Equivalence of Fluid Models for Gt/GI/N +GI Queues
Equivalence of Fluid Models for Gt/GI/N +GI Queues
复制标题
Gt/GI/N GI 队列流体模型的等效性
DOI：
10.1007/978-3-030-25498-8_14
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
G. Pang
中科院分区：
文献类型：
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作者：
W. Kang;G. Pang
最近已经为Gt/GI/N +GI队列开发了三种不同的流体模型公式，包括Whitt（2006）中通过跟踪每个客户的经过的服务和耐心时间的双参数流体模型，Kang和Ramanan（2010）中的测量值流体模型及其在Zuniga（2014）中通过跟踪每个客户的经过的服务和耐心时间的扩展，Zhang（2013）通过跟踪每个客户的剩余服务和耐心时间，建立了一个度量值流体模型。我们表明，在一般的初始条件下，前两个流体模型配方跟踪经过时间（Whitt和Kang和Ramanan的流体模型）是等价的，当服务时间和耐心时间分布具有密度时，可以用来描述相同的Gt/GI/N +GI排队，而Zuniga的流体模型和Zhang的流体模型只有在Gt/GI/N +GI排队的初始条件满足一定的假设时才是等价的。我们确定这些条件下，Zuniga的流体模型和张的流体模型可以来自彼此相同的系统。发现的等价性提供了重要的影响，了解最近的发展，非马尔可夫多服务器队列。
Three different fluid model formulations have been recently developed for Gt/GI/N +GI queues, including a two-parameter fluid model in Whitt (2006) by tracking elapsed service and patience times of each customer, a measure-valued fluid model in Kang and Ramanan (2010) and its extension in Zuniga (2014) by tracking elapsed service and patience times of each customer, and a measure-valued fluid model in Zhang (2013) by tracking residual service and patience times of each customer. We show that, under general initial conditions, the first two fluid model formulations tracking elapsed times (Whitt’s and Kang and Ramanan’s fluidmodels) are equivalent and can be used to describe the same Gt/GI/N +GI queue when the service and patience time distributions have densities, whereas, Zuniga’s fluid model and Zhang’s fluid model are equivalent only when the initial conditions for the Gt/GI/N +GI queue satisfy certain assumptions. We identify these conditions under which Zuniga’s fluid model and Zhang’s fluid model can be derived from each other for the same system. The equivalence properties discovered provide important implications for the understanding of the recent development for non-Markovian many-server queues.