Related papers: Properties of the LWR model with time delay
Many models of composite dark matter feature a first-order confinement transition in the early Universe, which would produce a stochastic background of gravitational waves that will be searched for by future gravitational-wave…
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…
Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for…
Iterative linear quadradic regulator(iLQR) has become a benchmark method to deal with nonlinear stochastic optimal control problem. However, it does not apply to delay system. In this paper, we extend the iLQR theory and prove new theorem…
We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movement. We apply this framework to the multi-intersection traffic light control…
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay…
Traffic-light modelling is a complex task, because many factors have to be taken into account. In particular, capturing all traffic flows in one model can significantly complicate the model. Therefore, several realistic features are…
We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…
We consider the problem of damping a control system with delay described by first-order functional-differential equations on a temporal tree. The delay in the system is time-proportional and propagates through the internal vertices. The…
Nonlinear hyperbolic partial differential equations govern continuum traffic flow models. Higher-order traffic flow models consisting of continuum equations and velocity dynamics were introduced to address the limitations of the Lighthill,…
The basic properties of traffic flow are analyzed using a simple deterministic one dimensional "car following model" with continuous variables based on a model introduced by Nagel and Herrmann [Physica A 199 254--269 (1993)] including a few…
In this paper we studied about the wavelet identification of the thresholds and time delay for more general case without the constraint that the time delay is smaller than the order of the model. Here we composed an empirical wavelet from…
We have numerically investigated the effect of the delay times $\tau_f$ and $\tau_s$ of a mixture of fast and slow vehicles on the fundamental diagram of the optimal velocity model. The optimal velocity function of the fast cars depends not…
Control of multihop Wireless networks in a distributed manner while providing end-to-end delay requirements for different flows, is a challenging problem. Using the notions of Draining Time and Discrete Review from the theory of fluid…
Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of…
We study a nonlocal particle model describing traffic flow on rough roads. In the model, each driver adjusts the speed of the car according to the condition over an interval in the front, leading to a system of nonlocal ODEs which we refer…
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…
In this paper we show that several dynamical systems with time delay can be described as vector fields associated to smooth functions via a bracket of Leibniz structure. Some examples illustrate the theoretical considerations.
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of…
We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…