Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times
针对循环垂直输送系统这类运输型批量队列，提出一种基于有限马尔可夫链的离散时间方法，用于精确分析队列长度、等待时间等关键性能指标，并研究了离散化误差及到达流变异性对系统性能的影响。
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.