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[{"title":"Snake Learning -- A Communication- and Computation-Efficient Distributed Learning Framework for 6G","url":"/2025/01/09/SnakeLearning/","content":"\n{% note info %}\n**Manuscript Information**\nXiaoxue Yu, Xingfu Yi, Rongpeng Li, Fei Wang, Chenghui Peng, Zhifeng Zhao and Honggang Zhang, [“Snake Learning: A Communication- and Computation-Efficient Distributed Learning Framework for 6G,”](https://arxiv.org/pdf/2405.03372) IEEE Commun. Mag., Jan. 2025.\n{% endnote %}\n\n# 背景介绍\n\n随着6G网络的快速发展，网络计算资源得到了进一步整合，智能用户设备（User Equipment，UE）和网络节点（Network Elements，NEs）不再只是数据的接收终端，还可以作为计算节点，参与网络智能化应用的协作计算。这种协作方式被称为“计算即服务”（Compute-as-a-Service，CaaS）和“AI即服务”（AI-as-a-Service，AIaaS）。在此背景下，6G将逐渐演化为一个动态的分布式计算平台，为网络智能和资源利用率的提升提供前所未有的机会。\n\n为了提高网络的智能化水平，分布式深度学习成为一种重要的技术手段。当前主流的分布式学习框架，如联邦学习（Federated Learning，FL）、拆分学习（Split Learning），已经在一些场景，尤其是大模型微调方面，展示出了潜力。然而，在6G网络环境下，这些框架仍面临着不少难题，尤其是在高度异构、通信不稳定和资源受限的环境中更是困难重重。因此，设计一种高效的、能够适应6G网络环境的学习框架，是未来推动网络智能化发展的关键一步。\n\n# 现有方法面临的挑战\n\n目前，广泛应用的分布式学习框架，包括联邦学习、拆分学习及其各种混合变体，主要面临以下几大挑战：\n\n1. **对通信同步高程度依赖**：联邦学习通常依赖多个设备与中心服务器之间频繁的双向通信来实现模型的同步，拆分学习更是需要在每一次学习过程中依靠通信传递中间激活值和梯度完成训练。这对于6G的无线网络环境来说并不理想，因为无线网络中的连接往往是不稳定的。环境变化、设备密度、设备移动性等因素都会导致上下行速率波动，从而影响实时数据和模型同步的稳定性。这种依赖同步通信的特性不仅增加了带宽的压力，还可能导致模型训练过程的不稳定，甚至无法收敛，从而严重影响分布式学习的效率和效果。\n2. **可用资源的异构性和动态性**：6G网络中的计算资源是动态且异构的。服务节点的可用性会因为服务间共享而不断变化，导致所谓的“潮汐效应”，即资源的可用性随时间波动。这意味着一些节点在特定时间内可能无法提供足够的计算能力来满足复杂模型的训练需求。此外，不同供应商提供的计算节点硬件性能各异，导致计算能力的不均衡，这给分布式学习带来了额外的复杂性。\n3. **数据异质性**：在分布式学习中，不同节点持有的数据通常存在显著差异，即非独立同分布（Non-IID）的情况。这种差异可能来自于用户的行为习惯、时间变化、地理位置等因素，导致各个节点在训练中面临不同的优化目标，影响模型的稳定性和泛化能力。单纯依赖数据增强或合成数据等传统手段难以有效解决这些问题，因此需要新的、更智能的训练策略。\n\n\n\n图1: 不同分布式学习框架对比\n\n# Snake Learning：一种新型分布式学习框架\n\n为了解决上述问题，我们提出了名为“Snake Learning”（蛇形学习）的新型分布式协同学习框架。该框架借鉴了经典游戏“贪吃蛇”的思路，逐层分配模型的中间部分给不同的节点进行训练，从而最大化利用6G网络中各节点的异构计算资源，降低通信和计算的负担。具体来说，Snake Learning 的核心理念是将模型的不同中间层分配给不同的节点来训练，而模型的第一层和最后一层由所有节点共同负责。其中，第一层提取基础特征，最后一层则用于任务的具体决策。每个节点在完成其负责的本地训练任务后，再将更新的参数上传，而不是实时同步所有节点的参数。通过这种逐层传递机制，以及必要的数据处理、蒸馏、自适应学习率等技术的应用，Snake Learning 显著减少了通信和计算资源的消耗，还能够在出现网络中断的情况下继续进行训练，具有极高的容错能力。\n\n\n\n图2: Snake Learning 工作流程\n\n## **Snake Learning** **的主要组件**\n\n1. **服务提供者（Service Provider，SP）**： 服务提供者（SP）负责Snake Learning中的训练任务管理和资源分配。它可以根据需要启动虚拟计算资源（如虚拟机或容器），以同时支持多个AI任务。在系统层面，SP可以根据服务需求和网络状况动态调整各任务的执行节点，以确保计算资源的高效利用。\n2. **过程控制器与计算引擎（Process Controller & Process Computation Engine，PC & PCE）**： 每个Snake Learning任务配备一个PC和一个PCE。PC负责任务分配和网络资源管理，比如节点的管理和任务调度；PCE则具体负责数据处理、模型训练和参数更新等计算工作。\n3. **本地管理器与本地计算引擎（Local Manager & Local Computation Engine，LM & LCE）**： 本地管理器（LM）负责管理每个节点的Snake Learning服务。在节点加入网络之前，LM需要获得SP的授权。LCE则负责处理节点上的具体计算任务，例如数据预处理、模型训练和参数更新。\n\n## **Snake Learning** **的工作流程**\n\n1. **初始化**： 在Snake Learning的过程中，SP首先通过AIaaS API注册学习任务，确定任务目标、需求及可能的约束（例如服务级协议、数据和设备、层的分配等）。接下来，PC负责对服务节点进行统一的管理，确认节点连通性、计算资源状况，并持续监控节点的性能指标，包括资源利用率、数据质量及训练状态。\n2. **层分配**： 在Snake Learning中，PC基于各节点的计算能力、网络连接状态（如延迟和带宽）、系统资源（如CPU和内存）等因素，将模型的不同层分配给各节点进行训练。层分配的目的是根据节点的计算能力及网络状况，为其分配适合的模型层，从而最大化节点利用效率。\n\n3. **本地训练：**在层分配完成后，每个节点基于其本地数据集对被分配的模型层进行本地训练。与联邦学习类似，Snake Learning强调数据隐私的保护，只有训练后的模型参数才会传输至其他节点，而非实时同步所有节点的数据。为了进一步提高数据的隐私性，Snake Learning还可以引入差分隐私和同态加密等技术，防止在参数传输过程中发生数据泄露。此外，每个节点会对数据进行标准化和增强处理，以提高模型的泛化能力。在数据不均衡或者数据特性差异明显的情况下，使用数据模块进行预处理。为了解决由于节点之间数据分布不同（Non-IID）而导致的训练不稳定性，Snake Learning引入了知识蒸馏（Knowledge Distillation, KD）模块。在训练过程中，KD模块对来自不同节点的知识进行融合，确保模型不会因数据差异而遗忘部分重要的特征信息。这种机制通过衡量各节点之间的数据分布差异触发跨节点知识的蒸馏与共享，保持模型的整体一致性和泛化能力。\n\n4. **节点管理与容错机制**：由于6G网络中节点的状态具有动态性，可能因设备移动、连接波动等因素出现节点失效或网络中断的情况。为此，Snake Learning设计了动态任务管理与节点替换机制。PC会持续监控每个节点的状态，如果某节点发生故障，PC会将其训练任务转移至其他具有足够计算能力的候选节点来确保训练的连续性和模型的稳定性。\n\n5. **参数传输与节点管理**： 在模型训练过程中，如果需要一定程度聚合则在参数服务器模式下每个节点在完成本地训练后将更新后的参数上传至PCE，由其负责参数聚合并分发至PC指定的下一个节点；否则，在点对点模式下，节点可以直接将参数传递至下一个目标节点，从而进一步减少通信延迟和系统复杂度。\n\n \n\n## **主要实验结果**\n\n为了验证Snake Learning的有效性，研究通过在经典分类任务和大型模型微调任务上分别进行了实验，结果显示Snake Learning表现出色，尤其是在资源受限的6G网络环境中展现了巨大的优势。\n\n1. **分类任务的训练**： 在VGG11模型、CIFAR-10数据集上的实验表明，相较于其他算法，Snake Learning (SL）通过较少的训练迭代次数更迅速地达到60%的准确率，显著提升了节点的训练效率。同时，Snake Learning在大幅降低了每次通信的开销的同时，最终性能超过了传统联邦学习的95%以上。\n\n\n\n图 3 : 不同训练总设备迭代次数下Snake Learning和其他算法的分类准确度性能比较，其中Non-iid数据服从$\\alpha=2$的Dirichlet分布. \n\n2. **大语言模型（LLM）微调**： 对于如Llama-3 8B和OPT-1.3B大语言模型，Snake Learning通过将模型层分配给不同的节点训练大幅降低了内存占用和计算需求。例如，在优化OPT-1.3B模型时，传统联邦学习需要大约19.37GB的内存，而Snake Learning仅需3.13GB，大大降低了硬件要求。\n\n\n\n图 4: FL和Snake Learning （SL）分别在24个节点数量下微调OPT-1.3B模型和32个节点数量下微调Llama-3 8B模型的性能比较，其中性能由perplexity （ppl）衡量，其值越低表明模型的确定性和有效性越高。","tags":["highlights"],"categories":["research"]},{"title":"ZJUNICE：再见2024，你好2025","url":"/2024/12/28/say-hello-2025-zjunice/","content":"\n<iframe src=\"//player.bilibili.com/player.html?isOutside=true&aid=113728351704353&bvid=BV1XqC4YyE4Q&cid=27570471499&p=1\" scrolling=\"no\" border=\"0\" frameborder=\"no\" framespacing=\"0\" allowfullscreen=\"true\"></iframe>\n","tags":["team"],"categories":["blog"]},{"title":"ZJUNICE@2024 掠影","url":"/2024/11/02/zjunice-2024-group-photo/","content":"\n<iframe src=\"//player.bilibili.com/player.html?isOutside=true&aid=113603176829858&bvid=BV1EkivYZE8L&cid=25722886637&p=1\" scrolling=\"no\" border=\"0\" frameborder=\"no\" framespacing=\"0\" allowfullscreen=\"true\"></iframe>\n\nClick [here](/images/videos/zjunice2024.mp4) to view the video offline.","tags":["team"],"categories":["blog"]},{"title":"Decentralized Consensus Inference-based Hierarchical Reinforcement Learning for Multi-Constrained UAV Pursuit-Evasion Game","url":"/2024/07/04/ci-hrl/","content":"\n <iframe src=\"https://player.bilibili.com/player.html?isOutside=true&aid=113603160052897&bvid=BV17yivY4E5C&cid=25722886238&p=1&high_quality=1&danmaku=0\" scrolling=\"no\" border=\"0\" frameborder=\"no\" framespacing=\"0\" allowfullscreen=\"true\"></iframe>\n \nClick [here](/images/videos/cohirl2024.mp4) to view the video offline.","tags":["highlights"],"categories":["research"]},{"title":"IEEE SIG on Artificial General Intelligence, Models, and Agents (AGILE) has been formally approved by IEEE Communications Society (ComSoc) Technical Committee on Big Data (TCBD). Dr. Li serves the founding chair.","url":"/2024/05/06/ieee-sig-on-agile/","content":"\n# Official Link\n\n- https://bdpan.committees.comsoc.org/special-interest-groups/ieee-sig-on-artificial-general-intelligence-models-and-agents-agile/\n- https://ieeesigagile.pages.dev\n\n\n\n# Officers\n\nChair: Rongpeng Li, Zhejiang University, China, lirongpeng AT zju.edu.cn\nVice Chair: Biao Zhang, Google DeepMind, UK, biaojiaxing AT google.com\nVice Chair: Lan Zhang, Clemson University, USA, lan7 AT clemson.edu\nVice Chair: Charilaos Zarakovitis, Axon Logic, Greece, c.zarakovitis AT axonlogic.gr\n\nAdvisor: Dusit Niyato, Nanyang Technological University, Singapore, dniyato AT ntu.edu.sg\nAdvisor: Honggang Zhang, honggangzhang AT zju.edu.cn\nAdvisor: Jun Zhang, Hong Kong University of Science and Technology, China, eejzhang AT ust.hk\nAdvisor: Mehdi Bennis, University of Oulu, Finland, mehdi.bennis AT oulu.fi\nAdvisor: Xianfu Chen, Shenzhen CyberAray Network Technology Company Ltd, China, xianfu.chen AT ieee.org\nAdvisor: Yan Zhang, University of Oslo, Norway, yanzhang AT ieee.org\nAdvisor: Yonghui Li, University of Sydney, China, yonghui.li AT sydney.edu.au\nAdvisor: Yusheng Ji, National Institute of Informatics, Japan, kei AT klab.nii.ac.jp\n\n\n# Scope and Objectives\n\nArtificial General Intelligence (AGI) is an implicit or explicit north-star goal since 1956 Dartmouth AI Conference. Given the rapid advancement of Machine Learning (ML) models, the concept of AGI has passed from being the subject of philosophical debate to one with near-term practical relevance. Nowadays, benefiting from the rapid progress and astonishing success in Natural Language Processing (NLP) and Computation Vision (CV), “sparks” of AGI are even regarded to be already present in the latest generation of Large Language Models (LLMs) and Large Vision Models (LVMs), with prominent examples like ChatGPT, Gemini, DALL-E and Sora. Meanwhile, techniques like generative Generative Adversarial Networks (GANs) and Diffusion models as well as scalable Transformers not only boost the arrival of these amazing Foundation Models (FMs), but also are seen as a transformative technology beyond shaping the AI field:\n\n- FMs promise a tangible enhancement to wireless communications and networks by leveraging the generative capabilities as well as the multimodality nature of the data acquired in wireless networks. It promises to overcome long-standing difficulties such as low generality, limited performance gain, complicated\nmanagement, and inconvenient collaboration.