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In recent years, we have witnessed a proliferation of core network (CN) virtualization, coupled with the emergence of self deployable architectures in cellular networks . These advances provide greater flexibility and allow CN functions to be virtualized and co-located with one or more base stations . However, they introduce new challenges, such as the optimal location of CN functions based on the physical architecture. In this paper, we tackle this problem and propose a new generic and efficient solution that locates the best base station to host the CN functions, while optimizing a given performance metric (e.g., maximum flow, max–min fairness, etc.) The core of our solution relies on jointly modeling the problem as a Mixed-Integer Nonlinear Programming (MINLP) and efficiently linearizing the nonlinear constraints. After presenting our model, we evaluate its performances, considering the global maximum flow as an optimization metric. The results showed that our joint modeling significantly reduces the run time compared to existing solutions while achieving the same optimal results. Furthermore, we highlight the genericity of our model, and we show how it can be easily adapted to handle different optimization metrics. We particularly consider some variants to address the fairness problem in conjunction with the local CN placement issue. We perform extensive simulations and discuss the obtained results. The latter allow us to derive insights regarding the tradeoff between maximum flow and fairness of proportional satisfaction, while highlighting the strengths of the proposed joint modeling. Introduction The field of cellular networks has been undergoing major developments in recent years. On the one hand, the democratization of mobile systems like robots and Unmanned Aerial Vehicles (UAVs) offers the possibility to embed base stations (Mozaffari et al., 2019, Chandrasekharan et al., 2016, Lin et al., 2018, Huang et al., 2019) or even the core network (Sundaresan et al., 2018, Moradi et al., 2018, Moradi et al., 2019, Moradi et al., 2020) on these mobile units. On the other hand, the field of cellular networks witnesses an increasing proliferation of Network Function Virtualization (NFV) and Software Defined Networking (SDN) which offer more flexibility in core network (Nguyen et al., 2017, Bagaa et al., 2018, Zhang et al., 2021). These two facts coupled with the self-organization capabilities offered by recent standards like 5G including self-configuration, self-optimization and self-healing gave birth to the self deployable cellular network concept allowing more flexible and timely deployment of cellular networks (Fourati et al., 2021, Oueis et al., 2019, Oueis, 2018). This concept is even more timely and challenging given the emergence of private networks (Sarver, 2022) and the place that drones take in the future 6G standardization (Mishra et al., 2021). Even though the concept of self deployable cellular network can be applicable and useful in different situations like coverage extension and management of crowded events, one of the main applications still is the communication rehabilitation in emergencies (Oueis, 2018, Selim and Kamal, 2018, Gomez et al., 2014). Indeed, in these situations that usually follow a natural or human made disaster, the traditional networks are partially or completely non-operational. Self deployable networks may offer here a key solution in order to easily and rapidly recover the communications between humans and first responders (Oueis, 2018). In self deployable networks, bases stations are deployed quickly and easily. They may be connected to a traditional network for coverage extension for instance or deployed standalone to be used separately in an autonomous way. We focus, in our work, on this kind of deployment where we have no backhaul to a traditional network and where all the functionalities of the core network may be grouped and co-located with one or more base stations of the network. A key point brought by self deployable networks is the continuum between radio access networks and core network. Indeed, the virtualized core network functions can be directly hosted in a base station forming local CN (Zhang et al., 2021). These functions may be hosted at each base station like considered in Moradi et al., 2018, Moradi et al., 2019, Moradi et al., 2020 or in one base station that hosts a shared local CN like considered in Zhang et al. (2021) and Oueis et al. (2019). In this work, we consider this second case, where all functionalities of the core network are grouped in one unit (named local CN) that will be co-located with one base station of the network. Although the benefits of self deployable networks and the continuum between radio access network and core network, these advances bring new scientific challenges. One of these multiple challenges concerns the optimal placement of shared local CN. Indeed, the choice of the base station that will host the local CN should be computed in a reasonable time in order to meet the need for reactivity. Also, this choice should be done rigorously, while considering different objectives like the overall throughput, the fairness, etc. We tackle this issue in this paper while considering the problem of efficient local CN placement. We propose for that a new one-shot generic model that allows to simultaneously locate the local CN while optimizing a given performance metric. The main contributions of this work can be summarized in the following points: • We design a Mixed Integer Non-Linear Program that allows to find in one shot the best optimal local CN while maximizing a performance metric. We linearize the constraints and discuss the resulting linear model. • We validate our model while comparing it to two existing ones based on an iterative modeling. We discuss the results that show that our model reduces significantly the run time