  Throughput and per-packet delay can present strong trade-offs that are
important in the cases of delay sensitive applications.We investigate such
trade-offs using a random linear network coding scheme for one or more
receivers in single hop wireless packet erasure broadcast channels. We capture
the delay sensitivities across different types of network applications using a
class of delay metrics based on the norms of packet arrival times. With these
delay metrics, we establish a unified framework to characterize the rate and
delay requirements of applications and optimize system parameters. In the
single receiver case, we demonstrate the trade-off between average packet
delay, which we view as the inverse of throughput, and maximum ordered
inter-arrival delay for various system parameters. For a single broadcast
channel with multiple receivers having different delay constraints and feedback
delays, we jointly optimize the coding parameters and time-division scheduling
parameters at the transmitters. We formulate the optimization problem as a
Generalized Geometric Program (GGP). This approach allows the transmitters to
adjust adaptively the coding and scheduling parameters for efficient allocation
of network resources under varying delay constraints. In the case where the
receivers are served by multiple non-interfering wireless broadcast channels,
the same optimization problem is formulated as a Signomial Program, which is
NP-hard in general. We provide approximation methods using successive
formulation of geometric programs and show the convergence of approximations.
