The Impact of Dependent Service Times on Large-Scale Service Systems
The Impact of Dependent Service Times on Large-Scale Service Systems
复制标题
依赖服务时间对大规模服务系统的影响
DOI：
10.1287/msom.1110.0363
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
G. Pang;W. Whitt
本文研究了连续服务时间间的相关性对大规模服务系统瞬态和稳态性能的影响。这是通过研究随时间变化的到达率，利用最近建立的大流量限制，允许服务时间之间的依赖性的无限服务器的排队模型。这个极限表明，在任何时候，系统中的客户数量近似为高斯分布，其中时变均值不受相关性的影响，但时变方差受相关性的影响。因此，所需的工作人员，以满足习惯的服务质量目标，在一个大规模的服务系统，许多服务器的基础上，正常的近似主要是受服务时间之间的依赖性，通过这种随时间变化的方差。本文开发的公式和算法，以量化的服务时间之间的依赖性的方差的影响。近似直接应用于无限服务器模型，但也间接应用于相关的有限服务器模型，利用基于峰值（无限服务器模型中方差与均值的比值）的近似。与模拟的比较证实，近似可以是有用的，以评估的依赖性的影响。
This paper investigates the impact of dependence among successive service times on the transient and steady-state performance of a large-scale service system. This is done by studying an infinite-server queueing model with time-varying arrival rate, exploiting a recently established heavy-traffic limit, allowing dependence among the service times. This limit shows that the number of customers in the system at any time is approximately Gaussian, where the time-varying mean is unaffected by the dependence, but the time-varying variance is affected by the dependence. As a consequence, required staffing to meet customary quality-of-service targets in a large-scale service system with finitely many servers based on a normal approximation is primarily affected by dependence among the service times through this time-varying variance. This paper develops formulas and algorithms to quantify the impact of the dependence among the service times on that variance. The approximation applies directly to infinite-server models but also indirectly to associated finite-server models, exploiting approximations based on the peakedness (the ratio of the variance to the mean in the infinite-server model). Comparisons with simulations confirm that the approximations can be useful to assess the impact of the dependence.