学 术 报 告
报告题目：A c/m‐Rule for Service Resource Allocation in Group‐Server Queues
报告学者：Zhe George Zhang
报告者单位：Western Washington University, United States；Simon Fraser University, Canada
摘要：Motivated by computer systems, data centers, and service systems, we study a dynamic server on/off scheduling problem in a queueing system with multi-class servers, where servers are heterogeneous and can be classified into K groups. Servers in the same group are homogeneous. Customer arrival is a Poisson process and service time is exponentially distributed. A scheduling policy determines the number of working servers (servers that are turned on) in each group at every state n (number of customers in the system). Our goal is to find the optimal scheduling policy to minimize the long-run average cost, which consists of an increasing convex holding cost and a linear operating cost. We use the sensitivity-based optimization theory to characterize the optimal policy. A necessary and sufficient condition of the optimal policy is derived. We also prove that the optimal policy has monotone structures and a quasi bang-bang control is optimal, i.e., at any state we should either turn on servers as many as possible or keep all the servers off for certain groups. We find that the optimal policy is indexed by a state-dependent computable value. Under a reasonable condition of scale economies for servers, we further prove that the optimal policy obeys a so-called c/m-rule. This rule can be viewed as a sister version of the famous cm-rule for polling queues. Finally, numerical illustrations are presented to demonstrate the main results.
(*joint work with L. Xia, Q. Li, and P. Glynn)