Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times
Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times
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DOI：
10.1080/00207543.2015.1092613
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发表时间：
2016-10
影响因子：
9.2
通讯作者：
J. Schwarz;Martin Epp
中科院分区：
文献类型：
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作者：
J. Schwarz;Martin Epp
本文的动机是循环垂直输送系统（CVCS）的性能评价。CVCS是运输类型的批量队列。这些材料处理系统的特点是通常分布的到达间隔时间，这可能比批量服务时间更长。这导致在连续服务间隔中到达的数量与队列中的负载数量之间的相互依赖性。我们提出了一个新的离散时间的方法，这种批量服务队列的运输类型的一般到达和服务过程和有限的服务器和有限的队列容量的稳态分析。该方法是基于一个有限的马尔可夫链，生成完整的概率分布的关键性能指标，包括队列长度，等待时间和离开批量大小。所提出的方法在离散时隙的情况下是精确的，例如在通信系统中。我们调查的离散化误差，如果使用的方法是作为一个近似的连续时间使用数值比较的离散事件模拟。此外，我们研究了到达流的可变性对系统性能的影响，并比较了更高频率的服务器访问的积极影响与较大的皮卡容量所产生的影响。
This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.