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  • Network Performance Engineering - Diffusion Approximation as a modelling tool
    Network Performance Engineering, 2020
    Co-Authors: Tadeusz Czachórski, Ferhan Pekergin
    Abstract:

    Diffusion theory is already a vast domain of knowledge. This tutorial lecture does not cover all results; it presents in a coherent way an approach we have adopted and used in analysis of a series of models concerning evoluation of some traffic control mechanisms in computer, especially ATM, networks. Diffusion Approximation is presented from engineer's point of view, stressing its utility and commenting numerical problems of its implementation. Diffusion Approximation is a method to model the behavior of a single queueing station or a network of stations. It allows one to include in the model general sevice times, general (also correlated) input streams and to investigate transient states, which, in presence of bursty streams (e.g. of multimedia transfers) in modern networks, are of interest.

  • Diffusion Approximation as a modelling tool
    International Symposium on Computer Modeling Measurement and Evaluation, 2011
    Co-Authors: Tadeusz Czachórski, Ferhan Pekergin
    Abstract:

    Diffusion theory is already a vast domain of knowledge. This tutorial lecture does not cover all results; it presents in a coherent way an approach we have adopted and used in analysis of a series of models concerning evoluation of some traffic control mechanisms in computer, especially ATM, networks. Diffusion Approximation is presented from engineer's point of view, stressing its utility and commenting numerical problems of its implementation. Diffusion Approximation is a method to model the behavior of a single queueing station or a network of stations. It allows one to include in the model general sevice times, general (also correlated) input streams and to investigate transient states, which, in presence of bursty streams (e.g. of multimedia transfers) in modern networks, are of interest.

  • Diffusion Approximation Models for Transient States and their Application to Priority Queues
    2009
    Co-Authors: Tadeusz Czachórski, Tomasz Nycz, Ferhan Pekergin
    Abstract:

    The article presents a Diffusion Approximation model applied to investigate the behavior of priority queues. We discusses the use of the Diffusion Approximation in transient analysis of queueing models in the case of a single station and of a queueing network presenting the solutions. We emphasize the numerical aspect of the solution and analyze the errors. In classical queuing theory, the analysis of transient states is complex and practically does not go far beyond M/M/1 queue and its modifications. However, the time dependent flows in computer networks and especially in Internet focus our interest on transient-state analysis, which is necessary to investigate the dynamics of TCP flows cooperating with active queue management or to see the changes of priority queues which assure the differentiated QoS. With the use of G/G/1/N and G/G/1/N/PRIOR models, we present the potentials of the Diffusion Approximation and in conclusions we compare it with alternative methods: Markovian queues solved numerically, fluid-flow Approximation and simulation. Diffusion Approximation allows us to include fairly general assumptions in queueing models. Besides the transient state analysis, it gives us a tool to consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models can be easily incorporated into the network of queues. Here we apply the Diffusion Approximation formalism to study transient and steadystate behavior of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to non-preemptive queueing discipline. The introduction of self-similar traffic is possible as well. The models can be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in IP routers, WiMAX, metro networks, etc. Index terms — Diffusion Approximation, transient states, priority queues.

  • Transient states analysis — Diffusion Approximation as an alternative to Markov models, fluid-flow Approximation and simulation
    2009 IEEE Symposium on Computers and Communications, 2009
    Co-Authors: Tadeusz Czachórski, Tomasz Nycz, Ferhan Pekergin
    Abstract:

    The article discusses the use of the Diffusion Approximation in transient analysis of queueing models applied to investigate some aspects of Internet transmissions. In classical queuing theory, the analysis of transient states is complex and practically does not go far beyond M/M/1 queue and its modifications. However, the time dependent flows in computer networks and especially in Internet focus our interest on transient-state analysis, which is necessary to investigate the dynamics of TCP flows cooperating with active queue management or to see the changes of priority queues which assure the differentiated QoS. With the use of G/G/1/N and G/G/1/N/PRIOR models, we present the potentials of the Diffusion Approximation and compare it with alternative methods: Markovian queues solved numerically, fluid-flow Approximation and simulation. We mention briefly an original software we dispose to use these methods.

  • Transient States of Priority Queues - A Diffusion Approximation Study
    2009 Fifth Advanced International Conference on Telecommunications, 2009
    Co-Authors: Tadeusz Czachórski, Tomasz Nycz, Ferhan Pekergin
    Abstract:

    The article presents a Diffusion Approximation model applied to investigate the behaviour of priority queues. Diffusion Approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. Here, we apply the Diffusion Approximation formalism to study transient and steady-state behavior of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to nonpreemptive queueing discipline. Also the introduction of self-similar traffic is possible. The models may be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in WiMAX, metro networks, etc.