  In this thesis, we study the optimal tradeoff of average delay, average
service cost, and average utility for single server queueing models, with and
without admission control. The continuous time and discrete time queueing
models that we consider are motivated by cross-layer models for noisy
point-to-point links, with random packet arrivals. We study the above tradeoff
problem for a class of admissible policies, which are monotone and stationary
and obtain an asymptotic characterization of the minimum average delay as a
function of the average service cost and average utility constraints.
