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The probability distribution of the state of the process that customers observe upon arrival to a queueing system. In general, it is not the same as the distribution seen by a random outside observer; but the two distributions are the same for queueing systems with Poisson arrivals. Since customers entering a queue must also exit, the probability distribution seen by arriving customers who are accepted is the same as that for the number of customers left behind by the departures. See Outside observer distribution; Queueing theory.