Staffing to Stabilize the Tail Probability of Delay in Service Systems with Time-Varying Demand
针对时变需求的服务系统，提出解析公式来动态配置服务器数量，以稳定顾客等待时间超过阈值的概率，并给出其他性能指标的近似公式，适用于中小规模系统。
Analytic formulas are developed to set the time-dependent number of servers to stabilize the tail probability of customer waiting times for the G t /GI/s t + GI queueing model, which has a nonstationary non-Poisson arrival process (the G t ), nonexponential service times (the first GI), and allows customer abandonment according to a nonexponential patience distribution (the +GI). Specifically, for any delay target w > 0 and probability target α ∈ (0, 1), we determine appropriate staffing levels (the s t ) so that the time-varying probability that the waiting time exceeds a maximum acceptable value w is stabilized at α at all times. In addition, effective approximating formulas are provided for other important performance functions such as the probabilities of delay and abandonment, and the means of delay and queue length. Many-server heavy-traffic limit theorems in the efficiency-driven regime are developed to show that (i) the proposed staffing function achieves the goal asymptotically as the scale increases, and (ii) the proposed approximating formulas for other performance measures are asymptotically accurate as the scale increases. Extensive simulations show that both the staffing functions and the performance approximations are effective, even for smaller systems having an average of three servers. The e-companion is available at https://doi.org/10.1287/opre.2017.1678 .