  In this paper we consider prioritized maximal scheduling in multi-hop
wireless networks, where the scheduler chooses a maximal independent set
greedily according to a sequence specified by certain priorities. We show that
if the probability distributions of the priorities are properly chosen, we can
achieve the optimal (maximum) stability region using an i.i.d random priority
assignment process, for any set of arrival processes that satisfy Law of Large
Numbers. The pre-computation of the priorities is, in general, NP-hard, but
there exists polynomial time approximation scheme (PTAS) to achieve any
fraction of the optimal stability region. We next focus on the simple case of
static priority and specify a greedy priority assignment algorithm, which can
achieve the same fraction of the optimal stability region as the state of art
result for Longest Queue First (LQF) schedulers. We also show that this
algorithm can be easily adapted to satisfy delay constraints in the large
deviations regime, and therefore, supports Quality of Service (QoS) for each
link.