\n- The application of FMs for inference and decision-making purposes have demonstrated appealing results. It is widely anticipated that FM-empowered (connected) autonomous agents with embodied intelligence are expected to emerge with the astonishing capabilities of accomplishing tasks autonomously and coherently. \n\nGiven these facts and visions, there is a clear need to establish a Special Interest Group (SIG) on AGI, Models, and Agents (AGILE) to address the emerging technical challenges therein. On one hand, it still requires ongoing significant efforts to deliver cost-effective AGI solutions. On the other hand, how to tackle the bloated parameters in FMs in edge and user equipment remain under-investigated. \n\nThis SIG aims to organize and solicit researchers from both the academia and the industry to accelerate the study on AGILE. Tentative topics include, but are not limited to\n\n- Artificial general intelligence techniques for AGILE\n- Model design and training for AGILE\n- Communication techniques in AGILE\n- Communication and learning theory in AGILE\n- Performance evaluation metrics of AGILE\n- Collaboration mechanism in AGILE\n- Network architecture for AGILE\n- Security and privacy of AGILE\n- Data collection and governance of AGILE\n- Full-lifecycle management and orchestration of AGILE\n- Architecture and protocol design & standarization of AGILE\n\n\n# Founding Members\n\n- Changyang She, University of Sydney, Australia, changyang.she AT sydney.edu.au\n- Chengchao Liang, Chongqing University of Posts and Telecommunications, China, liangcc AT cqupt.edu.cn\n- Chenghui Peng, Huawei Technologies, China, pengchenghui AT huawei.com\n- Chungang Yang, Xidian University, China, chgyang2010 AT 163.com\n- Dong Wang, China Telecom, China, wangd5 AT chinatelecom.cn\n- Guangxu Zhu, Shenzhen Research Institute of Big Data, China, gxzhu AT sribd.cn\n- Gang Feng, University of Electronic Science and Technology, China, fenggang AT uestc.edu.cn\n- Haijun Zhang, Beijing Science and Technology University, China, zhanghaijun AT ustb.edu.cn\n- Jihong Park, Deakin University, Australia, jihong.park AT deakin.edu.au\n- Kai Yang, Beijing Institute of Technology, China, yangkai AT bit.edu.cn\n- Qiang Liu, University of Nebraska-Lincoln, USA, qiang.liu AT unl.edu\n- Qimei Chen, Wuhan University, China, chenqimei AT whu.edu.cn\n- Sai Mounika Errapotu, University of Texas at El Paso, serrapotu AT utep.edu\n- Shangmin Guo, University of Edinburgh, UK, s.guo AT ed.ac.uk\n- Xinyue Zhang, Kennesaw State University, USA, xzhang48 AT kennesaw.edu\n- Xueli An, Huawei Technologies, Germany, xueli.an AT huawei.com\n- Yong Xiao, Huazhong University of Science and Technology, China, yongxiao AT hust.edu.cn\n- Yuanming Shi, Shanghai Tech University, China, shiym AT shanghaitech.edu.cn\n- Yao Sun, University of Glasgow, UK, Yao.Sun AT glasgow.ac.uk\n- Yixiong Wei, Zhejiang Lab, China, yx_wei AT zhejianglab.com\n- Zhi Liu, The University of Electro-Communications, Japan, liuzhi AT uec.ac.jp\n- Zhijin Qin, Tsinghua University, China, qinzhijin AT tsinghua.edu.cn","tags":["services"],"categories":["news"]},{"title":"第三届“受控核聚变与人工智能技术”学术会议成功举办","url":"/2024/04/27/ai_fusion_2024/","content":"\n4月24日至26日，由中国核学会核聚变与等离子体物理分会主办，浙江大学承办的第三届“受控核聚变与人工智能技术”学术会议于杭州之江实验室成功举行。本次会议聚焦于人工智能技术在受控核聚变领域的应用所取得的进展和成果，吸引了来自中核集团核工业西南物理研究院、之江实验室、中国科学院合肥物质科学研究院等离子体物理研究所、中国工程物理研究院激光聚变研究中心、清华大学、浙江大学、西湖大学、华中科技大学、新奥科技发展有限公司等35家科研院所、高校和企业的受控核聚变和人工智能相关领域的专家、青年研究人员、从业人员和学生，共计约140位参会代表齐聚一堂、共襄盛举。\n\n\n\n开幕式上，之江实验室总工程师赵志峰、浙江大学核科学技术研究中心主任张少泓教授发表了热情洋溢的致辞。出席开幕式的嘉宾还有中国核工业集团公司科技带头人刘东，国家磁约束聚变能发展研究专项首席科学家叶民友，新奥能源研究院院长刘敏胜，德国根特大学教授Geert Verdoolaege 等众多业内专家。开幕式由大会执行主席浙江大学李荣鹏副教授主持。\n\n\n\n\n\n本次会议共设5大议题：(a) 人工智能在核聚变装置运行控制中的探索和应用；(b) 受控核聚变的智能模拟；(c) Data Analysis for Plasma Diagnostics；(d) 受控核聚变中的数据规范管理及应用；(e) 受控核聚变与人工智能技术中的系统工程理论和实践。其中，议题(c) 采用国际研讨会全英文报告形式，以期为国内外核聚变能源开发领域和人工智能领域相关科技人员提供综合性学术交流平台。通过特别邀请和前期征稿，本次会议共呈现了16个特邀报告和21个口头报告，相关领域的知名专家和学者贡献并分享人工智能与等离子体模拟、诊断、控制和系统软件等方面向相结合的最新进展。\n\n\n\n\n\n\n\n为了促进来自全国各地的研究团队进行深度交流和探讨，本届会议首次设立海报（poster）交流环节，共有19个海报参与展出。活动现场讨论气氛热烈、参会人员交流热情高涨。\n\n\n\n\n\n本次会议的成功召开为国内人工智能技术与受控核聚变研究这两大前沿战略科学领域的交叉融合提供了一个重要的平台。来自全国各地的研究团队进行了充分交流与相互启发，在跨学科合作、人才培养、科研与产业的结合等多方面重要议题找到了切合点，达成了广泛的共识。会议的召开在国内聚变科学界引起了广泛关注，相信可以为聚变等离子体物理、未来聚变堆的运行控制等方面提供科学基础与技术支撑，为深化人工智能技术在受控核聚变领域的应用，推动学术界和产业界的融合发挥重要的作用。\n\n","tags":["services"],"categories":["blog"]},{"title":"NetGPT - An AI-Native Network Architecture for Provisioning Beyond Personalized Generative Services (NetGPT – 提供超越个性化生成式服务的AI原生网络架构)","url":"/2024/04/04/netgpt/","content":"\n{% note info %}\n**Manuscript Information**\n“NetGPT: An AI-Native Network Architecture for Provisioning Beyond Personalized Generative Services”, IEEE Network, [https://ieeexplore.ieee.org/document/10466747](https://ieeexplore.ieee.org/document/10466747).\n{% endnote %}\n\n\n# 摘要\n\n大语言模型（LLMs：Large language models）通过生成信息极大促进了我们日常生活的成功。LLMs的个性化可以通过与人类意图更好的对齐而进一步促进其应用。针对个性化生成式服务，云边端协作架构、机制和方法颇有前景，因为它便于有效地协调异构分布式通信、计算和存储资源。在本文中，我们提出了NetGPT（Network Generative Pre-trained Transformer），能够根据计算能力在边缘和云端有效协同、编排适当的LLMs。此外，边缘LLMs可以高效利用基于位置的信息进行个性化提示，从而有益于与云端LLMs的互动。我们通过采用低秩适应性（LoRA）技术和微调（Fine-Tuning）策略，基于开源LLMs（如LLaMA和GPT-2-base模型）的应用，验证了NetGPT架构的有效性和实用性。同时，我们对NetGPT进行了细致的数值分析，并与现有的云边协同技术及纯云技术进行比较，验证了NetGPT的显著优势。进一步地，我们强调了构建面向NetGPT的内生智能网络架构所需的根本性变革，包括通信与计算资源的深度整合以及人工智能逻辑工作流的精细调校。此外，本研究还探讨了NetGPT带来的多项益处，特别是边缘LLMs在预测业务趋势与推断用户意图方面的能力，这一能力预示着未来为智能网络管理与编排提供一体化解决方案的可能性。综上所述，NetGPT作为一种创新的内生智能网络架构，展现了其在提升个性化服务水平方面的巨大潜在价值。\n\n# 简介\n\n随着深度学习从AlphaGo到ChatGPT应用的飞跃，人工智能（AI: Artificial Intelligence）在6G网络领域的重要性日益凸显。一方面，随着边缘计算能力的增强，网络资源能够得到更高效的配置，业务服务质量（QoS: Quality of Service）显著提升，以AI为中心的服务供给效率研究受到广泛关注。另一方面，AI智能模型的应用往往受限于特定场景或任务；例如，大语言模型（LLMs：Large language models）在多项自然语言处理（NLP: Natural Language Processing）和计算机视觉任务中展现出卓越性能，但要其实现遵循人类意图并生成个性化输出，就需要对LLM进行精确的微调。仅在集中式云端部署LLM进行个性化微调，会导致云端存储多个完整模型参数副本，在资源利用效率方面存在短板。为了优化LLM的个性化调整问题，寻找合适的云边协同方案因而显得尤为关键。相较于仅在云端部署LLM，通过云边协同部署大型模型具备多重优势。这种策略不仅赋予边缘服务器更大的操作自由度，能够部署多样化微调的LLM以适应不同环境，实现服务的个性化和定制化，同时也能将数据密集的生成式设备与更多邻近服务器连接，减少数据向远程云服务器的传输延迟，降低通信成本。将生成式LLM集成到边缘网络中，有望促进通信和计算（C&C: Communication and Computing）资源的高效利用。\n\n实现大语言模型（LLM）云边协同部署的策略有多种，包括LLM卸载至本地微调和LLM拆分等方法。在本地微调的策略中，本地边缘服务器可以定制云端训练的LLM，通过微调实现服务的个性化和定制化，以满足用户的不同偏好和应用场景的动态需求。在此过程中，联邦学习或并行训练可以作为辅助手段，帮助优化模型。然而，对LLM进行频繁的微调不仅计算成本高昂，还可能引发模型开发人员在知识产权方面的顾虑，故此方法在实践中面临多重挑战。此外，全面微调边缘服务器上的LLM可能导致资源限制和过高的计算开销。卸载LLM同样会带来不小的通信成本。\n\n另一种策略是将LLM拆分，并分别部署至云端和边缘服务器，通过在边缘布署部分深度神经网络（DNN: Deep Neural Networks）层，其它层则部署在云端，从而在边缘与云端之间平衡计算负载。在这种模型拆分策略中，如何有效地在边缘和云端之间分配DNN层是一大挑战，需要在最小化端到端延时的同时，确保边缘服务器上保留的模型大小适中。鉴于典型LLM包含数十亿参数，此类拆分策略可能相当复杂，并且LLM中普遍使用的残差连接可能限制了合理拆分点的选择。此外，LLM的局部微调和模型分割策略可能会面临泄露训练数据中隐私细节的风险，给云边协同部署带来额外的挑战。\n\n\n\n附图：云边协同部署网络大模型NetGPT\n\n本文中，我们提出内生智能网络架构NetGPT，该架构利用云边计算中的资源不均衡，实现了云端与边缘之间不同规模LLM的高效协同。区别于仅仅具有通信与计算（C&C）资源解耦的外生AI网络，NetGPT通过整合网络内C&C资源，在边缘部署较小规模的LLM，而在云端部署较大规模的LLM，旨在执行有目标的云边协同计算，以提供定制化的内容生成服务。此外，NetGPT还融合并发展了逻辑化的AI工作流程，能够识别出性能相当的通信链路；例如，在NetGPT框架中，如果边缘LLM能够提供令人满意的内容，那么基于性能的通信链路将在边缘处终止，以加快响应速度。反之，受到即时学习理念的启发，边缘LLM可以推断上下文并主动添加（或填补）部分个性化信息，以便在云端实现更加综合的处理效果。同时，边缘LLM对于智能网络的管理和调度（如用户意图推断、业务趋势预测等）也提供了一种统一的解决方案。综上所述， NetGPT体现了通信与计算深度整合的发展趋势，并代表了一种由LLM推动的内生智能网络架构。\n\n\n\n附图：云边协同部署网络大模型NetGPT的模型结构与实验框架\n\n\n\n附图：云边协同部署网路大模型NetGPT的工作流程","tags":["highlights"],"categories":["research"]},{"title":"ZJUNICE@2023 冬游","url":"/2024/01/14/zjunice-2023-group-tour/","content":"\n<iframe src=\"//player.bilibili.com/player.html?isOutside=true&aid=113603160051923&bvid=BV17yivY4Ehs&cid=25722886353&p=1\" scrolling=\"no\" border=\"0\" frameborder=\"no\" framespacing=\"0\" allowfullscreen=\"true\"></iframe>\n\nClick [here](/images/videos/zjunice2023.mp4) to view the video offline.","tags":["team"],"categories":["blog"]},{"title":"A paper titled “Semantics-empowered communication: A tutorial-cum-survey” has been accepted by IEEE Communications Surveys & Tutorials.","url":"/2023/12/01/a-paper-titled-semantics-empowered-communication-a-tutorial-cum-survey-has-been-accepted-by-ieee-communications-surveys-tutorials/","content":"\nIEEE Communications Surveys & Tutorials is a quarterly peer-reviewed academic journal published by the IEEE Communications Society for tutorials and surveys covering all aspects of the communications field. According to the Journal Citation Reports, the journal has a 2022 impact factor of 35.6, which ranks 1st among all journals in the field of telecommunications.\n\nFor a long time, Dr. Li has focused on studying Networked Intelligence for sCience Exploring (NICE). In this envisioned NICE world, Semantic communications plays a crucial role in the Internet of Large Language Model-based Agents and bridges several intricate areas like multi-agent reinforcement learning (MARL), 6G, and beyond.","tags":["highlights"],"categories":["news"]},{"title":"He co-received First Prize, Jiangsu Provincial Science and Technology Award, China.","url":"/2023/07/01/he-received-first-prize-jiangsu-provincial-science-and-technology-award-china/","content":"\nDr. Rongpeng Li co-received First Prize, Jiangsu Provincial Science and Technology Award, China, for contributions to \"Deep sensing and efficient utilization methods of electronic-magnetic spectrum resources\".