  This paper describes TARDIS (Traffic Assignment and Retiming Dynamics with
Inherent Stability) which is an algorithmic procedure designed to reallocate
traffic within Internet Service Provider (ISP) networks. Recent work has
investigated the idea of shifting traffic in time (from peak to off-peak) or in
space (by using different links). This work gives a unified scheme for both
time and space shifting to reduce costs. Particular attention is given to the
commonly used 95th percentile pricing scheme.
  The work has three main innovations: firstly, introducing the Shapley
Gradient, a way of comparing traffic pricing between different links at
different times of day; secondly, a unified way of reallocating traffic in time
and/or in space; thirdly, a continuous approximation to this system is proved
to be stable. A trace-driven investigation using data from two service
providers shows that the algorithm can create large savings in transit costs
even when only small proportions of the traffic can be shifted.
