Stability and Asymptotic Optimality of Generalized MaxWeight Policies
Stability and Asymptotic Optimality of Generalized MaxWeight Policies
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广义MaxWeight策略的稳定性和渐近最优性
DOI：
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发表时间：
2008
期刊：
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通讯作者：
Sean P. Meyn
中科院分区：
文献类型：
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作者：
Sean P. Meyn
结果表明，著名的最大量级或背压政策的稳定性是以下解释的结果：这两种政策对于一种非常特殊形式的替代价值函数是近视的，其中“边际扩张”在缓冲区上消失了这一观察结果消失了。最大量级策略如下：（i）在多种一般条件下（ii）中不需要到达率数据，当$ h $是单调线性功能，单调二次函数或流体模型的单调Lyapunov函数（III）。对Markovian网络模型获得了第一个结果。
It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the “marginal disutility” at a buffer vanishes for a vanishingly small buffer population. This observation motivates the $h$-MaxWeight policy, defined for a wide class of functions $h$. These policies share many of the attractive properties of the MaxWeight policy as follows: (i) Arrival rate data is not required in the policy. (ii) Under a variety of general conditions, the policy is stabilizing when $h$ is a perturbation of a monotone linear function, a monotone quadratic, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately average-cost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a general Markovian network model. Asymptotic optimality is established for a general Markovian scheduling model with a single bottleneck, and with homogeneous servers.