  An information collection problem in a wireless network with random events is
considered. Wireless devices report on each event using one of multiple
reporting formats. Each format has a different quality and uses different data
lengths. Delivering all data in the highest quality format can overload system
resources. The goal is to make intelligent format selection and routing
decisions to maximize time-averaged information quality subject to network
stability. Lyapunov optimization theory can be used to solve such a problem by
repeatedly minimizing the linear terms of a quadratic drift-plus-penalty
expression. To reduce delays, this paper proposes a novel extension of this
technique that preserves the quadratic nature of the drift minimization while
maintaining a fully separable structure. In addition, to avoid high queuing
delay, paths are restricted to at most two hops. The resulting algorithm can
push average information quality arbitrarily close to optimum, with a trade-off
in queue backlog. The algorithm compares favorably to the basic
drift-plus-penalty scheme in terms of backlog and delay. Furthermore, the
technique is generalized to solve linear programs and yields smoother results
than the standard drift-plus-penalty scheme.
