A basically poisson queue with nonpoisson output

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Abstract
The output of the queueing system M/M/1 is well known to be Poisson. This has also been shown to be true for other more general models inclusive of M/Mn/1; the system in which arrivals and epochs of service completion are elements of a birth and death process with parameters Λ and nμ, respectively, when the system contains n ≥ 1 customers. We shall here show that this result is not true in MnM/1; a system where arrival parameter is state dependent quantity Λ/n+1. Expressions will be given for the steady state joint density of two consecutive output intervals as well as the coefficient of correlation between them.