Related papers: Nonlinear Instabilities in Computer Network Dynami…
In the era of heavy-duty transmission control protocols (TCP), adapted for extremely hi-bandwidth datacenters, the fundamental question of stable interaction with either proposed active queue management(AQM) or popularly discussed Random…
The problem of increased queueing delays in the Internet motivates the study of currently implemented transport protocols and active queue management (AQM) policies. We study Compound TCP (default protocol in Windows) with Random Early…
Transmission Control Protocol (TCP) continues to be the dominant transport protocol on the Internet. The stability of fluid models has been a key consideration in the design of TCP and the performance evaluation of TCP algorithms. Based on…
We analyze the stability of the Rate Control Protocol (RCP) using two different models that have been proposed in literature. Our objective is to better understand the impact of the protocol parameters and the effect different forms of…
Adaptive management of traffic congestion in the Internet is a complex problem that can gain useful insights from a dynamical approach. In this paper we propose and analyze a one-dimensional, discrete-time nonlinear model for Internet…
Congestion on the Internet is an old problem but still a subject of intensive research. The TCP protocol with its AIMD (Additive Increase and Multiplicative Decrease) behavior hides very challenging problems; one of them is to understand…
In this paper, we introduce two deterministic models aimed at capturing the dynamics of congested Internet connections. The first model is a continuous-time model that combines a system of differential equations with a sudden change in one…
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 study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
In this paper, we analyze some local stability and local bifurcation properties of the Proportionally fair, TCP fair, and the Delay-based dual algorithms in the presence of two distinct time delays. In particular, our focus is on the…
Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
This work proposes a new mathematical model for the TCP/AQM system that aims to improve the accuracy of existing fluid models, especially with respect to the sequential events that occur in the network. The analysis is based on the…
The equilibrium distributions of a Markovian model describing the interaction of several classes of permanent connections in a network are analyzed. It has been introduced by Graham and Robert. For this model each of the connections has a…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…
Motivated by recent concerns that queuing delays in the Internet are on the rise, we conduct a performance evaluation of Compound TCP (C-TCP) in two topologies: a single bottleneck and a multi-bottleneck topology, under different traffic…
Complex networks with expanding dimensions are studied, where the networks may be directed and weighted, and network nodes are varying in discrete time in the sense that some new nodes may be added and some old nodes may be removed from…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…