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In this work we propose a two-dimensional extension of a previously defined one-dimensional version of a model of counterflowing particles, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In…
This thesis focuses on link scheduling in wireless mesh networks by taking into account physical layer characteristics. The assumption made throughout is that a packet is received successfully only if the Signal to Interference and Noise…
In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated over time. All these features have an impact on the temporal properties of…
Employing multi-tier networks is among the most promising approaches to address the rapid growth of the data demand in cellular networks. In this paper, we study a two-tier uplink cellular network consisting of femtocells and a macrocell.…
This paper presents results on the typical number of simultaneous point-to-point transmissions above a minimum rate that can be sustained in a network with $n$ transmitter-receiver node pairs when all transmitting nodes can potentially…
The location of active users is an important factor in the performance analysis of mobile multicell networks, but it is difficult to quantify due to the wide variety of user mobility and session patterns. In particular, the channel holding…
In this work, we consider the case where a source with bursty traffic can adjust the transmission duration in order to increase the reliability. The source is equipped with a queue in order to store the arriving packets. We model the system…
A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…
In this article, we consider a nonlinear process with delayed dynamics to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of interference distributions in large-scale…
Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…
We study the problem of associating mobile terminals to base stations in a linear interference network, with the goal of maximizing the average rate achieved over both the uplink and downlink sessions. The cell association decision is made…
A Network Control System (NCS) consists of control components that interact with the plant over a shared network. The system dynamics of a NCS could be subject to noise arising from randomness in the times at which the data is transmitted…
Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I…
We present in this article traffic flow and control models for the train dynamics in metro lines. The first model, written in the max-plus algebra, takes into account minimum running, dwell and safety time constraints, without any control…
We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…
It is by now well-known that wireless networks with file arrivals and departures are stable if one uses alpha-fair congestion control and back-pressure based scheduling and routing. In this paper, we examine whether ?alpha-fair congestion…
For many power-limited networks, such as wireless sensor networks and mobile ad hoc networks, maximizing the network lifetime is the first concern in the related designing and maintaining activities. We study the network lifetime from the…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…