Philippe Robert

  1. Interacting branching processes and linear file-sharing networks.

    Authors: Philippe Robert, Florian Simatos, L. Leskelä
    Subjects: Probability
    Abstract

    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.

  2. Channel Fragmentation in Dynamic Spectrum Access Systems - a Theoretical Study.

    Authors: Philippe Robert, Ed Coffman, Florian Simatos, Shuzo Tarumi, Gil Zussman
    Subjects: Networking and Internet Architecture
    Abstract

    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.

  3. Upstream traffic capacity of a WDM EPON under online GATE-driven scheduling.

    Authors: Philippe Robert, Nelson Antunes, Christine Fricker, James Roberts
    Subjects: Networking and Internet Architecture
    Abstract

    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.

  4. Traffic Capacity of Large WDM Passive Optical Networks.

    Authors: Philippe Robert, Nelson Antunes, Christine Fricker, James Roberts
    Subjects: Networking and Internet Architecture
    Abstract

    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.

  5. Dynamic tree algorithms.

    Authors: Philippe Robert, Hanène Mohamed
    Subjects: Probability
    Abstract

    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).

  6. Stochastic Evolutions of Point Processes.

    Authors: Philippe Robert
    Subjects: Probability
    Abstract

    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.

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