The pinwheel is a hard-real-time scheduling problem for scheduling sat
ellite ground stations to service a number of satellites without data
loss. Given a multiset of positive integers (instance) A = (a1, ..., a
(n)), the problem is to find an infinite sequence (schedule) of symbol
s from {1, 2, ..., n) such that there is at least one symbol i within
any interval of a(i) symbols (slots). Not all instances A can be sched
uled; for example, no ''successful'' schedule exists for instances who
se density, rho(A) = SIGMA(i = 1)n(1/a(i), is larger than 1. It has be
en shown that all instances whose densities are less than a 0.5 densit
y threshold can always be scheduled. If a schedule exists, another con
cern is the design of a fast on-line scheduler (FOLS) which can genera
te each symbol of the schedule in constant time. Based on. the idea of
''integer reduction,'' two new FOLSs which can schedule different cla
sses of pinwheel instances, are proposed in this paper. One uses ''sin
gle-integer reduction'' and the other uses ''double-integer'' reductio
n. They both improve the previous 0.5 result and have density threshol
ds of 13/20 and 2/3 respectively. In particular, if the elements in A
are large, the density thresholds will asymptotically approach ln 2 an
d 1/square-root 2, respectively.