File-sharing networks are distributed systems used to disseminate files among
nodes of a communication network. The general simple principle of these systems
is that once a node has retrieved a file, it may become a server for this file.
In this paper, the capacity of these networks is analyzed with a stochastic
model when there is a constant flow of incoming requests for a given file. It
is shown that the problem can be solved by analyzing the asymptotic behavior of
a class of interacting branching processes.
Dynamic Spectrum Access systems exploit temporarily available spectrum
(`white spaces') and can spread transmissions over a number of non-contiguous
sub-channels. Such methods are highly beneficial in terms of spectrum
utilization. However, excessive fragmentation degrades performance and hence
off-sets the benefits. Thus, there is a need to study these processes so as to
determine how to ensure acceptable levels of fragmentation. Hence, we present
experimental and analytical results derived from a mathematical model.
Passive optical networks are increasingly used for access to the Internet and
it is important to understand the performance of future long-reach,
multi-channel variants. In this paper we discuss requirements on the dynamic
bandwidth allocation (DBA) algorithm used to manage the upstream resource in a
WDM EPON and propose a simple novel DBA algorithm that is considerably more
efficient than classical approaches. We demonstrate that the algorithm emulates
a multi-server polling system and derive capacity formulas that are valid for
general traffic processes.
As passive optical networks (PON) are increasingly deployed to provide high
speed Internet access, it is important to understand their fundamental traffic
capacity limits. The paper discusses performance models applicable to
wavelength division multiplexing (WDM) EPONs and GPONs under the assumption
that users access the fibre via optical network units equipped with tunable
transmitters. The considered stochastic models are based on multiserver polling
systems for which explicit analytical results are not known.
In this paper, a general tree algorithm processing a random flow of arrivals
is analyzed. Capetanakis--Tsybakov--Mikhailov's protocol in the context of
communication networks with random access is an example of such an algorithm.
In computer science, this corresponds to a trie structure with a dynamic input.
Mathematically, it is related to a stopped branching process with exogeneous
arrivals (immigration).
The asymptotic behavior of birth and death processes of particles in a
compact space is analyzed. Births: Particles are created at rate $\lambda_+$
and their location is independent of the current configuration. Deaths are due
to negative particles arriving at rate $\lambda_-$. The death of a particle
occurs when a negative particle arrives in its neighborhood and kills it.
Several killing schemes are considered. The arriving locations of positive and
negative particles are assumed to have the same distribution.