  Information-theoretic arguments focus on modeling the reliability of
information transmission, assuming availability of infinite data at sources,
thus ignoring randomness in message generation times at the respective sources.
However, in information transport networks, not only is reliable transmission
important, but also stability, i.e., finiteness of mean delay incurred by
messages from the time of generation to the time of successful reception.
Usually, delay analysis is done separately using queueing-theoretic arguments,
whereas reliable information transmission is studied using information theory.
In this thesis, we investigate these two important aspects of data
communication jointly by suitably combining models from these two fields. In
particular, we model scheduled communication of messages, that arrive in a
random process, (i) over multiaccess channels, with either independent decoding
or joint decoding, and (ii) over degraded broadcast channels. The scheduling
policies proposed permit up to a certain maximum number of messages for
simultaneous transmission.
  In the first part of the thesis, we develop a multi-class discrete-time
processor-sharing queueing model, and then investigate the stability of this
queue. In particular, we model the queue by a discrete-time Markov chain
defined on a countable state space, and then establish (i) a sufficient
condition for $c$-regularity of the chain, and hence positive recurrence and
finiteness of stationary mean of the function $c$ of the state, and (ii) a
sufficient condition for transience of the chain. These stability results form
the basis for the conclusions drawn in the thesis.
