In this paper we study single server queues with independent and identically distributed service times and a general nonstationary input stream. We discuss several notions of “being in equilibrium”. For queues with a doubly stochastic Poisson input we survey continuity and bounds of moments of some performance characteristics. We also discuss conjectures posed by Ross  to the effect that for a “more stationary” input we have a better performance characteristics. Some results are reviewed to typify a problem and then it is followed by a discussion, questions and related bibliography.
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Rolski, T. Queues with nonstationary inputs. Queueing Syst 5, 113–129 (1989). https://doi.org/10.1007/BF01149189
- stationary waiting time
- stationary work-load
- Ross' conjectures
- a.m.s. sequence
- uniform integrability