The energy-delay tradeoffs in wireless networks are studied using a game-theoretic framework. A multi-class multipleaccess network is considered in which users choose their transmit powers, and possibly transmission rates, in a distributed manner to maximize their own utilities while satisfying their delay quality-ofservice (QoS) requirements. The utility function considered here measures the number of reliable bits transmitted per Joule of energy consumed and is particularly useful for energy-constrained networks. The Nash equilibrium solution for the proposed noncooperative game is presented and closed-form expressions for the users' utilities at equilibrium are obtained. Based on this, the losses in energy efficiency and network capacity due to presence of delay-sensitive users are quantified. The analysis is extended to the scenario where the QoS requirements include both the average source rate and a bound on the average total delay (including queuing delay). It is shown that...
Farhad Meshkati, H. Vincent Poor, Stuart C. Schwar