  There have been recent attempts to develop scheduling schemes for downlink
transmission in a single cell of a multi-channel (e.g., OFDM-based) cellular
network. These works have been quite promising in that they have developed
low-complexity index scheduling policies that are delay-optimal (in a large
deviation rate-function sense). However, these policies require that the
channel is ON or OFF in each time-slot with a fixed probability (i.e., there is
no memory in the system), while the reality is that due to channel fading and
doppler shift, channels are often time-correlated in these cellular systems.
Thus, an important open question is whether one can find simple index
scheduling policies that are delay-optimal even when the channels are
time-correlated. In this paper, we attempt to answer this question for
time-correlated ON/OFF channels. In particular, we show that the class of
oldest packets first (OPF) policies that give a higher priority to packets with
a large delay is delay rate-function optimal under two conditions: 1) The
channel is non-negatively correlated, and 2) The distribution of the OFF period
is geometric. We use simulations to further elucidate the theoretical results.
