In this paper, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at points in space and the server stations have space-dependent processing rates. The workload is seen as a Radon measure and the server stations can adapt their power allocation to the current workload. We derive the stability region of the queueing system in the usual stationary ergodic framework. The analysis of this stability region gives some counter-intuitive results. Some specific subclasses of policy are also studied. Wireless communications networks is a natural field of application for the model.

Design of balancing control and the stability analysis of a biped during disturbed standing are investigated. A PD-based switching state feedback control is used to stabilize the biped at the upright position while satisfying the constraints between the feet and the ground. The concept of Lyapunov exponents is used for the stability analysis, and a stability region is determined. Furthermore, the stability region is compared and agrees well with the one from the previous work that predicts the feasible movement during which balance of human standing can be maintained. This agreement shows the potential of the concept of Lyapunov exponents to be used as a measure of balancing of human standing. The work contributes to bipedal balancing control, which is important in the development of bipedal robots.