Queueing-Theory

Lectures on queueing-theory

We present mathamatical results of queueing-theory useful for perfromance evaluation of communication networks. Both multiclass processor sharing and Erlang queues are considered. They permit to model variable bit-rate or best-effort services (such as Web navigation, email, …) and constant bit-rate services (such as voice and video calls) respectively.

Classical queues: Processor sharing and Erlang queues

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Waiting in line to be served is very common in everyday life.

  • 6 months of life waiting in line for things (e.g grocery checkout counter, waiting for an elevator, hospitals, post oce, theatres, etc.)
  • 43 days on hold with call centers.

Queueing theory is the mathematical study of the familiar concept of waiting for some service. It enables us to answer questions such as:

  • What is the average time we have to wait for the service ?
  • How should we split work between several resources ?

Outline:
Introduction
Processor sharing
    Single class
        Insensitivity properties
    Multiclass
        Class-dependent service rate
    Generalized processor sharing
        Loss
    Discriminatory processor sharing
    Examples
Erlang queues
    Single class
        Loss
    Multiclass
        Loss
    Delay queues
        Single class
Bibliography

Mohamed Kadhem KARRAY

My research activities at Orange aim to evaluate the performance of communication networks, by combining information, queueing theories, stochastic geometry, as well as machine and deep learning. Recently, I prepared video lectures on "Data science: From multivariate statistics to machine and deep learning" available on my YouTube channel. I also teached at Ecole Normale Supérieure, Ecole Polyetechnique, Ecole Centrale Paris, and prepared several mathematical books.

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