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Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
We propose a data-driven methodology for evaluating the impact of the introduction of a speed limit on the punctuality of bus services. In particular, we use high-frequency Automatic Vehicle Location data to parameterise a model that…
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…
Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…
Linear trajectory models provide mathematical advantages to autonomous driving applications such as motion prediction. However, linear models' expressive power and bias for real-world trajectories have not been thoroughly analyzed. We…
Human mobility patterns are complex and distinct from one person to another. Nevertheless, motivated by tremendous potential benefits of modeling such patterns in enabling new mobile services and technologies, researchers have attempted to…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
We provide an overview on superstatistical techniques applied to complex systems with time scale separation. Three examples of recent applications are dealt with in somewhat more detail: the statistics of small-scale velocity differences in…
In this paper we present the discrete-time networked SIR and SEIR models and present assumptions under which they are well defined. We analyze the limiting behavior of the models and present necessary and sufficient conditions for…
A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…
Computer network tends to be subjected to the proliferation of mobile demands and increasingly multifarious, therefore it poses a great challenge to guarantee the quality of network service. By designing the model according to different…
We present here a real-time control model for the train dynamics in a linear metro line system. The model describes the train dynamics taking into account average passenger arrival rates on platforms, including control laws for train dwell…
Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)-algebra based representation of network dynamics. The behaviour of the bounds under various assumptions…
This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties.…
Travel time prediction is a well-renowned topic of research. It is primarily influenced by traffic congestion, road conditions and route geometry. Among them route geometry at any point is not investigated enough to find a sound spatial…
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic,…
This paper proposes a macroscopic model to describe the equilibrium distribution of passenger arrivals for the morning commute problem in a congested urban rail transit system. We use a macroscopic train operation sub-model developed by Seo…
We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides…