New perspectives on the Erlang-A queue
New perspectives on the Erlang-A queue
复制标题
Erlang-A 队列的新视角
DOI：
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发表时间：
2017
影响因子：
1.2
通讯作者：
Jamol Pender
中科院分区：
文献类型：
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作者：
Andrew J. Daw;Jamol Pender
摘要 非平稳Erlang-A队列是一种基本的排队模型，用于描述可能会出现客户放弃的大规模多服务器服务系统的动态行为，例如呼叫中心、医院和城市交通系统。在本文中，我们对其所有瞬态和稳态矩、矩生成函数和累积生成函数开发了新颖的近似。我们还为我们的近似值和真实模型的差异提供了精确的界限。更重要的是，我们表明我们的近似具有明确的随机表示作为移位泊松随机变量。此外，我们还能够证明，在某些稳定性条件下，我们的近似值和界限也适用于非平稳 Erlang-B 和 Erlang-C 排队模型。
Abstract The nonstationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large-scale multiserver service systems that may experience customer abandonments, such as call centers, hospitals, and urban mobility systems. In this paper we develop novel approximations to all of its transient and steady state moments, the moment generating function, and the cumulant generating function. We also provide precise bounds for the difference of our approximations and the true model. More importantly, we show that our approximations have explicit stochastic representations as shifted Poisson random variables. Moreover, we are also able to show that our approximations and bounds also hold for nonstationary Erlang-B and Erlang-C queueing models under certain stability conditions.