\n\n李荣鹏获得江苏省科学技术一等奖，题目“电磁频谱深度感知及高效利用理论与方法”（排名5/11）。","tags":["highlights"],"categories":["news"]},{"title":"Dr. Li received the grant of Program of Distinguished Young Scholars of Zhejiang Natural Science Foundation, China.","url":"/2022/12/10/distinguished-young-scholars-of-zhejiang-natural-science-foundation-china/","content":"\nOn December 8, 2022, the Provincial Natural Science Foundation (i.e., Zhejiang Natural Science Foundation, China) announces this year's granted programs. Among 74 granted programs for \"Distinguished Young Scholars\" this year, Dr. Li's application (Task-oriented Mobile Networks for Decentralized Intelligence Service Provisioning) is proudly listed. This grant marks the latest acknowledgement of Dr Li's works from the community.\n\n浙江省科学技术厅、浙江省自然科学基金委员会2022年12月8日公布了《关于下达2023年度浙江省基础公益研究计划项目的通知》。通知指出，根据浙江省基础公益研究计划相关管理办法规定，包括74个杰出青年科学基金项目在内的2110个自然科学基金项目列入2023年度浙江省基础公益研究计划。\n\n新闻链接：[https://zjnsf.kjt.zj.gov.cn/portal/detail.html?typeid=2018515&postid=1050375499009753088](https://zjnsf.kjt.zj.gov.cn/portal/detail.html?typeid=2018515&postid=1050375499009753088)","tags":["highlights"],"categories":["news"]},{"title":"He received the Wu Wenjun Artificial Intelligence Excellent Youth Award from China Association of Artificial Intelligence (CAAI).","url":"/2022/01/27/he-received-the-wu-wenjun-artificial-intelligence-excellent-youth-award-from-china-association-of-artificial-intelligence-caai/","content":"\nChina Association of Artificial Intelligence (CAAI) has just announced the results of 2021 [_Wu Wenjun Artificial Intelligence Science and Technology Award_](https://en.caai.cn/index.php?s=/Home/Article/detail/id/57.html) ([吴文俊人工智能科学技术奖](http://wuwenjunkejijiang.cn)). Together with the other 14 scholars, Dr. Rongpeng Li has been awarded the **Wu Wenjun Artificial Intelligence Excellent Youth Award**, for its contribution to the integration of artificial intelligence and cellular networks (especially network slicing).\n\nAccording to the regulations on state science and technology awards, the _Wu Wenjun Artificial Intelligence Science and Technology Award_ will reward innovation achievements in the field of intelligent science and technology in China. Scientists and managers, who have made significant breakthroughs in the field of intelligent science and technology and have made outstanding contributions to the field, will be granted the prize. Initiated in 2008, the Award was supported by the pioneer of China's intelligent science research and the winner of the first Highest Science and Technology Awards _Wu Wenjun_, and was organized by CAAI. In 2021, [66 projects/scholars have been awarded](https://www.caai.cn/index.php?s=/home/article/detail/id/1593.html).","tags":["highlights"],"categories":["news"]},{"title":"Intelligent Network Slicing Platform (智能无线网络切片评估与测试验证平台)","url":"/2022/01/09/intelligent-network-slicing-platform/","content":"\n**An overview of the platform in Chinese**.\n\n<iframe width=\"760\" height=\"427\" id=\"video\" src=\"https://v.qq.com/txp/iframe/player.html?vid=y3317r5t9pg\" scrolling=\"no\" border=\"0\" frameborder=\"no\" framespacing=\"0\" allowfullscreen=\"true\"> </iframe>\n<script type=\"text/javascript\">document.getElementById(\"video\").style.height=document.getElementById(\"video\").scrollWidth*0.8+\"px\"</script>\n\nAn English introduction of the platform in **[IEEE INFOCOM 2022](/images/pdfs/2022_Xiao_DEMO.pdf)**.\n\nOther Relevant Publications:\n\n* Yuxiu Hua, *Rongpeng Li*, Zhifeng Zhao, Honggang Zhang, and Xianfu Chen, [\"GAN-Powered Deep Distributional Reinforcement Learning for Resource Management in Network Slicing,''](/images/pdfs/2020_Hua_GAN-powered%20deep%20distributional%20reinforcement%20learning%20for%20resource%20management.pdf) _IEEE J. Sel. Area. Commun._, vol. 38, no. 2, pp. 334–349, Feb. 2020. (Corresponding Author)\n* *Rongpeng Li*, Chujie Wang, Rongbin Guo, Zhifeng Zhao, and Honggang Zhang, [\"The LSTM-based advantage actor-critic learning for resource management in network slicing with user mobility,\"](/images/pdfs/2020_Li_The%20LSTM-based%20advantage%20actor-critic%20learning%20for%20resource%20management%20in.pdf) _IEEE Commun. Lett._, vol. 24, no. 9, pp. 2005–2009, Sep. 2020. \n\n* Xuan Zhou, *Rongpeng Li*, Tao Chen, and Honggang Zhang, [\"Network Slicing as a Service: Enable Industries Own Software-defined Cellular Networks,\"](/images/pdfs/2016_Zhou_Network%20slicing%20as%20a%20service%20-%20enable%20industries%20own%20software-defined%20cellular.pdf) _IEEE Commun. Mag._, vol. 54, no. 7, pp. 146 - 153, Jul. 2016.\n\n* Chen Qi, Yuxiu Hua, *Rongpeng Li*, Zhifeng Zhao, and Honggang Zhang, [\"Deep Reinforcement Learning with Discrete Normalized Advantage Functions for Resource Management in Network Slicing,''](/images/pdfs/2019_Qi_Deep%20Reinforcement%20Learning%20with%20Discrete%20Normalized%20Advantage%20Functions%20for.pdf) _IEEE Communications Letters_, vol. 23, no. 6, pp. 1337–1341, Aug. 2019. (Corresponding Author)\n\n* *Rongpeng Li*, Zhifeng Zhao, Rongpeng Li, Qi Sun, Chi-Lin I, Chenyang Yang, Xianfu Chen, Minjian Zhao, Honggang Zhang, [\"Deep Reinforcement Learning for Resource Management in Network Slicing,\"](/images/pdfs/2018_Li_Deep%20Reinforcement%20Learning%20for%20Resource%20Management%20in%20Network%20Slicing.pdf) _IEEE Access_, vol. 6, pp. 74429–74441, Nov. 2018.\n\n* Baidi Xiao, Yan Shao, *Rongpeng Li*, Zhifeng Zhao, and Honggang Zhang, [\"DEMO: Deep reinforcement learning for resource management in cellular network slicing,\"](/images/pdfs/2022_Xiao_DEMO.pdf) in _Proc.IEEE INFOCOM 2022_, Virtual Edition, May 2022.\n\n* Yan Shao, *Rongpeng Li*, Zhifeng Zhao, Honggang Zhang, and Yugeng Zhou, \"Graph attention network-based DRL for network slicing management in dense cellular networks,\" in _Proc. IEEE WCNC 2021_, Nanjing, China, Apr. 2021.\n\n* Yuxiu Hua, *Rongpeng Li*, Zhifeng Zhao, Honggang Zhang, and Xianfu Chen, \"GAN-based Deep Distributional Reinforcement Learning for Resource Management in Network Slicing,'' in _Proc. IEEE Globecom 2019_, Big Island, Hawaii, USA, Dec. 2019.\n\nRelevant Codes on [Github](https://github.com/ZJUNICE)\n\n* [GAN-DDQN](https://github.com/ZJUNICE/GAN-DDQN)\n* [LSTM-A2C](https://github.com/ZJUNICE/LSTM-based-A2C)","tags":["highlights"],"categories":["research"]},{"title":"A project titled Research on Full Service Awareness based Intelligence-Endogenous Networks has been approved by National Science Foundation of China.","url":"/2020/09/18/a-project-titled-research-on-full-service-awareness-based-intelligence-endogenous-networks-has-been-approved-by-national-science-foundation-of-china/","content":"\nProject name in Chinese (项目中文题目：基于业务感知的内生智能通信网络研究)\n\nAbstract: Faced with the ever-growing services with increasingly diversified and scenario-based requirements, researchers from both academia and industry are resorting to a deeper integration of artificial intelligence (AI) and communications, so as to provide endogenous intelligence within cellular networks and further enhance the agility and flexibility of cellular networks. Unfortunately, the unique characteristics of cellular networks (e.g., heterogenous infrastructure, diversified and dynamic service demands, random wireless environment, as well as user mobility) makes it challenging to directly apply the AI results. Therefore, it is highly essential to conduct the research on intelligence-endogenous networks based on full service awareness. This project (1) studies how to comprehensively leverage the information from wireless data, models and knowledge, and propose novel intelligent methods for service awareness and networks resource management, so as to improve the robustness of learning results and lay the foundation for further optimization; (2) tackles the issues incurred by the existence of multiple network entities and objective goals and designs multi-scale multi-agent reinforcement learning algorithms correspondingly, thus robustly, flexibly and dynamically adjusting the network resource allocation according to the service demands; (3) theoretically analyzes the potential bounds for the impact of endogenous intelligence on network performance; (4) builds a simulation platform. With all four pillars including service-aware modeling, algorithm designing, theoretical analyzing and simulations, this project will lay the theoretical foundation and provide essential techniques to the next-generation cellular networks for better provisioning diversified services in a smarter and more coherently manner.\n\nDuration: Jan. 2021 - Dec. 2024\n\nAmount: 550 000 RMB","tags":["highlights"],"categories":["news"]},{"title":"He visited University of Cambridge as a visiting scholar.","url":"/2020/08/02/visitcam/","content":"\nHe was a visiting scholar to Department of Computer Science and Technology, University of Cambridge from Feb. 1, 2020 to Aug.1, 2020. Prof. [Jon Crowcroft](https://www.cl.cam.ac.uk/~jac22/) is the host for this visit.\n\nThe visit unfortunately coincides with the pandemic, which disrupts many planed discussions and talking. But, it also gives more chances to read and think.