Characterize whether quiescent fairness implies Tokio fairness

Determine whether there exists a quiescently fair scheduler that is not Tokio fair, thereby characterizing the relationship between quiescent fairness and the bounded-delay fairness notion defined for Tokio schedulers.

Background

The paper proves that a quiescently fair scheduler equipped with a suitable well-founded scheduling-distance measure and a bounded distance is also Tokio fair. This establishes one implication between the two fairness notions.

The converse is explicitly left unresolved: the paper does not determine whether the class of quiescently fair schedulers strictly contains the class of Tokio-fair schedulers. Resolving this would clarify whether Tokio fairness is strictly weaker than quiescent fairness or whether the two notions coincide under some conditions.