Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes
Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes
复制标题
具有多个客户类别的 GI/GI/1 GI 队列的动态调度
DOI：
10.1007/s11134-012-9325-7
复制
发表时间：
2013
期刊：
影响因子：
1.2
通讯作者：
Amy R. Ward
中科院分区：
文献类型：
--
作者：
Jeunghyun Kim;Amy R. Ward
研究一类具有多类客户的GI/GI/1+GI队列的动态控制问题。客户类别通过到达间隔时间、服务时间和放弃时间分布来区分。对于每一个类k∈{1,2，…，N}的客户，在接受服务之前放弃队列的成本为ck>0。目标是在每次服务器可用时动态选择服务器下一步应该服务的客户类别（并且至少有来自两个类别的等待客户），从而最小化平均成本。这个控制问题不可能精确地求解，因此我们提出了一个近似的布朗控制问题。布朗控制问题包含了每个客户类别的整个放弃分布。我们在假定每个客户类别的放弃分布的故障率增加的情况下解决了布朗控制问题。然后，我们将布朗控制问题的解解释为对原始动态调度问题的控制。最后，我们进行了仿真研究，以证明我们所提出的控制的有效性。
We consider a dynamic control problem for a GI/GI/1+GI queue with multiclass customers. The customer classes are distinguished by their interarrival time, service time, and abandonment time distributions. There is a cost ck>0 for every class k∈{1,2,…,N} customer that abandons the queue before receiving service. The objective is to minimize average cost by dynamically choosing which customer class the server should next serve each time the server becomes available (and there are waiting customers from at least two classes).It is not possible to solve this control problem exactly, and so we formulate an approximating Brownian control problem. The Brownian control problem incorporates the entire abandonment distribution of each customer class. We solve the Brownian control problem under the assumption that the abandonment distribution for each customer class has an increasing failure rate. We then interpret the solution to the Brownian control problem as a control for the original dynamic scheduling problem. Finally, we perform a simulation study to demonstrate the effectiveness of our proposed control.