Abstract We study a state-dependent bulk matching queueing system with impatient customers, where customers and servers visit the system from both sides. Servers provide services in a batch with a maximum size and take matching customers away instantly. To characterize such a queueing system, the corresponding Markov process is constructed by the number of complete batches of customers and the number of remaining customers in the incomplete batch. By analyzing this system, we find it difficult to obtain the joint stationary distribution of the Markov process. Therefore, we consider the tail asymptotics for the joint probabilities. Using the matrix analytic method and censoring technique, we obtain the one-term and general expansions for the nonzero elements of the rate matrices, where the coefficients of the expansions are presented in the closed form. On the basis of these expansion formulae, the exact tail asymptotic result for the joint stationary probabilities is derived.

中文翻译：

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具有不耐烦客户的状态相关批量匹配排队系统的尾渐近性

摘要 我们研究了一个具有不耐烦客户的状态相关批量匹配排队系统，其中客户和服务器从双方访问系统。服务器批量提供最大大小的服务，并立即将匹配的客户带走。为了表征这样的排队系统，相应的马尔可夫过程由完整批次的客户数量和不完整批次中剩余客户的数量构建。通过分析这个系统，我们发现很难得到马尔可夫过程的联合平稳分布。因此，我们考虑联合概率的尾渐近。使用矩阵解析方法和删失技术，我们获得了速率矩阵的非零元素的一项和一般展开，其中展开系数以封闭形式表示。在这些展开公式的基础上，推导出联合平稳概率的精确尾渐近结果。