# Mobility- and Energy-Aware Cooperative Edge Offloading for Dependent Computation Tasks +
## 3 System Model  
### Overview  
We consider a three-layer heterogeneous network with multiple devices and small cells. As illustrated in Figure 1, each small cell has a base station (BS), which could, for instance, be a Wi-Fi access point or a femto cell base station. In addition, each BS is affiliated with an MEC server, e.g., an MEC server could be directly attached to the BS, or the MEC service could be provided to the BS via an edge cloud network architecture [58]. The devices, which in the 3 GPP standardization language are referred to as user equipment nodes, are mobile.  
While the 3 GPP standardization language uses the abbreviation UE for all user equipment nodes, we reserve the UE abbreviation for a device with a set of computation-intensive tasks. The remaining devices that have sufficient computation/communication resources to be able to act as helpers or relays, such as mobile phones, tablets, and laptop computers, are referred to as user equipment helper nodes (UHs). For simplicity of the system model, we consider a single UE with a set of computation-intensive tasks in this study. The system model with a single UE is directly applicable for scenarios that combine a low density of end devices (UEs) with computation-intensive tasks with a generally high density of UHs, such that each UE can essentially form its own surrounding cloud of adjacent D2D-connected UHs. Similar to our system model, the preceding non-cooperative dependent-task offloading studies considered either a single UE with a set of dependent tasks [51] or a set of UEs (each with one task) that, in the aggregate, form one set of dependent tasks [57]. The system model in this article can serve as a basis for future model extensions to multiple UEs (each with a set of dependent tasks) or, effectively, to multiple independent sets of dependent tasks. One possible strategy for this extension is to model the UHs with already assigned tasks as being outside of the D2D ranges of UEs that seek to offload tasks.  
The UHs are randomly distributed along the UE's path, and we let \(\mathcal{I}=\{\mathrm{UH}_{1},\mathrm{UH}_{2},\ldots,\mathrm{UH}_{l}\}\) represent the set of UHs. A \(\mathrm{UH}_{i}\in\mathcal{I}\) has a service coverage radius \(R_{i}\). Similarly, we denote \(\mathcal{M}=\{S_{1},S_{2},\ldots,S_{M}\}\) as the set of edge servers, whereby server \(S_{m}\in\mathcal{M}\) has the service coverage radius \(R_{m}\). The offloading process is  
Figure 1: System model: A user equipment node (UE) with a set of computation tasks moves through the coverage regions of different base stations (BSs) with associated MEC servers, with potentially overlapping coverage areas, and within the D2D link ranges of potential helper/relay (UH) nodes. The macro BS coordinates the task offloading.  
controlled by the macro BS (MBS), which knows the channel states and the user positions, whereby the computational load and reliability aspects of the MBS control can be addressed through decentralized control plane techniques [59]. The MBS is responsible for making the offloading decisions. The system model notations are summarized in Table 1.