consider the temporal pattern in traffic flow time series, and implement a deep learning model for traffic flow prediction. Detrending based methods decompose original flow series into trend and residual series, in which…
Jamitons are self-sustained traveling wave solutions that arise in certain second-order macroscopic models of vehicular traffic. A necessary condition for a jamiton to appear is that the local traffic density breaks the so-called…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
We extend the measure-valued fluid model, which tracks residuals of patience and service times, to allow for time-varying arrivals. The fluid model can be characterized by a one-dimensional convolution equation involving both the patience…
A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless…
Deep learning (DL) methods have outperformed parametric models such as historical average, ARIMA and variants in predicting traffic variables into short and near-short future, that are critical for traffic management. Specifically,…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
The advent of digital twins (DT) for the control and management of communication networks requires accurate and fast methods to estimate key performance indicators (KPI) needed for autonomous decision-making. Among several alternatives,…
We propose a semidiscrete scheme for approximation of entropy solutions of one-dimensional scalar conservation laws with nonnegative initial data. The scheme is based on the concept of particle paths for conservation laws and can be…
This paper is mainly concerned with the robustly stable adaptive control of single-input single-output impulse-free linear time-invariant singular dynamic systems of known order and unknown parameterizations subject to single external point…
Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
Self-driving vehicles plan around both static and dynamic objects, applying predictive models of behavior to estimate future locations of the objects in the environment. However, future behavior is inherently uncertain, and models of motion…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
Weighted round robin (WRR) is an effective, yet particularly easy-to-implement packet scheduler. A slight modification in the implementation of WRR, interleaved weighted round robin, has been proposed as an enhancement of the initial…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is…
We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots and show that the group-level behaviour can be described by a transport equation with a suitably incorporated delay. The results of our…