# Erlang C

## Call Queueing

In an Erlang-C telephone system,* N* channels are available. New calls are assigned a channel until all channels are full.
Whenever all channels are occupied, a new call is queued until it can be served.
This in contrast to an Erlang-B system, in which new calls are blocked.
## Model

New calls arrive according to Poisson process with rate calls per unit of time. Calls have a (memoryless) exponential duration with mean 1/*mu*. The number of active calls is a Markov process.

Figure: Markov model for number of occupied channels in a network with* N* channels.

### Exercise

Explain the transition rates the above Markov chain.

Why is the rate of going from state* i* to* i*-1 equal to
* i*mu* for* i* =< *N*
* N*mu* for *i* >= *N*

### Exercise

Compute the state probabilities and the call queuing probability.
Show that the probability of delaying a call is

* A*^*N* 1
P = --- ------------
* N*! 1 - *A*/*N*

where* A* is the offered traffic expressed in erlang (/mu)