超市模型的实时动态控制及其数值分析

超市模型是针对大型并行排队网络所进行的 实时动态控制的随机负载平衡策略, 它在计算机网络、云计算、制造系统、交通网络等领域有着重要的实际应用价值. 本文考虑了超市模型中的若干重要问题: 实时动态控制模式; 效率比较; 平均场黑洞; 马氏变动环境; 稳定性; 固定点; 系统性能评价等等. 同时, 本文也通过数值算例研究了上述重要问题, 包括对顾客加入最短队列的超市模型与服务台服务最长队列的超市模型进行了性能比较, 给出了他们效率的优劣分析; 在超市模型中对控制到达过程机制进行了三种情况的对比; 对马氏变动环境下的超市模型进行了性能评价.

Real-Time Dynamic Control in the Supermarket Models and Some Numerical Analysis

The supermarket model is a dynamic randomized load balancing scheme for real-time dynamic control of large-scale parallel queuing network. It has many important practical applications in, for example, computer networks, cloud computing, manufacturing systems and transportation networks. In this paper, for the supermarket models we consider some important issues, such as, real-time dynamic control modes; efficiency comparison; mean-field black hole; Markov changing environment; stability; fixed point; system performance analysis. At the same time, we also study these important issues through some numerical examples, include performance comparison, and efficiency analysis for advantages and disadvantages among the supermarket models with either customers joining the shortest queue, or customers joining any queue randomly, or customers joining the longest queue. Further, we consider a more general supermarket model under an Markov changing environment, and provide performance evaluation for the supermarket model under an Markov changing environment.