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

在规划和确定复杂的、网络化的物资搬运系统的尺寸时，设定了功能、布局和设施。各自的内部逻辑系统应该产生一定的逻辑性能。现代物流系统注重时间精准、交货期短的物资供应。物流绩效不仅包括每一次达到特定的运输量或分拣量(吞吐量)，而且还包括确保在预设时间(提前期)内完成订单结算。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平均值的倍数。当前项目阶段开发了一种分析工具(称为物质流分析仪)。时间离散分析模型构成了分析工具的基础。与经典的(连续)分析模型不同，离散时间模型不仅提供平均值，还提供关于实现特定特征的概率或可能性(所谓的分位数)的信息。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。有了物流分析器，就有了一种工具，它可以快速地计算所需的比率，如利用率，以及提前期和缓冲区分配的概率分布，而不需要以未知精度进行详细的模拟。很明显，基于物流节点的控制策略只能用修正系数来覆盖。为了准确地确定时间，必须对它们进行显式建模。改进后的主物流节点包括交叉单元和存取机，开发的测试环境通过系统的测试和计算表明，时间离散计算方法与期望值吻合较好。由所开发的测试环境和比较计算系统地进行的测试证明，与时间离散分析的期望值有很好的一致性。因此，可以假设，一些非平凡网络拓扑的结果不是由这种新的计算方法造成的，而是其他已知的、难以量化的影响，如相关性。因此，继续研究的目标是除了进一步发展计算方法，利用物质流分析仪工具进行更详细和系统的研究，探索复杂物质流系统的时间离散模型中相关性的控制策略或形成、影响和传播等不同的影响。

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.