while giving the same optimal solutions. • We show that our new one-shot model is generic and can be easily adapted to address different optimization metrics. In particular, we consider some fairness metrics and conduct extensive simulations to evaluate the performances of the resulting models and to derive some insights. We also evaluate the run time according to the optimization metrics. The rest of this paper is organized as follows. Section 2 discusses some representative related work. In Section 3, we present the problem formulation as well as the main notations. Section 4 focuses on the design and linearization of our one-shot model, while we discuss the performance evaluation and the comparison results in Section 5. In Section 6, we address the genericity of our model while presenting and discussing some fairness-aware variants. We discuss in Section 7 the evaluation of these variants in terms of the addressed metrics as well as the run time. We finally present some conclusions and future work in Section 8. Section snippets Related work Self deployable cellular networks have attracted much attention in recent years thanks to their benefits. Indeed, on the one hand, they facilitate the deployment in the situations where we have no connection to the traditional network. On the other hand, they allow increasing the coverage in some areas in critical situations (crowded area, rural area, etc.) While some researchers focus on the development and deployment of self deployable cellular networks (Sundaresan et al., 2018, Moradi et Notations and problem statement In this section, we present the formulation of our problem. We also discuss some assumptions and the notations that we use in the rest of the paper. Similarly to related work, we model the self deployable network as a weighted directed graph G(V, E) where V, the set of vertices, represents the base stations (BSs) and E, the set of arcs, models the communication links. In order to model the communication limited bandwidth, we suppose that each edge ( i , j ) ∈ E in the graph has a limited capacity Our one-shot model for local CN location and flow maximization One contribution of this work is to propose a new one-shot model that, unlike the model proposed in Oueis et al. (2019), optimizes at the same time the CN best location as well as the flow values. For that end, we use Mixed Integer Programming, and we define the binary decision variables, y i , which are equal to 1 if the BS (node) i should be selected as the best one to host the local CN and zero otherwise. Without loss of generality, we assume that we try to locate the CN at only one base Model validation and performance evaluation In order to validate our model and to highlight its features and benefits, we conduct extensive simulations while comparing our solutions to two existing ones. We present in this section the different simulation scenarios, and we discuss some main results. Fairness-aware models In the previous sections, we have proposed a one-shot model that allows at the same time finding the best BS to host the local CN as well as maximizing the total flow in the network. The metric of maximizing the total flow is widely used in the literature in multiple applications, but may lead to inequitable sharing between the flow of the different base stations both regarding BS supplies and regarding the proportional satisfaction unfairness between BSs. The fairness in traffic engineering Evaluation of proportional satisfaction fairness-aware models We implement the three additional models, following the same simulation setup presented in Section 5.1. We then compare the four models based on the four optimization metrics as well as the run time. The results are plotted in Fig. 4, Fig. 5. Conclusions and future work In this paper, we consider the problem of local Core Network (CN) placement and traffic optimization in self deployable networks. We first jointly model the problem as a Mixed Integer Non-Linear Program that allows to find at the same time the best location of the local CN, and maximizing the overall flow in the network. We linearize the constraints of our initial model and compare it to other solutions from the literature. The results are presented and discussed for both homogeneous and CRediT authorship contribution statement Asma Bechkit: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing – original draft, Writing – review & editing. Ali Melit: Supervision, Project administration, Conceptualization, Methodology, Validation, Writing – review & editing. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Asma Bechkit is currently Ph.D. student in the department of Computer Science of the University of Jijel — Algeria. She received her Master degree in Networks and Security in 2016 and her Bachelor degree in 2014 from the same university. She also serves as teaching assistant at the University of Jijel since 2022. References (35) Bozkaya Elif et al. SDN-enabled deployment and path planning of aerial base stations Comput. Netw. 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He received his Engineering degree in 1981 from USTHB University in Algiers and his Ph.D. in Computer Science in 1991 from the University of Pierre and Marie curie, Paris 6 – French. His research areas include: computer systems modeling and performance, queuing theory, optimization and simulation, wireless networks and biometrics. View full text © 2023 Elsevier Ltd. All rights reserved. About ScienceDirect Remote access Shopping cart Advertise Contact and support Terms and conditions Privacy policy We use cookies to help provide and enhance our service and tailor content and ads. By continuing you agree to the use of cookies . Copyright © 2023 Elsevier B.V. or its licensors or contributors. ScienceDirect® is a registered trademark of Elsevier B.V. ScienceDirect® is a registered trademark of Elsevier B.V.
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