Chapter 1Introduction



1.1. Traffic, load, Erlang, etc.

In electricity, we count the amps or volts; in meteorology, we measure the pressure; in telecommunications, we count the Erlangs.

The telephone came into existence in 1870. Most of the concepts and notations were derived during this period. Looking at a telephone connection over a time period of length T, we define its observed traffic flow as the percentage of time during which the connection is busy


A priori, traffic is a dimensionless quantity since it is the ratio of the occupation time to the total time. However, it still has a unit, Erlang, in remembrance of Erlang who, along with Palm, was one of the pioneers of the performance assessment of telephone networks. Therefore, a load of 1 Erlang corresponds to an always busy connection.

Figure 1.1. Traffic of a connection: ratio of the occupation time to the total time of observation


Looking at several connections, the traffic carried by this trunk is the sum of the traffic of each connection


This is no longer a percentage, but we can give a physical interpretation to this quantity according to the ergodic hypothesis. In fact, assume that the number of junctions is large, ...

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