Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty
Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty
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具有模型不确定性的大流量下多类排队控制问题的渐近分析
DOI：
10.1287/stsy.2019.0034
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发表时间：
2017
影响因子：
--
通讯作者：
A. Cohen
中科院分区：
文献类型：
--
作者：
A. Cohen
我们研究了在大流量下具有有限缓冲区的多类 M/M/1 排队控制问题，其中决策者不确定系统的到达率和服务，并通过调度和准入/拒绝决策来最小化考虑不确定性的折扣成本。主要结果是通过[16]中研究的基础随机微分博弈导出的 $c\mu$ 型策略的渐近最优性。在此策略下，当工作量低于某个取决于模糊程度的截止值时，很可能不会执行拒绝。当工作量超过此截止值时，将仅从具有最便宜的拒绝成本的缓冲区中执行拒绝，并以某些参考模型中的平均服务率加权。对于所有模糊级别，策略的分配部分都是相同的。这是第一个解决具有模型不确定性的大流量排队控制问题的工作。
We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions acts to minimize a discounted cost that accounts for the uncertainty. The main result is the asymptotic optimality of a $c\mu$-type of policy derived via underlying stochastic differential games studied in [16]. Under this policy, with high probability, rejections are not performed when the workload lies below some cut-off that depends on the ambiguity level. When the workload exceeds this cut-off, rejections are carried out and only from the buffer with the cheapest rejection cost weighted with the mean service rate in some reference model. The allocation part of the policy is the same for all the ambiguity levels. This is the first work to address a heavy-traffic queueing control problem with model uncertainty.