Analytical computation of sojourn time distributions in large-scale conveyer systemsAnalysis of the impact of material flow control policies on the material flow system

在复杂的网络化物料搬运系统的规划和尺寸确定中，确定了功能、布局和设施。各自的内部物流系统应产生一定的物流绩效。现代物流系统专注于在短交货期内提供准确的物料供应。物流绩效不仅包括达到特定的每次运输或分拣量（吞吐量），还包括确保在预设时间内（交货时间）完成订单。在粗略规划阶段使用的平均值在这里是不够的，因为具体的单个值有时可能是它的倍数。当前项目阶段开发了一个分析工具（称为物料流分析仪）。时间离散分析模型构成了分析工具的基础。与经典（连续）分析模型相反，离散时间模型不仅提供平均值，而且还提供实现特定特征的概率或可能性（所谓的分位数）。这包括等待时间、周转时间和所需的缓冲区大小，其结果只能通过精心设计的模拟实验来确定。物料流分析仪是一种工具，可以快速计算所需的比率，如利用率，以及提前期和缓冲区分配的概率分布，无需复杂的模拟，准确性未知。很明显，基于物料流节点的控制策略只能通过修正系数来解决。为了精确确定时间，必须显式地对它们进行建模。修正后的主物流节点包括交叉单元和存取机，在开发的试验环境中进行了系统的试验和计算，结果表明时间离散计算方法与预期值吻合较好。通过开发的测试环境和比较计算系统地进行的测试证明了与时间离散分析预期值的良好对应关系。因此，可以认为某些非平凡网络拓扑结构的结果不属于这种新的计算方法，而是其他已知的难以量化的影响，如相关性。因此，继续研究项目的目标除了进一步开发计算方法之外，还可以使用“物质流分析仪”工具进行更详细和系统的研究，探讨复杂物流系统时间离散模型中的不同效应，如控制策略或相关性的形成、效应和传播。

In the planning and dimensioning of complex, networked material handling systems, functionality, layout and facilities were set. The respective intralogistical system should produce a certain logistic performance. Modern logistic systems focus on a time-accurate material supply with short lead times. The logistic performance consists not only of reaching a specific transport or sort amount per time (throughput), but also of ensuring the settlement of orders within a preset time (lead time). The mean values used in the rough planning phase do not suffice here as concrete individual values can sometimes be a multiple of that.The current project phase developed an analysis tool (called Material Flow Analyzer). Time-discrete analytical models form the basis of the analysis tool. In contrast to classical (continuous) analytical models, discrete time models provide not only mean values but also about the probability or likelihood that particular characteristics are achieved (so-called quantiles). This includes waiting times, turnaround and required buffer sizes, for which results can be determined only by means of elaborate simulation experiments. With the Material Flow Analyzer there is a tool available which can calculate required ratios such as utilization, but also probability distributions of lead times and buffer allocations, quickly and without elaborate simulation in not known accuracy.It became evident that control strategies based on material flow node can only inadequately covered by correction factors. For a precise determination of the time they must be modeled explicitly. The amended main material flow node includes crossing elements and storage/retrieval machines.The developed test environment by systematically made tests and calculations show that the time-discrete calculation method has a good agreement with the expected values. The tests systematically carried out by the developed test environment and comparative calculations certify a good correspondence with the values to be expected to the time-discrete analyses. For this reason, it can be assumed that results in some non-trivial network topologies are not owed this new calculation method, but other, already known, hardly quantifiable effects like correlation are responsible.The goal for the continuation of the research project is therefore in addition to the further development of calculation methods to make more detailed and systematic studies with the 'Material Flow Analyzer' tool, to explore different effects such as control strategies or formation, effect and propagation of correlation in time-discrete models of complex material flow systems.