Abstract In this paper, we consider a single-server retrial model with multiple classes of customers. Arrival of customers follow independent Poisson rule. A new customer, facing a busy server upon his arrival, may join the corresponding (class-dependent) orbit queue with a class-dependent probability, or leaves the system forever (balks). The orbit queues follow constant retrial rate discipline, that is, only one (oldest) orbital customer of each orbit queue makes attempts to occupy the server, in a gap of class-dependent exponential times. Within each class, service times are assumed to be independent and identically distributed (iid). We show that this setting generalizes the so-called two-way communication systems. This multiclass system with general service time distributions is analysed using regenerative approach. Necessary and sufficient stability conditions, as well as some explicit expressions for the basic steady-state probabilities, are obtained. A restricted, two-way communication model with exponential service time distributions, is analysed by matrix-analytic method. Moreover, we combine both methods to efficiently derive explicit solutions for the restricted model. An extensive simulation analysis is performed to gain deep insight into the model stability and performance. It is shown that both the simulated and exact results agree on some important measures for which analytical expressions are available, and hence establish the validity of our theoretical treatment. We numerically study the sophisticated dependence structure of the model to uncover the orbits interaction. We give further details and intuitive explanation for the system performance which complements the derived explicit expressions.

中文翻译：

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恒重试率和停顿的多类轨道队列的性能分析和稳定性

摘要 在本文中，我们考虑具有多类客户的单服务器重试模型。客户的到达遵循独立的泊松规则。新客户在到达时面对繁忙的服务器，可能以类相关的概率加入相应的（类相关的）轨道队列，或者永远离开系统（犹豫）。轨道队列遵循恒定的重试率规则，即每个轨道队列中只有一个（最老的）轨道客户尝试占用服务器，间隔与类别相关的指数倍。在每一类中，服务时间被假定为独立同分布（iid）。我们表明这种设置概括了所谓的双向通信系统。使用再生方法分析具有一般服务时间分布的多类系统。得到了必要和充分的稳定性条件，以及基本稳态概率的一些显式表达式。用矩阵分析方法分析了具有指数服务时间分布的受限双向通信模型。此外，我们结合这两种方法来有效地推导出受限模型的显式解决方案。执行广泛的仿真分析以深入了解模型的稳定性和性能。结果表明，模拟结果和精确结果都与一些可用分析表达式的重要度量一致，因此建立了我们理论处理的有效性。我们通过数值研究模型的复杂依赖结构以揭示轨道相互作用。