\n\n{% grouppicture 5-3 %}\n<img src=\"visitcam/1581614555193-3f8abb1656123180-3fd9460309c9453c.JPG\" alt=\"1581614555193-3f8abb1656123180-3fd9460309c9453c\" style=\"zoom:25%;\" />\n\n<img src=\"visitcam/1596281061941-3fe8e82e08f50b55-3feb9e7c96daece3.JPG\" alt=\"1596281061941-3fe8e82e08f50b55-3feb9e7c96daece3\" style=\"zoom:25%;\" />\n\n\n\n<img src=\"visitcam/1595182836842-bwvbru9pkz3m6bun-3f85705ddbc0adc0.JPG\" alt=\"1595182836842-bwvbru9pkz3m6bun-3f85705ddbc0adc0\" style=\"zoom:25%;\" />\n\n<img src=\"visitcam/1595182836842-bwvbru9pkz3m6bun-3fe29346489557d7.JPG\" alt=\"1595182836842-bwvbru9pkz3m6bun-3fe29346489557d7\" style=\"zoom:25%;\" />\n{% endgrouppicture %}\n","tags":["highlights"],"categories":["news"]},{"title":"A paper titled GAN-powered Deep Distributional Reinforcement Learning for Resource Management in Network Slicing with Dr. Li as Corresponding Author has been accepted by IEEE JSAC.","url":"/2019/12/13/a-paper-titled-gan-powered-deep-distributional-reinforcement-learning-for-resource-management-in-network-slicing-with-dr-li-as-corresponding-author-has-been-accepted-by-ieee-jsac/","content":"\n**Paper abstract:**\n\nNetwork slicing is a key technology in 5G communications system. Its purpose is to dynamically and efficiently allocate resources for diversified services with distinct requirements over a common underlying physical infrastructure. Therein, demand-aware resource allocation is of significant importance to network slicing. In this paper, we consider a scenario that contains several slices in a radio access network with base stations that share the same physical resources (e.g., bandwidth or slots). We leverage deep reinforcement learning (DRL) to solve this problem by considering the varying service demands as the environment state and the allocated resources as the environment action. In order to reduce the effects of the annoying randomness and noise embedded in the received service level agreement (SLA) satisfaction ratio (SSR) and spectrum efficiency (SE), we primarily propose generative adversarial network-powered deep distributional Q network (GAN-DDQN) to learn the action-value distribution driven by minimizing the discrepancy between the estimated action-value distribution and the target action-value distribution. We put forward a reward-clipping mechanism to stabilize GAN-DDQN training against the effects of widely-spanning utility values. Moreover, we further develop Dueling GAN-DDQN, which uses a specially designed dueling generator, to learn the action-value distribution by estimating the state-value distribution and the action advantage function. Finally, we verify the performance of the proposed GAN-DDQN and Dueling GAN-DDQN algorithms through extensive simulations.\n\n**External Link:**\n\nhttps://arxiv.org/abs/1905.03929","tags":["highlights"],"categories":["news"]},{"title":"He received the grant National Postdoctoral Program for Innovative Talents, which has an awarding ratio of 13% in 2016.","url":"/2016/11/07/he-received-the-grant-national-postdoctoral-program-for-innovative-talents/","content":"\nBackground:\n\nNational Postdoctoral Program for Innovative Talents is a new program organized by [Ministry of Human Resources and Social Security of the People's Republic of China (MOHRSS)](http://www.mohrss.gov.cn/) and National Postdoc Management Committee, to encourage newly graduated (from universities in the Chinese mainland) PhD students or soon-to-be graduated(from universities in the Chinese mainland) PhD students to engage in further postdoctoral research work.\n\nFunding amount and period:\n\n* 200 awardees from 1563 qualified applicants in 2016 (the awarding ratio is merely 13%).\n* 600,000RMB/person/2 years.\n\nHere below is the program introduction in Chinese:\n\n中国博士后科学基金会网站2016年8月2日报道，博士后创新人才支持计划2016年资助率仅为13%：\n\n原标题：[2016年度博士后创新人才支持计划专家评审会议在京召开](http://jj.chinapostdoctor.org.cn/V1/Program3/Info_Show2.aspx?InfoID=16ece15b-e9ef-4b18-b4d7-25e085b422e7&InfoCategoryID=2&Show=0)\n\n> 日前，2016年度博士后创新人才支持计划（简称“博新计划”）专家评审会议在北京召开，人力资源社会保障部副部长、全国博士后管委会主任汤涛出席会议并讲话，\n> \n> 博士后创新人才支持计划旨在加速培养造就一批进入世界科技前沿的优秀青年科技创新人才，是我国培养高层次创新型青年拔尖人才的又一重要举措，是人力资源社会保障部、全国博士后管委会“十三五”期间实施的博士后专项支持计划。计划实施的主要目的有三个：**一是着眼于国际人才竞争，为国留才；二是以提高培养质量为核心，为国选才；三是服务国家重大发展战略，为国育才**。\n> \n> 2016年博士后创新人才支持计划将资助200人，资助标准为60万元/人/两年，其中40万元为可以发工资的博士后日常经费，20万元为博士后科学基金。本次共有2228名博士提交申请，其中1563人通过资格审核。\n\n人社部网站2016年3月14日报道，启动博新计划：\n\n原标题：[人社部启动博士后创新人才支持计划](http://www.mohrss.gov.cn/SYrlzyhshbzb/dongtaixinwen/buneiyaowen/201603/t20160314_235384.htm)\n\n> 2015年11月，国务院办公厅印发《关于改革完善博士后制度的意见》，明确提出要通过博士后制度培养更多高层次创新型青年人才。为贯彻落实《意见》精神，人社部、全国博士后管委会拟于近期启动“博士后创新人才支持计划”，旨在鼓励和吸引优秀应届博士毕业生和新近毕业博士进入博士后人才队伍。\n> \n> “博士后创新人才支持计划”主要瞄准国家重大战略领域、战略性高新技术领域、前沿和基础科学领域，坚持高起点、高标准，通过“个人申报、拟进站单位推荐、专家评审”的办法，每年择优遴选数百名新近毕业(含应届)的优秀博士，给予每人每2年60万元的经费资助，支持其进入国内一流的高校、科研院所或企业的重大科技平台从事创新性研究，力争加速培养其成为国际一流的创新型人才。","tags":["highlights"],"categories":["news"]},{"title":"He successfully defended his dissertation.","url":"/2015/06/01/dissertationdefense/","content":"\n<img src=\"dissertationdefense/IMG_6490.jpg\" style=\"zoom:40%;\" />\n\nGroup photo taken after the defense (May 31, 2015). From Left: Dr. **Zhifeng Zhao** (_Secretary, Zhejiang University_), Prof. **Liang Zhou** (_Committee Member, Nanjing University of Posts and Telecommunications_), Prof. **Xudong Wang** (_Committee Member, Shanghai Jiaotong University_), Prof. **Honggang Zhang** (_Supervisor, Zhejiang University_), ME, Prof. **Jinkang Zhu** (_Committee Chair, University of Science and Technology of China_), Prof. **Chunming Wu** (_Committee Member, Zhejiang University_), and Prof. **Chunguang Li** (_Committee Member, Zhejiang University_).","tags":["highlights"],"categories":["news"]},{"title":"$\\alpha$-Stable Distribution and its Applications in Cellular Networks","url":"/2015/05/19/stable/","content":"\n# Introduction\n\nEnabled by wireless **Big Data**, this website is proudly reserved for **$\\alpha$-Stable distribution** and its applications in wireless cellular networks, the works of which have been recently completed by Rongpeng Li, Yifan Zhou, Meng Li, Chen Qi, Xuan Zhou, Zhifeng Zhao and Honggang Zhang from Zhejiang University, Hangzhou, China, and Luca Chiaraviglio, Francesca Cuomo, Andrea Gigli, Maurizio Maisto from University of Rome, Sapienza, Rome, Italy, respectively.\n\nBased on practical **Big Data** measurements of on-operating cellular networks, they unveiled the suitability of **$\\alpha$-Stable** distribution in several scenarios of cellular networks, including spatial distribution of base station, dependence between base stations deployment and traffic spatial distribution, temporal distribution of traffic series. Meanwhile, several interesting features could be well explained by **$\\alpha$-Stable** distributions. In particular, rooted in the **$\\alpha$-Stable** distribution, it has been found that **fractal patterns**, **scale-free** law and **Small-World** features coexist in the complex wireless “cellular” networks.\n\n**MATLAB source codes:**\n\n1. The MATLAB source codes for base station spatial distribution identification can be downloaded here: [BS_density_pdf](/images/BS_density_pdf.zip).\n\n# Model Description\n\nFollowing the generalized central limit theorem, $\\alpha$-Stable models manifest themselves in the capability to approximate the distribution of normalized sums of a relatively large number of independent identically distributed random variables. Besides, $\\alpha$-Stable models produce strong bursty results with properties of heavy-tailed distributions and long range dependence \\[1\\]. Therefore, they arose in a natural way to characterize the traffic in fixed broadband networks \\[2,5\\] and have been exploited in resource management analyses \\[8,9\\].\n\n$\\alpha$-Stable models, with few exceptions, lack a closed-form expression of the PDF, and are generally specified by their characteristic functions.\n\n## Definition\n\nA random variable $X$ is said to obey $\\alpha$-Stable models if there are parameters $0<\\alpha \\leq 2$, $c \\geq 0$, $-1\\leq \\beta \\leq 1$, and $\\mu \\in \\mathcal{R}$ such that its characteristic function is of the following form:\n\n- If $\\alpha= 1$, $\\Phi(\\omega)= E(\\exp j\\omega X) =\\exp\\{-\\sigma \\vert c \\vert (1+j\\beta(\\text{sgn} (c)) \\ln\\vert c\\vert ) + j\\mu c \\}$;\n- Otherwise, $ \\Phi(\\omega)= E(\\exp j\\omega X) = \\exp\\{-\\sigma^{\\alpha} \\vert c \\vert^{\\alpha} (1-j\\beta(\\text{sgn} (c)) \\tan \\frac{\\pi \\alpha}{2} ) + j\\mu c \\} $.\n\nHere, the function $E(\\cdot)$ represents the expectation operation with respect to a random variable. $\\alpha$ is called the characteristic exponent and indicates the index of stability, while $\\beta$ is identified as the skewness parameter. $\\alpha$ and $\\beta$ together determine the shape of the models. Moreover, $c$ and $\\mu$ are called scale and shift parameters, respectively. Specifically, if $\\alpha=2$, $\\alpha$-Stable models reduce to Gaussian distributions.\n\nFurthermore, for an $\\alpha$-Stable modeled random variable $X$, there exists a linear relationship between the parameter $\\alpha$ and the function $\\Psi(\\omega) = \\ln\\{- \\text{Re} \\ln (\\Phi(\\omega) )\\}$ as $ \\Psi(\\omega) = \\ln\\{- \\text{Re} \\ln (\\Phi(\\omega) )\\} =\\alpha \\ln (\\omega) + \\alpha \\ln(\\sigma), $ where the function $\\text{Re}(\\cdot)$ calculates the real part of the input variable.