After some historical notes concerning queueing output processes N
dep, the paper discusses methods for establishing asymptotic linear relations for var N
dep(0,t], whether in the crude form B
1
t or the more detailed form B
1
t+B
0+o(1) for t→∞. The crude form holds whenever the process N
adm of customers admitted to service has a linear asymptote, and then (var N
dep (0,t])/t and (var N
adm(0,t])/t share a common limit (that may be infinite) in stationary G/G/k/K systems. A standard integral formula for the variance of a stationary orderly point process shows that, if N
dep is a renewal process whose generic lifetime X has finite second moment, then B
1=(var X)/([E(X)]2), and the more detailed linear asymptote holds when E(X
3) is finite. Geometric ergodicity of the queue size process Q(·) in stationary M/M/k/K systems establishes that the more detailed linear asymptote is true for them. It is conjectured that var N(0,t]∼B
1
t for any stationary point process N possessing an embedded regenerative structure.
