Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered.

在排队应用程序的推动下，我们研究了各种具有依赖性的反射自回归过程。除此之外，我们研究了到达间隔和服务时间成比例地取决于加法和/或减法延迟的情况，以及到达间隔时间取决于先前到达的服务持续时间是否超过随机阈值的情况。此外，我们研究自回归参数恒定以及离散或连续随机变量的情况。还讨论了更一般的依赖结构。我们的主要目的是研究一类广泛的自回归类型的递归，其中提出了一些独立性假设，并提供了详细的精确分析。我们根据已知拉普拉斯变换的乘积的无限和来提供系统中客户等待时间分布的拉普拉斯变换的表达式。还考虑了整数值反射自回归过程，该过程可用于对具有不耐烦客户和一般依赖结构的新颖重试排队系统进行建模。对于这样的模型，我们以已知生成函数的乘积的无限和的形式提供了静止轨道队列长度分布的概率生成函数的表达式。还考虑了对多维设置的首次尝试。