Abstract
SummaryIn a stationaryGI/G/1 queueing system in which the waiting time variance is finite, it can be shown that the serial correlation coefficients {ρn} of a (stationary) sequence of waiting times are non-negative and decrease monotonically to zero. By means of renewal theory we find a representation for Σ∞0ρnfrom which necessary and sufficient condition for its finiteness can be found. InM/G/1 rather more can be said: {ρn} is convex sequence, the asymptotic form of ρncan be given in a nearly saturated queue, and a simple explicit expression for Σ∞0ρnexists. For the stationaryM/M/1queue we find the ρn's explicitly, illustrate them numerically, and derive a representation which shows that {ρn} is completely monotonic.
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