Related papers: Functional Limits of Generalized Jackson Networks …
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
We prove a functional limit theorem for Markov chains that, in each step, move up or down by a possibly state dependent constant with probability $1/2$, respectively. The theorem entails that the law of every one-dimensional regular…
We introduce four algorithms for packet transport in complex networks. These algorithms use deterministic rules which depend, in different ways, on the degree of the node, the number of packets posted down each edge, the mean delivery time…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
In this paper, we study systems where each job or request can be split into a flexible number of sub-jobs up to a maximum limit. The number of sub-jobs a job is split into depends on the number of available servers found upon its arrival.…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…
We model information traffic on scale-free networks by introducing the bandwidth as the delivering ability of links. We focus on the effects of bandwidth on the packet delivering ability of the traffic system to better understand traffic…
We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show…
This paper investigates the problem of synthesizing joint distributions in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distribution approximation $\epsilon$, we prove a capacity result for fixed-length…
We study in this paper a variation of the acclaimed CSMA random access protocol. We will focus on the case where back-off rates at each node is polynomial in the size of the queue. Under a condition relating the exponent in the polynomial…
In areas such as computer software and hardware, manufacturing systems, and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized systems provide a framework for modeling such…
Traffic congestion continues to escalate with urbanization and socioeconomic development, necessitating advanced modeling to understand and mitigate its impacts. In large-scale networks, traffic congestion can be studied using cascade…
We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have…
In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to…
The busy period length distribution function knowledge is important for any queue system, and for the MGINF queue. But the mathematical expressions are in general very complicated, with a few exceptions, involving usually infinite sums and…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
We consider a load balancing system consisting of $n$ single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival.…
We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…
This paper studies the heavy-traffic asymptotics for the multiclass FIFO M${}^X$/G/1 queue. We first derive the probability generating function of the joint queue length distribution. Using the probability generating function, we then…