A calculus approach to minimum energy transmission policies with quality of service guarantees

We consider a queueing system with controllable service rate; for example, a transmitter whose rate can be controlled by varying the transmission power. For such a system we obtain optimal data transmission policies that satisfy given quality of service (QoS) constraints and also minimize the total transmission energy expenditure. First, we consider the deterministic case of known arrivals and present a formulation based on a calculus approach using arrival and minimum departure curves. The problem is posed as a continuous time optimization and an optimal solution is obtained for general arrival curves and QoS constraints. In the latter half of the paper, we consider a stochastic arrival process (Poisson process) and a single deadline constraint. The objective is to obtain a transmission policy that minimizes the expected energy expenditure. The problem is formulated as a stochastic optimal control problem and an explicit solution is obtained with some relaxation. Finally, simulation results comparing various policies are presented.