当服务器具有战略行为时的路由与调度
Routing and Staffing when Servers are Strategic
AI总结：
本文研究了服务系统中服务器战略行为对路由和调度政策的影响，提出了一种考虑服务器努力成本和空闲价值的模型，并探讨了在质量驱动模式下优化总成本的方法。
摘要：
传统上，服务系统路由和调度政策的研究将服务器建模为具有固定（可能异质）服务速率。然而，服务系统通常由人组成，且人们会响应工作负荷激励；即，一个人的工作努力程度取决于工作量以及工作如何分配给负责的人。在服务系统中，路由和调度政策控制此类工作激励；因此，服务器的工作速率会受到系统路由和调度政策的影响。这一观察在建模服务系统性能时有影响，我们的目标是研究这些影响。我们在此背景下研究了M/M/N队列，这是大型服务系统的标准模型。首先，我们提出了一种
英文摘要：
Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.
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