# Characterization of Dynamic Blockage Probability in Industrial Millimeter Wave 5G Deployments
## 3 System Model
### Models of Individual Machines  
For individual machines, we utilize 3D high-precision animated models freely available in the BlenderKit database [24]. To assess LoS blockage probability in different mmWave 5G deployment conditions, we differentiate between models inherent for light and heavy industries. The size of machines--width \(u_{M}\), length \(u_{M}\), and height \(h_{M}\)--are dictated by the model and provided as a part of the model's description. For heavy industry, the following models have been selected:  
* _Universal Robot Ur5e with two-finger grip RG2 [25]_. A lightweight, very flexible, and compatible industrial robot arm allows to automate repetitive and dangerous tasks with a load capacity of up to 50 kg. This robot is ideal for optimizing small collaborative processes such as collection, placement, and testing. Thanks to a working radius of up to 0.85 m, it ensures accessibility of everything within reach. The RG2 flexible gripper can be used for parts of a wide variety of sizes and shapes;
* _Kuka Quantec robot with pallet gripper [26]_. A heavy-weight robot equipped with a pallet gripper. It has a load capacity of up to 240 kg and a range of up to 3.2 m. It is specially designed for complex pallet stacking tasks, its power and dynamic characteristics are suitable for trouble-free stacking of several pallets to a large height. It is also possible to use in conditions of low temperatures up to \(-\)30 degrees. Due to its versatility, the robot is suitable for use in almost all industries from the medical sector to the automotive industry and foundry. For the light industry, the following have been chosen:
* _Two-handed robot KUKA Iwa 14 [27]_. A special robot with a double lever with an additional central vertical axis and two parallel grips. Each arm has a load capacity of up to 14 kg and a range of up to 0.9 m. It is excellent for coating, machining and polishing, palletizing, assembling, moving and other operations with materials;
* _KUKA Iwa 14 robot with linear block and two-finger grip [27]_. A lightweight robot with a load capacity of up to 14 kg and a linear block, which is used as an additional axis, significantly expands the working space of the robot, in this case, up to 3.8 m. Up to four robots can be used on one control unit. This model is suitable for delicate assembly work.  
Note that all the considered autonomous machines perform periodic movements of their mobile parts. The intensity of these movements depends on the particular use case. We also assume that movements of different machines appear to be de-synchronized for an external observer, i.e., communications technology. Note that this does not necessarily mean that these machines do not perform a certain procedure aligned in time. Synchronized movements can also be taken into account by redesigning the model as discussed below. When deriving the generic model below we will also consider two cases of machines' heights, \(H_{B}\): (i) \(H_{B}\) is a random variable with probability density function (pdf), \(f_{H_{B}}(x)\), and cumulative distribution function \(F_{H_{B}}(x)\); and (ii) \(H_{B}\) is constant and given by the machine model's dimension.