并行计算中时延负载平衡系统的稳定性

Stability of Delay Load Balancing System During Parallel Computation

针对并行环境中动态负载平衡系统问题,提出了一个近似的线性时延模型.通过对模型的稳定性分析,得出了系统渐近稳定的时延相关条件,并在此基础上使用LMI工具近似求解出在不同时延与系统规模情况下的理论负载平衡增益.模拟实验结果表明,最优负载平衡增益值与通信时延和传输时延成反比,与系统规模成正比.所提出的理论适用于不同通信时延、传输时延和系统规模,对设计时延环境下的实用负载平衡算法有着重要的指导性意义.

An approximate linear delay model is proposed to solve the dynamic load balancing problem during parallel computation.Analyzing the stability of the model,the delay-dependent asymptotic stable conditions are obtained,then the theoretical load balancing gain with different time delays and on different system scales is solved approximately by LMI toolkit.The simulation results indicated that the optimal load balancing gain is in inverse proportion to communication/transmission delay and in direct proportion to system scale.Such a conclusion drawn here applies to different communication/transmission delays and system scales,and has guiding effect on designing a more useful load balancing algorithm under time delay conditions.