\n\n## Figure Illustrations\n\n<img src=\"stable/stable.png\" alt=\"stable\" style=\"zoom:48%;\" />\n\n_Symmetric $\\alpha$-Stable distributions with unit scale factor. Courtesy to [Wikipedia](http://en.wikipedia.org/wiki/Stable_distribution)._\n\n<img src=\"stable/stable1.png\" alt=\"stable1\" style=\"zoom:48%;\" />\n\n_Skewed centered Stable distributions with unit scale factor. Courtesy to [Wikipedia](http://en.wikipedia.org/wiki/Stable_distribution)._\n\n## Validation Methodology\n\nUsually, it's challenging to prove whether a dataset follows a specific distribution, especially for $\\alpha$-Stable models without a closed-form expression for their PDF. Therefore, when a dataset is said to satisfy $\\alpha$-Stable models, it usually means the dataset is consistent with the hypothetical distribution and the corresponding properties. In other words, the validation needs to firstly estimate parameters of $\\alpha$-Stable models from the given dataset, and then compare the real distribution of the dataset with the estimated $\\alpha$-Stable model. Specifically, the corresponding parameters in $\\alpha$-Stable models can be determined by quantile methods, or sample characteristic function methods.\n\n## Useful references\n\n1. G. Samorodnitsky, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman and Hall/CRC, 1994.\n2. J. R. Gallardo, D. Makrakis, and L. Orozco-Barbosa, “Use of alpha-Stable self-similar stochastic processes for modeling traffic in broadband networks,” in Proc. SPIE Conf. P. Soc. Photo-Opt. Ins, Boston. Massachusetts, Nov. 1998, vol. 3530, pp. 281–296.\n3. S. M. Koyon and D. B. Williams, “On the characterization of impulsive noise with $\\alpha$-Stable distributions using Fourier techniques,” in Proc. Asilomar Conf. Signals, Systems, Computers, Oct. 1995.\n4. J. B. Hill, “Minimum Dispersion and Unbiasedness: ‘Best’ Linear Predictors for Stationary ARMA a-Stable Processes,” University of Colorado at Boulder, Discussion Papers in Economics Working Paper No. 00-06, Sep. 2000.\n5. X. Ge, G. Zhu, and Y. Zhu, “On the testing for alpha-Stable distributions of network traffic,” Comput. Commun., vol. 27, no. 5, pp. 447–457, Mar. 2004.\n6. A. Karasaridis and D. Hatzinakos, “Network heavy traffic modeling using alpha-Stable self-similar processes,” IEEE Trans. Commun., vol. 49, no. 7, pp. 1203–1214, Jul. 2001.\n7. P. Zagaglia, “Estimation of alpha-Stable distribution parameters using a quantile method,” 25-Jan-2012. \\[Online\\]. Available: http://www.mathworks.com/matlabcentral/fileexchange/34783-estimation-of-alpha-Stable-distribution-parameters-using-a-quantile-method. \\[Accessed: 09-Oct-2014\\].\n8. W. Song and W. Zhuang, “Resource Reservation for Self-Similar Data Traffic in Cellular/WLAN Integrated Mobile Hotspots,” in Proc. IEEE ICC 2010, Cape Town, South Africa, May 2010.\n9. J. C.-I. Chuang and N. R. Sollenberger, “Spectrum resource allocation for wireless packet access with application to advanced cellular Internet service,” IEEE J. Sel. Area. Comm., vol. 16, no. 6, pp. 820–829, Aug. 1998.\n10. Rongpeng Li, Zhifeng Zhao, Chen Qi, Xuan Zhou, Yifan Zhou, and Honggang Zhang, “Understanding the Traffic Nature of Mobile Instantaneous Messaging in Cellular Networks: A Revisiting to alpha-Stable Models” , IEEE Access, vol. 3, pp. 1416-1422, 2015.\n11. Luca Chiaraviglio, Francesca Cuomo, Maurizio Maisto, Andrea Gigli, Josip Lorincz, Yifan Zhou, Zhifeng Zhao, Chen Qi, Honggang Zhang, “What is the Best Spatial Distribution to Model Base Station Density? A Deep Dive in Two European Mobile Networks”, IEEE Access, Apr. 2016.\n12. Yifan Zhou, Rongpeng Li, Zhifeng Zhao, Xuan Zhou, and Honggang Zhang, “On the $\\alpha$-Stable Distribution of Base Stations in Cellular Networks”, IEEE Communications Letters, vol. 19, no. 10, pp. 1750-1753, Aug. 2015.\n\n# Spatial Distribution of Base Stations\n\n## Motivation\n\nConfronting the fundamental challenges of the long-term evolution of the ever-growing complication, heterogeneity and densification in wireless cellular networks (**2G/3G/LTE/5G**), the networking architecture and the base stations spatial distribution have been expressing the features of geometric topology irregularity.\n\nBasically, in the wireless cellular networks, the base stations (BSs) appear to be the essential part in the whole system. The spatial structure of BSs has a great impact on the performance of cellular networks, since the received signal strength varies depending on the distance between transmitter and receiver. Moreover, interference characterization is very complicated and challenging due to path loss and multipath fading effect, in particular for a heterogeneous networking (HetNets) scenario consisting of different types of BSs. In order to evaluate the network performance more accurately and tractably, it is essential to obtain realistic spatial models for the BSs deployment in cellular networks.\n\n<img src=\"stable/07-1457077701-6947841.jpg\" alt=\"07-1457077701-6947841\" style=\"zoom:80%;\" />\n\nRecently, **Poisson** distribution has been widely adopted to characterize the spatial distribution of BSs, and leads to a tractable approach to calculate the coverage probability and rate distribution in cellular networks, by taking advantage of a **Poisson point process (PPP)** based theory (i.e., stochastic geometry). However, the modeling accuracy of **Poisson** distribution has been recently questioned in regard to a number of realistic cellular networking scenarios. Consequently, in order to reduce the modeling error between **Poisson** distributed BSs and the practical distributed ones, some variants of **PPP** have been exploited to obtain precise analysis results. On the other hand, the actual deployment of BSs in long term is highly correlated with human activities.\n\nInspired by the clustering reality of BSs and the intrinsic heavy-tailed characteristics of human activities, we aim to re-examine the statistical pattern of BSs in cellular networks, and find the most appropriate spatial density distribution of BSs. Interestingly, by taking advantage of large amount (**Big Data**) of realistic deployment information of BSs from on-operating cellular networks around the world, we find that the widely adopted **Poisson distribution** (i.e. **PPP**) severely diverges from the practical/actual spatial distribution of BSs. Instead, heavy-tailed distributions could more precisely match the practical/actual distribution. In particular, **$\\alpha$-S****table distribution**, the heavy-tailed distribution also found in various traffic patterns of wired broadband networks and wireless cellular networks, is most consistent with the practical/actual measured data. Moreover, rooted in the **$\\alpha$-Stable distribution**, it has also been found that _fractal patterns, scale-free law and Small-World_ features coexist in the complex wireless \"cellular\" networks.\n\n<img src=\"stable/PPP-PCP-MCP.png\" alt=\"PPP-PCP-MCP\" style=\"zoom:40%;\" />\n\nMoreover, by in-depth statistical comparisons based on the above large-scale (**Big Data**) identification, we also investigated the **Gibbs** point processes (**Geyer, Strauss & PHCP**) as well as the **Neyman-Scott** point processes (**MCP & TCP: Matern cluster process & Thomas cluster process**), and compared their performance in the view of a large-scale modeling test, and finally found the general clustering nature of BSs deployment. However, either Gibbs point processes (**Geyer, Strauss & PHCP**) or Neyman-Scott point processes (**MCP & TCP**), diverged from the practical/actual spatial distribution of BSs, to some extent (see the following Table).\n\n<img src=\"stable/07-1457152920-6948131.jpg\" style=\"zoom:60%;\" />\n\n<img src=\"stable/图片2.png\" style=\"zoom:50%;\" />\n\n<img src=\"stable/图片3.png\" style=\"zoom:50%;\" />\n\nIn summary, we have carried out an large-scale identification based on real data of base station locations from both Chinese and European mobile operators. For detailed description, please check the subsections on this topic as well as the following references.\n\n* * *\n\n**Related references:**\n\n* Yifan Zhou, Rongpeng Li, Zhifeng Zhao, Xuan Zhou, and Honggang Zhang, \"**On the $\\alpha $-Stable Distribution of Base Stations in Cellular Networks**\", IEEE Communications Letters, vol. 19, no. 10, pp. 1750-1753, Aug. 2015.\n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, “**The Stochastic Geometry Analyses of Cellular Networks with $\\alpha$-Stable Self-Similarity**,” IEEE Trans. on Communications, March 2019.