  We consider the performance modeling and evaluation of network systems
powered with renewable energy sources such as solar and wind energy. Such
energy sources largely depend on environmental conditions, which are hard to
predict accurately. As such, it may only make sense to require the network
systems to support a soft quality of service (QoS) guarantee, i.e., to
guarantee a service requirement with a certain high probability. In this paper,
we intend to build a solid mathematical foundation to help better understand
the stochastic energy constraint and the inherent correlation between QoS and
the uncertain energy supply. We utilize a calculus approach to model the
cumulative amount of charged energy and the cumulative amount of consumed
energy. We derive upper and lower bounds on the remaining energy level based on
a stochastic energy charging rate and a stochastic energy discharging rate. By
building the bridge between energy consumption and task execution (i.e.,
service), we study the QoS guarantee under the constraint of uncertain energy
sources. We further show how performance bounds can be improved if some strong
assumptions can be made.
