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 o ce, 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