# Resource Assignment Algorithms for Autonomous Mobile Robots with Task Offloading
## 5 Simulation Results and Discussion  
We tested the algorithms of Section 4 in different scenarios, for which we consider high-speed ULs implemented with IEEE 802.11 ad [38] and 5G NR [39]. This scenario is compatible with the testbed hardware (HW) in [10], where a mobile robot uses both IEEE 802.11 ad and 5G connections to offload an object detection AI task. In that case, a tracking application needs, hypothetically, to detect objects from a video stream at about 30 frames per second to operate with good performance. This corresponds to a typical service latency of 33 ms if the service is placed in powerful edge or cloud computers. This latency may exceed 100 ms if the service runs in the AV CPU, which is less powerful. The network delay experienced when connecting to an edge server using the IEEE 802.11 ad link is of few ms, while it rises to dozens of ms if the service lies in the cloud and is accessed through a 5G link. The access bit rates, correspondingly, may be as large as about 100 Mbit/s for 5G or about 2 Gbit/s for IEEE 802.11 ad. More in general, the problem dimensions might correspond to systems composed of few elements, such as in an industrial environment, or to larger systems composed of several AVs and dozens of BSs, such as in a smart city. We present the performance of our algorithms with a few typical scenarios (a detailed description is given in Sections 5.1-5.3), which can be classified as follows:  
* _6/7/4_fixed, 6/7/4_variable_: These correspond to a small-medium industrial application managing intelligent vehicles used for internal logistics [40]. For instance, a small fleet of parts delivery robots moves both inside and about the enterprise location, which is covered by cheap but fast access points and served by a powerful remote cloud data center and a few in-premises edge computers. The robots could make use of computer vision to match the moved goods and verify their integrity status.
* _10/25/13_fixed, 10/25/5_variable_: These correspond to a medium-large deployment of mobile robots in a medium city to be used for services such as food/meal delivery [41]. In this case, the city wireless network can be used to offer computer vision and lidar-related services to the robots or drones to extend their operational range by offloading such tasks instead of consuming their internal energy.
* _40/60/20_variable_: This scenario corresponds to a large-sized fleet of mobile robots, which could be used for example as autonomous street sweepers in a big smart city [42]. The complex scenario in which they move, characterized by varying obstacles and constraints, requires centralized management, and task offloading accelerates video-based litter detection, lidar-based map augmentation, and cooperative data fusion to optimize the paths and times.  
For the simulated scenarios, we present some of the resulting KPIs, notably the total and average latency of the configuration, the average radio load, the number \(V_{\text{BS}}\) of radio-overloaded BSs, the average DC load, the number \(V_{\text{DC}}\) of CPU-overloaded DCs, the number \(N_{\text{call}}\) of calls to (17), and the running time. (Simulations are performed with MATLAB R2024a on an AMD Ryzen 9 4900H CPU running at 3.3 GHz.) Additionally, we show the solution on the connection graph and report a summary of the optimal configurations.  
In the fixed case, the parameters (connection matrices, bit rates, delays) are kept fixed for the whole simulation. In the variable case, new randomly generated parameters are used within the simulation, and the averaged results are shown.  
As for the comparison between the algorithms, where feasible, since VEX achieves the real optimum value, it is considered as a reference. When the problem is intractable, we consider GA to approximate the real solution, and it will serve as a reference.