论文标题
带有Mittag-Leffler活动间的排队模型
Queuing models with Mittag-Leffler inter-event times
论文作者
论文摘要
我们在连续时间研究三个非等效的排队模型，每个模型都以不同的方式概括了经典的M/M/1队列。在所有型号中，事件间的时间是Mittag-Leffler分布式，这是一个沉重的尾巴分布，没有时刻。对于每个模型，我们回答了队列经常（``复发''或``稳定''制度）或不（瞬态制度）的问题。除了这个问题外，每个模型的不同分析属性使我们能够回答许多问题，例如平衡分布的存在和描述，混合时间，回报概率的渐近行为以及矩和功能极限定理。
We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no moments. For each of the models we answer the question of the queue being at zero infinitely often (the `recurrence' or `stable' regime) or not (the transient regime). Aside from this question, the different analytical properties of each models allow us to answer a number of questions such as existence and description of equilibrium distributions, mixing times, asymptotic behaviour of return probabilities and moments and functional limit theorems.
