Related papers: Validity of heavy traffic steady-state approximati…

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical.…

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this…

Motivated by application in wireless networks, cloud computing, data centers etc, Stochastic Processing Networks have been studied in the literature under various asymptotic regimes. In the heavy-traffic regime, the steady state mean queue…

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…

Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…

We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load…

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods…

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…

This study focuses on the challenge of predicting network traffic within complex topological environments. It introduces a spatiotemporal modeling approach that integrates Graph Convolutional Networks (GCN) with Gated Recurrent Units (GRU).…

Time-Sensitive Networking (TSN) and Deterministic Networking (DetNet) are emerging standards to enable deterministic, delay-critical communication in such networks. This naturally (re-)calls attention to the network calculus theory (NC),…

The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…

We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the…

We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…

We consider the family of multiplicative Brownian motions $G_{\lambda,\tau}$ on the general linear group introduced by Driver-Hall-Kemp. They are parametrized by the real variance $\lambda\in \mathbb{R}$ and the complex covariance $\tau \in…

We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…

Schedule-based transit assignment describes congestion in public transport services by modeling the interactions of passenger behavior in a time-space network built directly on a transit schedule. This study investigates the theoretical…

To capture spatial relationships and temporal dynamics in traffic data, spatio-temporal models for traffic forecasting have drawn significant attention in recent years. Most of the recent works employed graph neural networks(GNN) with…

In this paper, we present a stochastic queuing model for the road traffic, which captures the stationary density-flow relationships in both uncongested and congestion conditions. The proposed model is based on the $M/g/c/c$ state dependent…