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The probability distribution is called the truncated Poisson distribution or Erlang's loss distribution. In particular when k = N, the probability of loss is given by

This result is variously referred to as Erlang's formula of the first kind, the Erlangs-B formula or Erlangs loss formula.

Equation 8.54 specifies the probability of blocking for a system with random arrivals from an infinite source and arbitrary holding time ditributions. The Erlang B formula gives the time congestion of the system and relates the probability of blocking to the offered traffic and the number of trunk lines.

Values from B(N, A) obtained from equation 8.54, have been plotted against the offered traffic 'A' erlangs for different values of the number of N lines in Fig. 8.6.

In design problems, it is necessary to find the number of trunk lines needed for a given offered traffic and a specified grade of service. The offered load generated by a Poisson input process with a rate X calls per hour may be defined as

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