  We consider non-preemptive scheduling problems on parallel identical machines
where machines change their status from being available to being unavailable
and vice versa along the time horizon. The particular form of unavailability we
consider is when the starting time of each downtime depends upon the
cardinality of the job subset processed on that machine since the previous
downtime. We consider the problem of minimizing the makespan in such scenarios
as well as its dual problem where we have a fixed common deadline of $1$ and
the goal is to minimize the number of machines for which there is a feasible
schedule. We develop an EPTAS for the first variant and an AFPTAS for the
second variant.
