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Probability Of Queueing (Internetworking)


  • Total Users: nn
  • Each has a probability of pp being active

The probability that exactly kk users are present is:

(nk)ร—(1โˆ’p)nโˆ’kร—pk\binom{n}{k} \times (1-p) ^ {n-k} \times p^k

For example, for a population of 35 independent users, each with a probability 0.1 of being present, the likelihood that > 10 users are current is:

โˆ‘k=10n=35(nk)ร—(1โˆ’p)nโˆ’kร—pk\sum_{k=10}^{n=35} \binom{n}{k} \times (1-p) ^ {n-k} \times p^k