  We address the problem of video streaming packets from an Access Point (AP)
to multiple clients over a shared wireless channel with fading. In such
systems, each client maintains a buffer of packets from which to play the
video, and an outage occurs in the streaming whenever the buffer is empty.
Clients can switch to a lower-quality of video packet, or request packet
transmission at a higher energy level in order to minimize the number of
outages plus the number of outage periods and the number of low quality video
packets streamed, while there is an average power constraint on the AP.
  We pose the problem of choosing the video quality and transmission power as a
Constrained Markov Decision Process (CMDP). We show that the problem involving
$N$ clients decomposes into $N$ MDPs, each involving only a single client, and
furthermore that the optimal policy has a threshold structure, in which the
decision to choose the video-quality and power-level of transmission depends
solely on the buffer-level.
