In this paper, we study a priority queueing-inventory problem with two types of customers. Arrival of customers follows Marked Markovian arrival process and service times have phase-type distribution with parameters depending on the type of customer in service. For service of each type of customer, a certain number of additional items are needed. High priority customers do not have waiting space and so leave the system when on their arrival a priority 1 customer is in service or the number of available additional items is less than the required threshold. Preemptive priority is assumed. Type 2 customers, encountering a busy server or idle with the number of available additional items less than a threshold, go to an orbit of infinite capacity to retry for service. The customers in orbit are non-persistent: if on retrial the server is found to be busy/idle with the number of additional items less than the threshold, this customer abandons the system with certain probability. Such a system represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems. The probability distribution of the system states is computed, using which several of the characteristics are derived. A detailed numerical study of the system, including the analysis of the influence of the threshold, is performed.

中文翻译：

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具有其他项的两优先级单服务器重试队列

在本文中，我们研究了两种类型的客户的优先级排队库存问题。客户的到达遵循明显的马尔可夫到达过程，服务时间具有阶段类型的分布，其参数取决于服务客户的类型。为了为每种类型的客户提供服务，需要一定数量的其他物品。高优先级客户没有等待空间，因此在他们到达时，优先级为1的客户正在使用中，或者可用其他项目的数量少于要求的阈值，请离开系统。假定具有抢占优先权。第2类客户遇到服务器繁忙或闲置而可用的附加项目数少于阈值的情况，将进入无限容量的轨道重试服务。轨道上的客户是非永久性的：如果重试后发现服务器繁忙/空闲，且其他项目数少于阈值，则该客户有一定的概率放弃系统。这样的系统代表了许多实际系统的足够精确的模型，包括无线传感器网络以及带有能量收集和医疗保健系统的认知无线电系统。计算系统状态的概率分布，使用该分布可以导出几个特征。对系统进行了详细的数值研究，包括对阈值影响的分析。包括无线传感器网络以及带有能量收集和医疗保健系统的认知无线电系统。计算系统状态的概率分布，使用该分布可以导出几个特征。对系统进行了详细的数值研究，包括对阈值影响的分析。包括无线传感器网络以及带有能量收集和医疗保健系统的认知无线电系统。计算系统状态的概率分布，使用该分布可以导出几个特征。对系统进行了详细的数值研究，包括对阈值影响的分析。