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On the optimality and the asymptotic optimality of the smallest weighted available buffer policy

机译：最小加权可用缓冲区策略的最优性和渐近最优性

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A major design challenge of Asynchronous Transfer Mode (ATM) networks is to efficiently provide the quality of service (QOS) specified by users with different demands. We classify sources so that sources in one class join the same buffer and have the same requirement for the ATM cell loss ratio. it is important to search for the service discipline that minimizes the accumulated cell loss under the constrains that the cell loss ratios of the sources are proportional to their QOS requirements. In this paper we consider a model that has N finite buffers and a single server. Buffer i, of size Bi, is assigned a positive number omega(i). The server serves from one of the non-empty buffers whose indices are equal to argmin omega(i)(B-i - Q(i)), where Q(i) is the queue length of buffer i. This scheduling policy is called the smallest weighted available buffer policy (SWAB). We show that in a completely symmetric setting, the SWAB policy minimizes the discounted expected loss of cells under some technical conditions. For asymmetric models, we show that the accumulated loss of cells of the SWAB service discipline is asymptotically optimal under heavy traffic conditions in the diffusion limit. Finally, we obtain the expression of omega(i) SO that the cell loss ratios of the sources in the diffusion limit are proportional to their QOS requirements. AMS 1991 Subject Classification: Primary 60K95 Secondary 93E20. [References: 36]
机译：异步传输模式（ATM）网络的主要设计挑战是有效地提供具有不同需求的用户指定的服务质量（QOS）。我们对源进行分类，以使一类中的源加入相同的缓冲区，并对ATM信元丢失率具有相同的要求。重要的是，在源的信元损耗比与它们的QOS要求成比例的约束下，寻求使累积的信元损耗最小化的服务准则。在本文中，我们考虑一个具有N个有限缓冲区和单个服务器的模型。大小为Bi的缓冲区i被分配了一个正数omega（i）。服务器从索引等于argmin omega（i）（B-i-Q（i））的非空缓冲区之一服务，其中Q（i）是缓冲区i的队列长度。此调度策略称为最小加权可用缓冲区策略（SWAB）。我们显示，在完全对称的设置中，SWAB策略在某些技术条件下将单元的折现预期损失最小化。对于非对称模型，我们表明，在扩散限制下，在交通繁忙的情况下，SWAB服务学科的单元格累积损失是渐近最优的。最后，我们获得了omega（i）SO的表达式，表示源在扩散极限中的细胞损失率与其QOS要求成正比。 AMS 1991年主题分类：小学60K95中学93E20。 [参考：36]

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