Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State
Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State
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DOI：
10.1287/moor.2013.0606
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发表时间：
2014-05-01
影响因子：
1.7
通讯作者：
Mandelbaum, Avishai
中科院分区：
文献类型：
--
作者：
Gurvich, Itai;Huang, Junfei;Mandelbaum, Avishai
我们对研究得很好的Erlang-A队列重新讨论了许多多服务器近似。这是一个系统，只有一个id服务器池，服务于一类不耐烦的id客户。到达遵循泊松过程，服务时间呈指数分布，顾客的耐心时间也呈指数分布。我们提出了一个同时适用于所有现有的多服务器大流量机制的扩散近似：质量和效率驱动、效率驱动、质量驱动和非退化减速。我们证明了近似提供了一个广泛的稳态度量的准确估计。我们的方法是“无度量的”，因为我们不使用Erlang-A队列稳态分布的特定公式。相反，我们研究潜在的生与死过程的漂移，并将这些漂移与相应扩散过程的适当定义的漂移相耦合。再生过程和鞅参数，以及某些常微分方程解的导数界，使我们能够控制近似的精度。我们通过研究两个具有实际意义的人员配置优化问题来证明普遍近似的吸引力。
We revisit many-server approximations for the well-studied Erlang-A queue. This is a system with a single pool of i.i.d. servers that serve one class of impatient i.i.d. customers. Arrivals follow a Poisson process and service times are exponentially distributed as are the customers' patience times. We propose a diffusion approximation that applies simultaneously to all existing many-server heavy-traffic regimes: quality and efficiency driven, efficiency driven, quality driven, and nondegenerate slowdown. We prove that the approximation provides accurate estimates for a broad family of steady-state metrics. Our approach is "metric-free" in that we do not use the specific formulas for the steady-state distribution of the Erlang-A queue. Rather, we study excursions of the underlying birth-and-death process and couple these to properly defined excursions of the corresponding diffusion process. Regenerative process and martingale arguments, together with derivative bounds for solutions to certain ordinary differential equations, allow us to control the accuracy of the approximation. We demonstrate the appeal of universal approximation by studying two staffing optimization problems of practical interest.