We consider a single-server queueing system with server vacations as the important component of the polling queueing model of a real-world system. Period of continuous operation of the server (the maximum server attendance time) is restricted, but the service of a customer cannot be interrupted when this period expires. Such features are inherent for many real-world systems with resource sharing. We assume that the customers arrival is described by the Markovian Arrival Process and service, vacation and maximum server attendance times have a phase-type distribution. We derive the stationary distributions of the system states and waiting time. Taking in mind the necessity of further application of the results to modeling the polling queueing systems, the distribution of the server visiting time is derived. Extensive numerical results are presented. They highlight that an account of the coefficient of variation of vacation and maximum attendance time is very important for exact evaluation of the key performance measures of the system, while only the results for the coefficient of variation equal to zero or one are known in the literature. Impact of the possible customers impatience, which is intuitively important because the time-limited service is considered, is confirmed by the results of the numerical experiments. Optimization problem of matching the durations of vacation and maximum attendance time is considered.

中文翻译：

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非抢占式限时排队服务系统的分析

我们将具有服务器休假的单服务器排队系统视为现实系统的轮询排队模型的重要组成部分。服务器的连续运行时间（最大服务器上班时间）受到限制，但是在此时间段过后，不能中断客户的服务。对于具有资源共享的许多实际系统而言，此类功能是固有的。我们假设客户的到达是由马尔可夫到达过程描述的，服务，休假和最大服务器出勤时间具有阶段类型的分布。我们得出系统状态和等待时间的平稳分布。考虑到需要进一步将结果应用于轮询排队系统的建模，得出服务器访问时间的分布。给出了广泛的数值结果。他们强调指出，休假和最大出勤时间的变异系数的帐户对于准确评估系统的关键绩效指标非常重要，而文献中仅知道变异系数等于零或一的结果。潜在客户不耐烦的影响，这在直觉上很重要，因为考虑到限时服务，由数值实验的结果证实。考虑了使休假时间与最大出勤时间匹配的优化问题。