论文标题
M/g/1重试队列与事件依赖性到达
The M/G/1 retrial queue with event-dependent arrivals
论文作者
论文摘要
我们介绍了一个新型的单人队列，并具有一般的重试时间和事件依赖性到达。这是用于研究服务系统的多功能模型，在该模型中，服务器需要一个不可忽略的时间来在服务完成后检索等待客户，而将来的到来取决于上次实现的事件。这样的模型是由客户在服务系统中的行为激励的，他们决定根据上次实现的事件加入。我们研究了在服务完成时期和使用补充变量技术的任意时期内调查必要和充分的稳定性条件，并在任意时期内得出固定分布。我们还研究了高回收率下的渐近行为。绩效指标是明确得出的，并进行了广泛的数值示例，以研究事件依赖性的影响。此外，有限的优化问题得到制定和解决，以最终的目标来研究入院控制问题。
We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon a service completion, while future arrivals depend on the last realized event. Such a model is motivated by the customers' behaviour in service systems where they decide to join based on the last realized event. We investigate the necessary and sufficient stability condition and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch using the supplementary variable technique. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to investigate the admission control problem.
