  A game-theoretic model is proposed to study the cross-layer problem of joint
power and rate control with quality of service (QoS) constraints in
multiple-access networks. In the proposed game, each user seeks to choose its
transmit power and rate in a distributed manner in order to maximize its own
utility while satisfying its QoS requirements. The user's QoS constraints are
specified in terms of the average source rate and an upper bound on the average
delay where the delay includes both transmission and queuing delays. The
utility function considered here measures energy efficiency and is particularly
suitable for wireless networks with energy constraints. The Nash equilibrium
solution for the proposed non-cooperative game is derived and a closed-form
expression for the utility achieved at equilibrium is obtained. It is shown
that the QoS requirements of a user translate into a "size" for the user which
is an indication of the amount of network resources consumed by the user. Using
this competitive multiuser framework, the tradeoffs among throughput, delay,
network capacity and energy efficiency are studied. In addition, analytical
expressions are given for users' delay profiles and the delay performance of
the users at Nash equilibrium is quantified.
