  We investigate the satisfaction of specifications in Prompt Linear Temporal
Logic (Prompt-LTL) by concurrent systems. Prompt-LTL is an extension of LTL
that allows to specify parametric bounds on the satisfaction of eventualities,
thus adding a quantitative aspect to the specification language. We establish a
connection between bounded fairness, bounded stutter equivalence, and the
satisfaction of Prompt-LTL\X formulas. Based on this connection, we prove the
first cutoff results for different classes of systems with a parametric number
of components and quantitative specifications, thereby identifying previously
unknown decidable fragments of the parameterized model checking problem.