\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**Study on Base Station Topology in National Cellular Networks: Take Advantage of Alpha Shapes, Betti Numbers, and Euler Characteristics**,” IEEE Systems Journal, Q3/Q4 2019\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology**,” IEEE Wireless Communications Letters, April 2019. \n\n* Yifan Zhou, Zhifeng Zhao, Yves Louet, Qianlan Ying, Rongpeng Li, Xuan Zhou, Xianfu Chen, and Honggang Zhang, “**Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks,”** IEEE Access, vol. 3, pp. 2987-2999, Dec. 2015. \n\n* Zhifeng Zhao, Meng Li, Rongpeng Li, and Yifan Zhou, “**Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,”** IET Communications, Q3 2017.\n\n* Luca Chiaraviglio, Francesca Cuomo, Maurizio Maisto, Andrea Gigli, Josip Lorincz, Yifan Zhou, Zhifeng Zhao, Chen Qi, Honggang Zhang, “**What is the Best Spatial Distribution to Model Base Station Density? A Deep Dive in Two European Mobile Networks,”** IEEE Access, Apr. 2016.\n\n* Luca Chiaraviglio, Francesca Cuomo, Andrea Gigli, Maurizio Maisto, Yifan Zhou, Zhifeng Zhao, Honggang Zhang, “**A Reality Check of Base Station Spatial Distribution in Mobile Networks,”** IEEE INFOCOM 2016 (Poster), San Francisco, Apr. 2016. \n\n## China Datasets\n\n### Background\n\n#### Data description\n\nIn order to reach credible results, we collect a massive amount of practical data of BSs information from China Mobile in a well-developed eastern province of China. The collected dataset, containing over 47,000 BSs of GSM cellular networks and serving over 40 million subscribers, encompasses all BS-related records like location information (i.e. longitude, latitude, etc.) and BS type (i.e. macrocell or microcell). Based on the coverage area and location information, we divide the dataset into disjoint subsets. Accordingly, we can classify the data set as subsets of urban areas and rural areas, by matching the geographical land forms with local maps, as depicted in Fig. 1.\n\n<img src=\"stable/cities.png\" alt=\"cities\" style=\"zoom:75%;\" />\n\nFig. 1 An illustration of the deployment of base stations in three typical cities with geographical landforms, namely City A, B, C, respectively.\n\n#### Mathematical model\n\nHeavy-tailed distributions could be widely applied to explain a number of natural phenomena, including the Internet topology. Mathematically, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded. In other words, they have heavier tails than the exponential distribution.\n\nThere exist many statistical distributions proving to be heavy-tailed. Among them, generalized Pareto (GP) distribution, Weibull distribution, and log-normal distribution belong to one-tailed ones with the probability density function (PDF) in closed-forms (see Table II). Another famous heavy-tailed distribution is $\\alpha $-Stable distribution, who manifests itself in the capability to characterize the distribution of normalized sums of a relatively large number of independent identically distributed random variables. However, $\\alpha $-Stable distribution, with few exceptions, lacks a closed-form expression of the PDF, and is generally specified by its characteristic function, as presented in the [model description](http://www.rongpeng.info/stable/index.php/model-description/) page.\n\nTABLE II: The List of Candidate Distributions and Estimated Parameters.\n\n\n\n### Statistical Pattern of Base Stations with Large-scale Identification\n\n Based on the large amount of BS location data, we sample one certain city randomly with a fixed sample area size. Then, we compute the spatial density for different 10000 sample areas and obtain the empirical density distribution, by counting and sorting the number of BSs in each sample area. Next, we estimated the unknown parameters in candidate distributions (except $\\alpha $-Stable distribution) using maximum likelihood estimation (MLE) methodology. For $\\alpha $-Stable distribution, we estimate the relevant parameters using quantile methods, correspondingly build the model to generate the corresponding random variable, and finally compare its induced PDF with the exact (empirical) one.\n\n In the first place, we refer to City B as an example, and compute the PDF of BS density under the sample area size 4×4 km ² . After fitting the corresponding PDF to distributions in Table II, we provide the comparison between the empirical BS density distribution with candidate ones in Fig. 2 and Fig. 3. As depicted in Fig. 3, the statistical pattern of BSs obviously exhibits heavy-tailed characteristics. Besides, among all candidate distributions, $\\alpha$ -Stable distribution most precisely match the empirical PDF. On the other hand, we provide the numerical comparison in Table III, in terms of root mean square error (RMSE). Indeed, the RMSE results in Table III show $\\alpha$-Stable distribution has the minimum RMSE value (0.0279) while Poisson distribution has the maximum one (0.2537), and once again strengthen this aforementioned conclusion. All of the estimated parameters of the fitted candidate distributions are also listed in Table II.\n\n<img src=\"stable/b_4x4_loglog.png\" alt=\"b_4x4_loglog\" style=\"zoom:75%;\" />\n\nFig. 2: The log-log comparison between practical BS density distribution in City B with candidate ones, when sample area size equals 4×4 km².\n\nFig. 3: The results after fitting BS density distribution in City B to candidate distributions, when sample area sizes vary. (a) 3×3 km² ; (b) 4×4 km²; (c) 5×5 km².\n\nIn order to examine the geographical impact on the fitting results, we further analyze the density distribution of BSs in City A and City C using a sample area size of 4×4 km². Due to the factor of geographical irregularity, there is a noticeable gap between the $\\alpha$-Stable distribution and the empirical PDF of City A and C in comparison with City B. Nevertheless, as shown in Table III and Fig. 4, it can be observed that, $\\alpha$-Stable distribution could match the practical one in both cities, with RMSE values equaling 0.0177 and 0.0451 respectively and being less than those of other candidate distributions. Moreover, the same conclusions concerned with sample area sizes of 3×3 km ² and 5×5 km ², could be also testified in Table III.\n\n<img src=\"stable/rmse.png\" alt=\"rmse\" style=\"zoom:75%;\" />\n\nBased on the extensive analyses above, we could confidently reach the following remark.\n\n_The spatial pattern of deployed BSs exhibits strong heavy-tailed characteristics. Based on the large-scale identification, $\\alpha$-Stable distribution manifests itself as the most precise one. On the contrary, the popular Poisson distribution is an inappropriate model for the BS density distribution, in terms of the root mean square error._\n\n<img src=\"stable/fig4.png\" alt=\"fig4\" style=\"zoom:75%;\" />\n\nFig. 4. The comparison between BS density distribution and $\\alpha$-Stable distribution in City A and City C, when sample area size equals 4×4 km².\n\n### Conclusions and Future Works\n\nBased on the practical BS deployment information of one on-operating cellular networks, we carried out a thorough investigation over the statistical pattern of BS density. Our study showed that the distribution of BS density exhibits strong heavy-tailed characteristics. Furthermore, we found that the widely adopted Poisson distribution severely diverges from the realistic distribution. Instead, $\\alpha$-Stable distribution, the distribution also found in the traffic dynamics of broadband networks and cellular networks, most precisely match the practical one. Moreover, our study could contribute to the understanding of evolution trend of BS deployment, as well as the impact of human social activities in long term.\n\nCurrently, the lack of closed-form for $\\alpha$-Stable distribution makes it difficult to reach tractable solutions and might hinder its applications in networking performance (e.g., coverage, rate, etc) analyses. Therefore, we are dedicated to handle the related meaningful yet more challenging issues over applications of $\\alpha$-Stable distribution in the future.\n\n**Related references:**\n\n* Yifan Zhou, Rongpeng Li, Zhifeng Zhao, Xuan Zhou, and Honggang Zhang, \"**On the $\\alpha $-Stable Distribution of Base Stations in Cellular Networks**\", IEEE Communications Letters, vol. 19, no. 10, pp. 1750-1753, Aug. 2015. \n\n\n* Yifan Zhou, Zhifeng Zhao, Yves Louet, Qianlan Ying, Rongpeng Li, Xuan Zhou, Xianfu Chen, and Honggang Zhang, “**Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks,”** IEEE Access, vol. 3, pp. 2987-2999, Dec. 2015. \n\n* Zhifeng Zhao, Meng Li, Rongpeng Li, and Yifan Zhou, “**Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,”** IET Communications, August 2017.