  This paper studies the problem of utility maximization for clients with delay
based QoS requirements in wireless networks. We adopt a model used in a
previous work that characterizes the QoS requirements of clients by their delay
constraints, channel reliabilities, and delivery ratio requirements. In this
work, we assume that the utility of a client is a function of the delivery
ratio it obtains. We treat the delivery ratio for a client as a tunable
parameter by the access point (AP), instead of a given value as in the previous
work. We then study how the AP should assign delivery ratios to clients so that
the total utility of all clients is maximized.
  We apply the techniques introduced in two previous papers to decompose the
utility maximization problem into two simpler problems, a CLIENT problem and an
ACCESS-POINT problem. We show that this decomposition actually describes a
bidding game, where clients bid for the service time from the AP. We prove that
although all clients behave selfishly in this game, the resulting equilibrium
point of the game maximizes the total utility. In addition, we also establish
an efficient scheduling policy for the AP to reach the optimal point of the
ACCESS-POINT problem. We prove that the policy not only approaches the optimal
point but also achieves some forms of fairness among clients. Finally,
simulation results show that our proposed policy does achieve higher utility
than all other compared policies.
