Telephony Traffic Models
Erlang: unit of traffic
Averaged over time, one erlang of telephone traffic occupies exactly one channel.
However, the arrival and closing of telephone calls are a random processes. As time elapses, one erlang of traffic may occupy zero, one or multiple channels. The definition of the unit erlang does not say anything about how the traffic behaves statistically about this average.
Thus one erlang of traffic can be generated for instance by
The unit of telephone traffic is called after Erlang, a Danish mathematician, who published in 1914 and 1917 the first basic results on the number of subscribers that can be served with a given number of channels at a required Quality of Service (blocking probability).
- One call of infinite duration, or
- A random process of many calls arriving and closing, such that the average number of active calls is one.
In a telephone system, a finite number of N channels are available. New calls are assigned a channel until all channels are full.
Whenever all channels are occupied, a new call either is
Often it is assumed that new calls arrive according to Poisson process with rate l
calls per unit of time.
Note that this assumption may be less realistic is blocked calls result in new attempts by impatient subscribers.
Calls have a (memoryless) exponential duration with mean 1/m. Under such assumptions, the number of active calls is a Markov process.
If calls can always served, i.e., if the system has infinite resources,
the successful traffic is
The added feature of the Engset model is that it does not assume an infinite user population, like the Erlang
model does. One can specify (or compute) the number of users. Traffic can now be expressed in erlang or in
erlang per user. The traffic value in the dimensionless quantity 'erlang' signifies the number of lines that would
be occupied on average if there were no blocking.