Gated Polling Systems with Lévy Inflow and Inter-Dependent Switchover Times: A Dynamical-Systems Approach
Gated Polling Systems with Lévy Inflow and Inter-Dependent Switchover Times: A Dynamical-Systems Approach
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DOI：
10.1007/s11134-004-5555-7
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发表时间：
2005
期刊：
影响因子：
1.2
通讯作者：
I. Eliazar
中科院分区：
文献类型：
--
作者：
I. Eliazar
我们研究asymmetricpolling系统，其中：（i）传入的工作流程遵循generalLévy-subordinatorstatistics;和，（ii）服务器出席通道根据门控服务制度，并招致随机inter-dependenttimes时，从一个通道移动到其他。分析如下的动态系统的方法：一个stochasticPoincaré地图，执政的一个周期动态的轮询系统的介绍，并研究其统计特性。显式公式的平均值，协方差，和拉普拉斯变换的庞加莱映射的演变。映射变换的前向轨道--一个拉普拉斯空间中的非线性确定性动力系统--充分表征了轮询系统的随机动力学。这使我们能够探索系统的长期行为：我们证明收敛到一个（唯一的）稳态平衡，证明平衡是平稳的，并计算其统计特征。
We studyasymmetricpolling systems where: (i) the incoming workflow processes follow generalLévy-subordinatorstatistics; and, (ii) the server attends the channels according to the gated service regime, and incurs randominter-dependentswitchover times when moving from one channel to the other. The analysis follows a dynamical-systems approach: a stochasticPoincaré map, governing the one-cycle dynamics of the polling system is introduced, and its statistical characteristics are studied. Explicit formulae regarding the evolution of the mean, covariance, and Laplace transform of the Poincaré map are derived. The forward orbit of the map’s transform – a nonlineardeterministicdynamical system in Laplace space – fully characterizes thestochasticdynamics of the polling system. This enables us to explore the long-term behavior of the system: we prove convergence to a (unique) steady-state equilibrium, prove the equilibrium is stationary, and compute its statistical characteristics.