# A Mobility Management Using Follow-Me Cloud-Cloudlet in Fog-Computing-Based RANs for Smart Cities
## 5 Performance Analysis  
Our paper presents a mobility management using FMCL approach F-RAN for smart cities. A mathematical analysis and simulation results are provided. Our paper presents a mobility management using FMCL approach. To evaluate our handover protocol (proposed scheme with FMCL), and [PERSON] et al.'s. proxy MIPv6-based FMC (PMIPv6 with FMC) [24], all these protocols are mainly implemented using the Ryu and Mininet as illustrated in Table 1. Ryu [35] is a component-based software defined networking framework. Ryu provides software components with well defined API that make it easy for developers to create new network management and control applications. Ryu supports various protocols for managing network devices, such as OpenFlow, Netconf, OF-config, etc. About OpenFlow, Ryu supports fully 1.0, 1.2, 1.3, 1.4, 1.5 and Nicira Extensions. All of the code is freely available under the Apache 2.0 license [35]. Mininet [36] creates a realistic virtual network, running real kernel, switch and application code, on a single machine (VM, cloud or native). Mininet is a way to develop, share, and experiment with OpenFlow and Software-Defined Networking systems [36]. In our simulation, we built two two computers; one is installed a SDN controller, Ryu 4.1 (IP: 172.24.4.2); and another one is installed OpenFlow-based Software-Defined Networking systems by mininet (IP: 172.24.24.2) under the same IP domain. Before describing the performance metrics, the mathematical analysis of the total transmission time and space cost is described. **Theorem 1**. : _The total transmission time of the proposed mobility management with FMCL approach is \(T=\sum\limits_{1\leq i\leq m}[\alpha t_{FM_{i}}(p_{i})+(1-\alpha)t_{FM_{i}}(p_{ i})]+\sum\limits_{m<i\leq m^{\prime}}t_{FML}(p_{i})+\sum\limits_{m^{\prime}<i\leq m ^{\prime}}t_{FMC}(p_{i})+\sum\limits_{m^{\prime\prime}<i\leq n}[\beta t_{FML _{i}}(p_{i})+(1-\beta)t_{FML_{i}}(p_{i})]+\sum\limits_{m^{\prime}<i\leq n}t_{ m}(p_{i})\), where the cache hit rates of packets in caches of \(l_{s}\) and \(l_{d}\) are \(\alpha\) and \(\beta\), respectively._  
Figure 10: An example of _follow me cloud-cloudlet_ phase. Proof. : Following notations in Section 4, a data file is divided into \(n\) packets, \(F=\{p_{1},p_{2},\cdots,p_{m},\cdots,p_{m^{\prime}},\cdots,p_{m^{\prime\prime}}, \cdots,p_{n}\}\), where \(1\leq m<m^{\prime}<m^{\prime\prime}<n\). The total transmission time is divided into four phases, \(T_{FM}\), \(T_{FML}\), \(T_{FMC}\), and \(T_{FML}\) as illustrated in Figure 11a-c, where \(T_{FM}\) is the time cost of performing _follow-me_ phase, \(T_{FML}\) is the time cost of performing _follow-me cloudlet_ phase, \(T_{FMC}\) denotes as the time cost of performing _follow-me cloud_ phase, and \(T_{FML}\) is the time cost of executing _follow-me cloud-cloudlet_ phase. \(T_{FM}=\sum\limits_{1\leq i\leq m}[\alpha t_{FM_{i}}(p_{i})+(1-\alpha)t_{FM_{ c}}(p_{i})]\), where the cache hit rate of packets in cache of \(l_{s}\) is \(\alpha\), and \(t_{FM_{i}}(p_{i})\) and \(t_{FM_{c}}(p_{i})\) denote as the unit transmission time of packet \(p_{i}\) transmitted from cloudlet \(l_{s}\) or data center \(c_{s}\), which is depended on packet \(p_{i}\in l_{s}\) or \(c_{s}\), where \(1\leq i\leq m\). The data migration time \(T_{m}\) is \(\sum\limits_{m^{\prime}<i\leq n}t_{m}(p_{i})\), where \(t_{m}\) as the unit time of packet \(p_{i}\) migrated from \(c_{s}\) to \(c_{d}\), where \(m^{\prime}<i\leq n\). \(T_{FML}=\sum\limits_{m<i\leq m^{\prime}}t_{FML}(p_{i})\), where \(t_{FML}(p_{i})\) is the unit transmission time of packet \(p_{i}\) transmitted from data center \(c_{s}\) to cloudlet \(l_{d}\), where \(m<i\leq m^{\prime}\). \(T_{FMC}=\sum\limits_{m^{\prime}<i\leq m^{\prime\prime}}t_{FMC}(p_{i})\), where \(t_{FMC}(p_{i})\) is the unit transmission time of packet \(p_{i}\) transmitted from data center \(c_{d}\) to cloudlet \(l_{s}\), where \(m^{\prime}<i\leq m^{\prime\prime}\).