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.
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.
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
Compute the state probabilities and the call queuing probability.
Show that the probability of delaying a call is
P = --- ------------
N! 1 - A/N
where A is the offered traffic expressed in erlang (/mu)