A vacation queue with setup and close-down times and batch Markovian arrival processes
A vacation queue with setup and close-down times and batch Markovian arrival processes
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DOI：
10.1016/s0166-5316(03)00058-0
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发表时间：
2003-11-01
影响因子：
2.2
通讯作者：
Takahashi, Y
中科院分区：
文献类型：
--
作者：
Niu, ZS;Shu, T;Takahashi, Y
我们考虑一个具有关闭/启动时间以及批量马尔可夫到达过程（BMAP）的有限容量单服务器休假队列，其中服务时间、休假时间、启动时间和关闭时间一般是分布式的。该排队模型在基于交换虚拟连接（SVC）的IP - over - ATM网络和多协议标签交换（MPLS）网络中具有潜在应用。通过应用补充变量技术，我们针对单休假和多休假模型以及部分批量接受策略（PBAS）或整体批量接受策略（WBAS）服务规则开发了一种统一的解决方案。对于这两种模型，我们得到了批量到达时刻和任意时刻的队列长度分布、整批或一批中任意顾客的丢失概率、服务器启动率、服务器利用率以及等待时间分布的拉普拉斯 - 斯蒂尔杰斯变换（LST）。通过数值例子，我们发现：（1）在用户的服务质量（例如，丢失概率、等待时间）和系统性能（例如，服务器启动率、服务器利用率）之间存在一种权衡；（2）系统性能不仅与到达过程的一阶和二阶矩密切相关，还与顾客到达的模式（分布）密切相关；（3）平均批量大小是影响排队系统性能比批量大小分布类型更为关键的因素。这些结论在基于IP - over - ATM或更一般的基于MPLS的网络设计中具有指导意义。（C）2003 Elsevier Science B.V.保留所有权利。
We consider a finite-capacity single-server vacation queue with close-down/setup times and batch Markovian arrival process (BMAP), where both the service time, the vacation time, the setup time, and the close-down time are generally distributed. The queueing model has potential applications in SVC (switched virtual connection)-based IP-over-ATM networks and multiple protocol label switched (MPLS) networks. By applying the supplementary variable technique, we develop a unified solution to both the single-vacation and multiple-vacation models and for either the PBAS (partial batch acceptance strategy) or the WBAS (whole batch acceptance strategy) service disciplines. For both models, we obtain the queue length distribution at batch arrival epochs and that at an arbitrary time instant, the loss probability of a whole batch or an arbitrary customer in a batch, server setup rate, server utilization ratio, and the LST of the waiting time distribution. Through the numerical examples, we find that: (1) there is a trade-off between the user's quality-of-service (e.g., loss probabilities, wanting times) and the system performance (e.g., server setup rate, server utilization ratio); (2) the system performance is closely related not only to the first and second order moments of the arrival process but also the pattern (distribution) of the customer arrivals; (3) mean batch size is a much more critical factor to influence the queueing system's performance than the type of batch size distribution. These conclusions are of instructive meanings in the design of IP-over-ATM or more generally MPLS-based networks. (C) 2003 Elsevier Science B.V. All rights reserved.