Congestion control and pricing of volume intensive applications

We consider fair sharing of network resources over a period of time between offline and interactive users. The former value total transferred volume while the latter have time-dependent valuations for instantaneous bandwidth. Following the work of Kelly on fair bandwidth sharing, we express the system optimum as an equilibrium of traditional congestion control taking place in a fast timescale and a volume charging mechanism in a slow timescale. The problem is very much related to multipath congestion control where paths are unfolded also in the dimension of time, and our algorithms can be regarded as multipath congestion control algorithms operating on two separate timescales that combine congestion control with scheduling. A novel feature of our algorithms is that, contrary to ordinary dual algorithms, users are not overcharged at any time while approaching the equilibrium. This is a sensible economical property not recognized before in the context of congestion control over long timescales.