Question: . M / M/00 queue. Show that given N(0) = i, the correlation coeffi- cient p between N(t) and N(0) equals e-' and is independent

. M / M/00 queue. Show that given N(0) = i, the correlation coeffi-

cient p between N(t) and N(0) equals e-"' and is independent of the arrival rate & and of the batch size X. Ast -> oo, p -> 0, as is expected

(Reynolds, 1968).

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