## 1 Introduction
### The Multi-Tiered Networked Simulated Environment  
According to these considerations, Figure 1 reports the general architecture of the virtualized 5G-enabled Mobile-Fog-Cloud technological platform that is considered in this paper. The platform is composed of a virtualized Mobile device, a proximate virtualized Fog node, and a remote virtualized Cloud node. These nodes inter-communicate through Transport -layer TCP/IP connections that are supported, in turn, by the underlying 5G networking infrastructure. Specifically, in Figure 1, we have that:  
1. Mobile-Fog communication is supported by a two-way WiFi-based (possibly, mobile) single-hop TCP/IP connection. \(R_{U}\) (resp., \(R_{D}\)) is the steady-state throughput of the Mobile-to-Fog (resp., Fog-to-Mobile) upstream (resp., downstream) TCP/IP one-way connection. Their peak values depend, in turn, on the adopted WiFi technology;
2. Mobile-Cloud communication is supported by a two-way 3G/4G cellular (possibly, mobile and/or multi-hop) TCP/IP connection. \(B_{U}\) (resp., \(B_{D}\)) is the steady-state throughput of the Mobile-to-Cloud (resp., Cloud-to-Mobile) upstream (resp., downstream) TCP/IP one-way connection;
3. Cloud-Fog communication is supported by a two-way (possibly, wired and multi-hop) backhaul TCP/IP connection. \(R_{0}\) is the corresponding steady-state throughput. From a technological perspective, the key role of the 5G paradigm is to allow the computing nodes of Figure 1 to exploit simultaneously multiple heterogeneous radio technologies, in order to perform bandwidth pooling and/or trading network energy versus access latency (see the last column of Table 1). According to this consideration, the reference architecture of Figure 1 assumes that: (i) the mobile device is equipped with at least two Network Interface Cards (NICs), typically, a WiFi NIC and a 3G/4G Cellular NIC; (ii) the Fog node is equipped with a WiFi NIC and an Ethernet NIC; and (iii) the Cloud node is equipped with a Cellular NIC and an Ethernet NIC. Figure 1: The considered 5G-supported Mobile-Fog-Cloud virtualized infrastructure. WAN: Wide Area Network; LAN: Local Area Network; CT: Cellular Tower; AP: Access Point; GWR: GateWay Router. Single (resp., double)-arrowed paths indicate one-way (resp., two-way) TCP/IP connections. The mobile device must run a given application that is composed of multiple inter-connected tasks (i.e., subroutines or methods). Being energy limited and equipped with limited computing resources, the mobile device may decide to execute each task locally or offload it to the Fog node or the Cloud node. For this purpose, the Fog node (resp., the Cloud node) is virtualized, in order to host a Fog clone (resp., a Cloud clone) of the mobile device. These clones act as virtual processors and execute the offloaded tasks on behalf of the mobile device. At the Application layer, inter-task communications exploit the (aforementioned) Mobile-Fog, Mobile-Cloud, and Cloud-Fog 5G-supported TCP/IP connections. In the considered reference scenario, the mobile clones at the Fog and Cloud nodes are implemented by resorting to the emerging CoNtainer (CNT)-based technology [7]. Its main peculiar feature is that it uses an Execution Engine, in order to _dynamically_ carry out resource allocation (see Figure 2 of the _VirtFogSim_ user guide for a description of the virtualized clone organization). As a consequence, the physical resources required by a container may be scaled up/down in _real time_ by the corresponding Execution Engine. For this purpose, each server at the Mobile, Fog, and Cloud nodes hosts a number \(nc\geq 1\) of containers. All the containers hosted by a same physical server share the pool of computing (e.g., CPU cycles) and networking (e.g., I/O bandwidth) physical resources made available by the physical CPU and NICs that equip the host server. The main task of the Execution Engine managing each container is to allocate dynamically the bandwidth and computing resources made available by the host server.