\n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, \"**The Stochastic Geometry Analyses of Cellular Networks with alpha-Stable Self-Similarity**,\" arxiv.org/abs/1709.05733v1, September 2017. \n\n## European Datasets\n\n### Data Description\n\n#### Itallian dataset description\n\nWe initially focus on the Emilia-Romagna region of Italy, which is covered by four different cellular operators (referred as A, B, C and D in the following). Table 1 reports the main features of the considered dataset. The total number of deployed BSs considering the whole set of operators is more than 4900 BSs. Focusing then on each operator, the number of deployed BSs is similar for operator A and operator B, while it is slightly lower for operators C and D. More in depth, operator D reuses part of the cellular infrastructure of the two largest operators to guarantee coverage in the zones not covered by its own BSs. As for the morphological characteristics of the area, the whole region spans over 22000 km^2^, which includes rural areas, town areas and one metropolitan area. This is also reflected in the number of subscribers, which is larger than 6.5 millions in total, with the largest number of subscribers living in the metropolitan area. Finally, the average BS density (i.e., the total number of deployed BSs for each operator over the total region), is always lower than one, due to the fact that in rural areas less BSs are deployed compared to urban ones. However, the density is larger for operator A and B, and slightly lower for the other operators.\n\n<img src=\"stable/Italian-bs.jpg\" alt=\"Italian-bs\" style=\"zoom:75%;\" />\n\nFIGURE 1. Italian Dataset: BS positions and considered scenarios (inside the rectangular boxes). (a) IT urban scenario. (b) IT rural scenario.\n\n<img src=\"stable/Table-I.jpg\" alt=\"Table-I\" style=\"zoom:95%;\" />\n\nTABLE 1. Main features of the Italian data set.\n\n#### CROATIAN dataset description\n\nIn addition to the Italian dataset, we have considered the set of BSs sites having freestanding masts from the country of Croatia. In particular, more than 2600 BSs are deployed in an area of around 56000 km^2^. The database is composed of the BSs sites owned by the telecom operators currently active in Croatia, serving in total more than 4.6 millions of users. The morphological characteristics of the country include one large metropolitan area around the capital Zagreb, different rural zones, and one coastal zone including most of tourist attractions. In addition to the BSs sites actually deployed in the network, the positions of planned BSs sites to be installed in the future is also provided, considering a vast region in the north of the country. Moreover, Table 2 reports the characteristics of each scenario in terms of: number of considered BSs, size of the area, and average BS density.\n\n<img src=\"stable/Croatian-BS.jpg\" alt=\"Croatian-BS\" style=\"zoom:75%;\" />\n\nFIGURE 2. Croatian Dataset: BS positions and considered scenarios (inside the rectangular boxes). (a) CRO coastal scenario. (b) CRO rural scenario. (c) CRO urban scenario. (d) CRO urban scenario including future planned BSs.\n\n### Model Description\n\nThe mathematical models adopted here are the same with that in **China dataset**.\n\n### Case-Studies Results\n\nGiven the BS positions in each scenario, we then compute the empirical spatial distribution of the BS density. Initially, we sample each scenario with a small area of fixed size. We then randomly select 10000 squares of fixed area size. For each square, we compute the number of BSs falling into it. This number, divided by the area size, represents the BS density. From the BS densities, we derive the PDF. This spatial distribution is then used as reference one vs. the possible candidates (i.e., Poisson, GP, Weibull, Lognormal and $\\alpha$-Stable). For each candidate distribution, we estimate the unknown parameters by applying the Maximum Likelihood Estimation (MLE) criterion. For estimating the parameters of the $\\alpha $-Stable distribution, we adopted a similar procedure like the one reported in, due to the fact that the closed-form for this distribution does not always exist.\n\nWe initially focus on the urban area of the Italian scenario. As a showcase, we compute the PDF of BS density with a sample area of size 10 x10 km^2^. Moreover, we have taken into account the BSs from all the operators in order to maximize the number of BSs under consideration. Fig. 3 reports the empirical PDF (i.e., the real one) with the fitting of various candidate distributions. Interestingly, the best fitting is obtained with the $\\alpha$-Stable distribution, while the other ones perform consistently worse.\n\n<img src=\"stable/Italian-Urban-PDF.jpg\" alt=\"Italian-Urban-PDF\" style=\"zoom:75%;\" />\n\nFIGURE 3. Italian urban scenario: probability density function of the BS density with all operators and sample squared area with size 100 km^2^.\n\nIn the following, we have computed the Root Mean Square Error (RMSE) of the different fittings against the empirical PDF. This metric is useful to capture the fitting accuracy of the considered distribution. In this case, for modeling generalization purpose, we have also considered the variation of the sample area between 5x5 km^2^ and 11x11 km^2^ in the scenario. Recall that for each sample area size we randomly select 10000 samples in the scenario. Fig. 4 illustrates the obtained results. Obviously, the $\\alpha$-Stable is the best fitting for all the considered sample areas, with a RMSE always lower than 0.3. On the other hand, the Poisson distribution exhibits a RMSE always larger than 0.5, thus confirming our intuition that it is not suitable to capture the spatial density distribution of real BSs.\n\n<img src=\"stable/RMSE-to-Sample-Area.jpg\" alt=\"RMSE-to-Sample-Area\" style=\"zoom:75%;\" />\n\nFIGURE 4. Italian urban scenario: RMSE vs. size of the sample squared area.\n\nFurthermore, we have investigated the impact of single operators. Fig. 5(a) reports the RMSE values for each single operator. Recall that A and B exhibit the largest number of BSs, while operator D tends to exploit the BSs of the other operators to provide user coverage. Surely, the $\\alpha$-Stable is the best fitting for operators A, B and C. On the contrary, for operator D the $\\alpha$-Stable RMSE is lower than the Poisson distribution but higher than the other ones. This is due to the fact that this operator does not spread its own BSs in the same way like the other ones, resulting in a different density distribution. Moreover, we can see that the RMSE tends to increase from left to right (i.e., towards operators with less BSs). To give more insight, Fig. 5(b) provides the results when multiple operators are considered to compute the BS density.\n\n<img src=\"stable/RMSE-to-Operator-ID.jpg\" alt=\"RMSE-to-Operator-ID\" style=\"zoom:75%;\" />\n\nFIGURE 5. Italian urban scenario: RMSE for single and multiple operators. (a) Single operators. (b) Multiple operators.\n\nInterestingly, the $\\alpha$-Stable fitting tends to be almost constant, while the RMSEs of the other distributions tend to increase when the number of operators is decreased. In particular, operator A, which is also the largest one, has deployed its BSs in the scenario in order to always provide coverage to users with its own BSs. On the contrary, operator D tends to lease the infrastructure from the other operators. The case with the single operator A matches better a complete BSs deployment in the targeted region, resulting in a low RMSE with the $\\alpha$-Stable model.\n\n<img src=\"stable/Table-2.jpg\" alt=\"Table-2\" style=\"zoom:85%;\" />\n\n\n\nTABLE 2. Italian urban scenario: RMSE values vs. BS technology.\n\nIn the following part we have taken into account the impact of various cellular networking technologies on the BS density. Together with each BS position, in fact, our dataset includes information about the technology, which can be GSM, UMTS, LTE, or not specied. Each BS entry in the BS database includes a list of the supported technologies. Specifically, by manually checking in the BS database, we have found that the UMTS service is always provided in the considered region, except for the BSs for which the technology is not specied. At the same time, when the LTE service is provided, also GSM and UMTS services are available. Therefore, we have considered the following categories: GSM/UMTS, GSM/UMTS/LTE, or the entire dataset (i.e., including the BSs for which the technology is not specified). For each category, we have then computed the empirical PDF as well as the distribution fitting. Table 2 describes the obtained RMSE values. Once again, these results confirm that the $\\alpha$-Stable fitting reaches the highest accuracy in this scenario, while all the other distributions have a RMSE at least more than doubled.\n\n<img src=\"stable/RMSE-to-Technology.jpg\" alt=\"RMSE-to-Technology\" style=\"zoom:75%;\" />\n\nFIGURE 6. Italian rural scenario results. (a) Sample area size 5x5 km^2^. (b) Sample area size 7x7 km^2^. (c) Sample area size 9x9 km^2^. (d) Sample area size 11x11 km^2^.