Non-stationary processes in queueing networks
Seminar Room 2, Newton Institute Gatehouse
The long-term behavior of large mean field networks may depend on the initial state. In particular, both stationary and time-periodic modes may coexist in the limit case of infinite mean field network. We introduce a new measure of non-stationarity for point processes in order to prove that this situation is impossible in topical (shift-invariant and monotone) networks. For open networks of this kind the outflow is "more stationary"
than the inflow, hence, in the closed case, oscillations never happen.