  Demand shaping is a promising way to mitigate the wireless cellular capacity
shortfall in the presence of ever-increasing wireless data demand. In this
paper, we formulate demand shaping as an optimization problem that minimizes
the variation in aggregate traffic. We design a distributed and randomized
offline demand shaping algorithm under complete traffic information and prove
its almost surely convergence. We further consider a more realistic setting
where the traffic information is incomplete but the future traffic can be
predicted to a certain degree of accuracy. We design an online demand shaping
algorithm that updates the schedules of deferrable applications (DAs) each time
when new information is available, based on solving at each timeslot an
optimization problem over a shrinking horizon from the current time to the end
of the day. We compare the performance of the online algorithm against the
optimal offline algorithm, and provide numerical examples to complement the
theoretical analysis.
