Queues Applied to Telecoms

5Notion of Teletraffic

When you’re poor, the only resource left is to be wise.

Jean-Pierre Florian (1755–1794)

Resources are the most important parts in a telecommunication network. They are generally rare and always need to be shared. This sharing concerns almost all of the components of a network:

• – transmission channels, memory, processors;
• – transmission components (repeaters, amplifiers);
• – switching components (telephone exchanges, routers, couplers);
• – control devices (processors, signaling equipment);
• – even the resources we think are indivisible (power, bandwidth, frequency spectrums).

This chapter is devoted to the introduction of a notion that is useful in the mathematical study of this kind of sharing, which is based on statistical speculation relating to the number of users who might make use of these components, relative to the available number of them.

5.1. Teletraffic and its objectives

DEFINITION 5.1.– Teletraffic can be defined as a stochastic process that corresponds to the set of uses (real or fictitious) of resources in a telecommunication network, whatever their cause and independently of whether or not they are connected to complete, effective communication.

According to this definition, teletraffic has a stochastic nature. It depends on random variables that are themselves dependent on time. We can cite discrete random variables such as the number of requests to use resources, the number of resources that are busy, the length of the messages in ...