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A Roots Method in GI/PH/1 Queueing Model and Its Application

机译：GI / pH / 1排队模型的根方法及其应用

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In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post- departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is com- posed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF’s (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribu- tion with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.
机译：在本文中，我们介绍了一个根方法，它使用了相关特性方程单元圆内的根部，以评估三个时期的稳态系统长度分布（抵达，任意，和后）和索Jou- GI / pH / 1排队模型中的时间分布。对于空气基地来检查飞机油是非常重要的，因为低质量的油导致飞机的掉落或分解。由于飞机的电压检查是若干检查步骤，它有时会导致列车拥塞和库存补充的延迟。我们分析了从实际数据中提供的来自实际数据的运动时间和检查（服务）时间，该数据来自罗基法（韩国共和国）基地。我们发现，油的组织时间遵循正常分布，较小的偏差，并且服务时间遵循相型分布，这首先由Neges引入指数分布的短缺。最后，我们将GI / ph / 1排队模型应用于石油火车拥塞问题，并分析了队列中客户数量（石油列车）的分布及其使用Chaudhry建议的根方法的平均索音时间gi / c-msp / 1。

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