Technical Note - The Busy Probability in M/G/N Loss Systems
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If K + 1 servers in an equilibrium M/G/N-loss system are chosen randomly without replacement and the first K servers chosen are busy, the conditional probability that the K + 1st server chosen is busy is shown to be equal to the a priori probability that a randomly chosen server in an equilibrium M/G/N-K-loss system with the same offered load is busy.
[1] D. Jagerman. Some properties of the erlang loss function , 1974 .
[2] L. Takács. On Erlang's Formula , 1969 .