In this paper, we analyze a priority queueing system with a regular queue and an orbit. Customers in the regular queue have priority over the customers in the orbit. Only the first customer in the orbit (if any) retries to get access to the server, if the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. Closed-form expressions are obtained for the probability generating functions of the number of customers in the queue and orbit, in steady-state. Another contribution is the extensive singularity analysis of these probability generating functions to obtain the stationary (asymptotic) probability mass functions of the queue and orbit lengths. Influences of the service times and the retrial policy are illustrated by means of some numerical examples.

中文翻译：

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具有恒定重试策略的优先级重试队列中的队列长度分析

在本文中，我们分析了具有规则队列和轨道的优先级排队系统。常规队列中的客户优先于在轨客户。如果队列和服务器为空（恒定的重试策略），则只有在轨的第一个客户（如果有）重试以访问服务器。与现有文献相比，我们假设高优先级和低优先级客户的服务时间分布不同。在稳态下，获得队列和轨道中客户数量的概率生成函数的封闭式表达式。另一个贡献是对这些概率生成函数进行了广泛的奇异性分析，以获得队列和轨道长度的固定（渐近）概率质量函数。