Equivalence on Quadratic Lyapunov Function Based Algorithms in Stochastic Networks

Quadratic Lyapunov function based Algorithms (QLAs) for stochastic network optimization problems, which are cross-layer scheduling algorithms designed by Lyapunov optimization technique, have been widely used and studied. In this paper, we investigate the performance of using Lyapunov drift and perturbation in QLAs. By analyzing attraction points and utility performance of four variants of OQLA (Original QLA), we examine the rationality of OQLA for using the first- order part of an upper bound of Lyapunov drift of a function L_1. It is proved that either using the real Lyapunov function (L_2) of networks under QLA or using the entire expression of Lyapunov drift does not improve backlog-utility performance. The linear relationship between the attraction point of backlog and perturbation in the queue is found. Simulations verify the results above.