Erlang B system:

The Erlang B formula is expressed as GoS or the probability of finding N channels busy.

The assumptions made in the Erlang B formula are as follows:

• Traffic originates independently from an infinite number of traffic sources.
• Lost calls are cleared assuming a zero holding time.
• Limited number of trunks or service channels.
• Full availability.
• Inter-arrival times of call requests are independent of each other.
• The service time (probability of a user occupying a channel) is based on an exponential distribution.
• Traffic requests are represented by a Poisson distribution implying exponentially distributed call inter-arrival times.

B(N, A) = blocking probability

$\mathrm{G_B = \dfrac{A^N/A!}{\Sigma^{N-1}_{k=0} \dfrac{A^k}{k!}}}$

where N = number of serving channels and A = offered load.

Erlang C system

The Erlang C formula assumes that a queue is formed to hold all requested calls that cannot be served immediately. Customers who find all N servers busy Join a queue and wait as long as necessary to receive service. This means that the blocked customers are delayed. No server remains idle if a customer is waiting.

The assumptions in the Erlang C formula are as follows:

• Traffic originates from an infinite number of traffic sources independently.
• Lost calls are delayed.
• Number of trunks or service channels is limited.
• The probability of a user occupying a channel (called service time) is based on an exponential distribution.
• Calls are served in the order of arrival.

$\mathrm{\text{Blocking probability C(N,A) }=\dfrac{A^N /[N!(1-A/N)]} {\Sigma^{N-1}_{k=0}\dfrac{A^k}{k!}+\dfrac{A^N}{N!(1-A/N)}}}$

where N = number of service channels and A= offered load.

The Erlang B formula holds even when the load is greater than number of servers (A > N) because, unlike the BCD model in which all calls are eventually served, the BCC model allows calls to be lost when all servers are busy. Therefore, the BCC system never becomes unstable.