多优先级可调速率队列中延迟与速率优化控制研究

Study on the Control Optimization of Delay and Rate in Multiple-priority Rate-adjustable Queues

在队列网络中,延迟和速率优化控制是一个复杂的问题。针对多优先级、可调服务速率的M/G/1队列,在约束条件为每种优先级业务的平均延迟的情况下,研究了队列的两种凸优化问题,即最小化平均延迟向量的凸函数和最小化平均业务代价的凸函数,并分别提出了一种优化算法。算法使用虚拟队列技术,对这两种具有动态cμ规则变量的优化问题进行了求解。然后算法自适应选择一个严格的优先级政策,以响应在每个忙阶段中观察时刻前的各种业务级别的延迟。利亚普诺夫漂移分析和仿真结果验证了算法的优化性能,并且表明文中所提优先级政策所花费的队列统计资源有限,或者为0。

It is a complicated problem in queue networks to optimally control the delay and service rate.For multi-class priority queue and adjustable service rate M/G/1 queues,two convex optimization problems were studied,i.e.,minimizing convex functions of the average delay vector,and minimizing average service cost,both under the constraints of perclass delay,and consiquently an optimization algorithm was proposed for each of them.These algorithms use virtual queue techniques to solve the two problems with variants of dynamic cμ rules.Then these algorithms adaptively choose a strictly priority policy,in response to past observed delays in all job classes,in every busy period.Lyapunov drift analysis and simulation results validate the optimal performance of these two algorithms,and show that the proposed polices require limited or no statics of the queue.