State Dependent Control of Closed Queueing Networks
State Dependent Control of Closed Queueing Networks
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DOI：
10.1145/3219617.3219619
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发表时间：
2018-03
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影响因子：
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通讯作者：
Siddhartha Banerjee;Yashodhan Kanoria;Pengyu Qian
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文献类型：
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作者：
Siddhartha Banerjee;Yashodhan Kanoria;Pengyu Qian
受共享交通系统（如拼车）的启发，我们研究了一个封闭的共享网络模型的状态相关控制设计。特别是，我们专注于分配政策的设计，其中平台可以选择哪个供应单位派遣，以满足传入的客户请求。供应单元随后在客户下车后在目的地可用。我们将稳定状态下需求下降的比例视为绩效指标。我们提出了一个家庭的简单和明确的状态依赖的政策，称为缩放最大权重（SMW）的政策，并证明了在完全资源池（CRP）的条件下（类似于严格版本的霍尔条件的二分匹配），任何SMW政策引起的需求下降概率的指数衰减的供应单位的数量扩展到无穷大。此外，我们表明，有一个SMW的政策，达到最佳指数之间的所有分配政策，并分析指定此政策的矩阵的客户请求到达率。最佳的法定最低工资政策可保障结构性供应不足的地区。
We study the design of state dependent control for a closed queueing network model, inspired by shared transportation systems such as ridesharing. In particular, we focus on the design of assignment policies, wherein the platform can choose which supply unit to dispatch to meet an incoming customer request. The supply unit subsequently becomes available at the destination after dropping the customer. We consider the proportion of dropped demand in steady state as the performance measure. We propose a family of simple and explicit state dependent policies called Scaled MaxWeight (SMW) policies and prove that under the complete resource pooling (CRP) condition (analogous to a strict version of Hall's condition for bipartite matchings), any SMW policy induces an exponential decay of demand-dropping probability as the number of supply units scales to infinity. Furthermore, we show that there is an SMW policy that achieves the optimal exponent among all assignment policies, and analytically specify this policy in terms of the matrix of customer-request arrival rates. The optimal SMW policy protects structurally under-supplied locations.