On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers
研究了顾客不耐烦且可能离队的排队系统，用流体模型推导出大到达率下渐近最优的容量规划方案，并证明该方案的最优性差距有界。
We consider queueing systems in which customers arrive according to a Poisson process and have exponentially distributed service requirements. The customers are impatient and may abandon the system while waiting for service after a generally distributed amount of time. The system incurs customer-related costs that consist of waiting and abandonment penalty costs. We study capacity sizing in such systems to minimize the sum of the long-term average customer-related costs and capacity costs. We use fluid models to derive prescriptions that are asymptotically optimal for large customer arrival rates. Although these prescriptions are easy to characterize, they depend intricately upon the distribution of the customers' time to abandon and may prescribe operating in a regime with offered load (the ratio of the arrival rate to the capacity) greater than 1. In such cases, we demonstrate that the fluid prescription is optimal up to O(1). That is, as the customer arrival rate increases, the optimality gap of the prescription remains bounded.