\n\nIn the following, we have moved our attention to the Italian rural scenario. Differently, from the previous case, in this scenario there are no big towns, and the BS distribution over the territory is rather sparse. In order to evaluate the behavior of the different distributions, we have computed the RMSE for different sample area sizes, and for different technologies, as reported in Fig. 6. As expected, the Poisson distribution does not adhere to the empirical distribution, resulting in the highest RMSE. The other distributions tend to have a lower RMSE. Among them, the best candidate is the Lognormal distribution in most of the cases. On the contrary, the $\\alpha$-Stable distribution exhibits a higher RMSE than the Lognormal one (but lower than the Poisson one). This fact is confirmed across the different technologies, and for the different area sizes. Therefore, the $\\alpha$-Stable distribution is useful to capture the BS spatial behavior in urban maps. When the BS distribution becomes more sparse than in a city, like in this case, the best candidates are other types of distributions (i.e., like the Lognormal one in this case).\n\n<img src=\"stable/Croatian-RMSE-to-Sample-Area.jpg\" alt=\"Croatian-RMSE-to-Sample-Area\" style=\"zoom:75%;\" />\n\nFIGURE 7. Croatian scenarios: RMSE of the distributions for different sample area sizes. (a) Coastal. (b) Rural. (c) Urban. (d) Urban with Future Planned BSs.\n\nWe have investigated in the next step the Croatian scenarios. Fig. 7 reports the obtained results in terms of RMSE for the different distributions. In this case, we have also varied the size of the sample area. Particularly, since the BSs are rather sparse in the rural, coastal and urban scenarios (without planned BSs), we have adopted a larger sample area size than the Italian cases (i.e., ranging between 14x 14 km^2^ and 20x20 km^2^). On the contrary, we have adopted a sample area comparable with the Italian case for the urban scenario with future planned BS, since the BS density is quite similar in these two cases. Focusing on the obtained results, the best fitting for the coastal case is the Weibull distribution (reported in Fig. 7(a)), while the Lognormal one tends to achieve comparable RMSE values when the rural case in considered (see Fig. 7(b)). However, when the urban scenarios are considered (Fig. 7(c) and Fig. 7(d)) the distribution achieving the lowest RMSE is the $\\alpha$-Stable. This fact further confirms our intuition that the $\\alpha$-Stable model matches the BS spatial distribution in urban areas. Moreover, our results also imply that the definition of a universal model, covering all kinds of urban, coastal, and rural scenarios, is still an open issue.\n\n### Conclusions and Future Works\n\nWe have studied the BS spatial distributions across different scenarios obtained from Italy and Croatia, considering urban, coastal, and rural zones.We have compared the real distribution against different candidate ones. Our results show that the best distribution matching the real one is the $\\alpha$-Stable model in urban scenarios. This fact is confirmed across different sample area sizes, operators, and technologies. On the contrary, the Lognormal and Weibull distributions tend to fit better the real one in coastal and rural scenarios. We believe that this work can be used to derive fruitful guidelines for the BS deployment. As next step, we will complement these findings with a detailed study of spatial and temporal variations of user traffic. Moreover, we will extend our analysis to other countries (such as in Asia and in North America). Finally, we will study the possibility of deriving a universal model covering rural, urban and coastal zones.\n\n**Related references:**\n\n* Luca Chiaraviglio, Francesca Cuomo, Maurizio Maisto, Andrea Gigli, Josip Lorincz, Yifan Zhou, Zhifeng Zhao, Chen Qi, Honggang Zhang, “**What is the Best Spatial Distribution to Model Base Station Density? A Deep Dive in Two European Mobile Networks,”** IEEE Access, Apr. 2016. \n\n* Luca Chiaraviglio, Francesca Cuomo, Andrea Gigli, Maurizio Maisto, Yifan Zhou, Zhifeng Zhao, Honggang Zhang, “**A Reality Check of Base Station Spatial Distribution in Mobile Networks,”** IEEE INFOCOM 2016 (Poster), San Francisco, Apr. 2016. \n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, \"**The Stochastic Geometry Analyses of Cellular Networks with alpha-Stable Self-Similarity**,\" arxiv.org/abs/1709.05733v1, September 2017. \n\n# Temporal Distribution of Traffic Series (Mobile Traffic Big Data)\n\n## Background\n\nMobile instant messaging (MIM) services significantly facilitate personal and business communications, inevitably consume substantial network resources, and potentially affect the network stability. It is meaningful to carefully examine the traffic nature of MIM (e.g. WeChat/Weixin) services, so as to design MIM service-oriented protocols to overcome their induced negative influence to cellular networks.\n\n## MIM Working Mechanisms\n\n<img src=\"stable/1.jpg\" alt=\"1\" style=\"zoom:75%;\" />\n\nMIM services, which solely rely on mobile Internet to exchange information, have quite working mechanisms from traditional short messaging services. One of the prominent differences is that born with stanard protocols, traditional short messaging services could conveniently fulfill timely information delivery and provision \"always-online\" service. However, for mobile Internet in packet switching domain, a TCP connection would release itself if exceeding a TCP inactivity timer. Therefore, as depicted in the above picture, besides transmitting (TX) and receiving (RX) normal packets after logging onto a server, MIM services commonly take advantages of keep-alive mechanisms to send packets containing little information periodically and maintain a long-lived TCP connection.\n\nHereinafter, message refers to a series of packets transmitted between the user equipment (UE) and the servers of service provider on application layer. Therefore, the messages delivered on every TCP connection constitute the fundamental elements of MIM services, and are named as individual message-level (IML) traffic. Comparatively, when the messages are transmitted through one BS, they become accumulated and could be regarded as the aggregated traffic from a slightly macroscopical perspective.\n\n## The Statistical Pattern and Inherited Methodology of MIM Services\n\n<img src=\"stable/2.jpg\" alt=\"2\" style=\"zoom:75%;\" />\n\n<img src=\"stable/3.jpg\" alt=\"3\" style=\"zoom:75%;\" />\n\nCompared with the geometric and exponential distribution functions recommended by 3GPP, power-law and lognormal distributions functions are more suitable to model the statistical pattern of message lengths and inter-arrival time of consecutive messages, respectively.\n\n<img src=\"stable/4.jpg\" alt=\"4\" style=\"zoom:75%;\" />\n\nDue to their generality, $\\alpha$-Stable models are most suitable to characterize the aggregated traffic in cellular networks. Together with previous findings in fixed broadband networks, $\\alpha$-Stable models are proven to accurately model the aggregated traffic from cellular access networks to core networks.\n\nIn addition, according to the generalized central limit theorem, the aggregated traffic within one BS, following $\\alpha$-Stable models, can be explained as the accumulation of a number of power-law distributed messages.\n\nOn the other hand, we have also investigated and characterized various kinds of traffic in wireless cellular networks, based on a large amount of real traffic data measurement. In particular, our dataset is based on a significant number of practical traffic records from one of the biggest cellular operators in an eastern provincial capital in China. The records in dataset are originated from nearly 10000 BSs with more than 10 million subscribers involved. Each traffic record has a resolution of 5 minutes, including timestamps, location area code (LAC), cell ID, application name and the corresponding volume of data traffic.\n\nConcretely, IM(WeChat/Weixin), HTTP web browsing and QQLive Video are selected as the representatives of the three typical types of mobile service, IM, web browsing and video for discussion, respectively. Particularly, WeChat/Weixin is a widely booming social IM service which allows over 6 hundred million mobile users to exchange text messages and multimedia files like voices, pictures and videos with each other via smart phones, in China as well as around the world. The summary information on the mobile traffic dataset under study is listed in the following Table and Figures (e.g., Traffic time series of different mobile service types during one day).\n\n<img src=\"stable/图片1-001-2372731.png\" alt=\"图片1-001\" style=\"zoom:50%;\" />\n\n<img src=\"stable/图片1-002.png\" alt=\"图片1-002\" style=\"zoom:50%;\" />\n\n**Remark 1**. _Application-level cellular data traffic series for IM, Web Browsing and video service appear bursty across a long range of time scales. The burstiness remains significant as the time scale increases_.\n\nBurst commonly implies sharp increase in volume of information interaction in seconds, which is potentially accompanied with the emergence of unexpected events or centralized activities of human beings. It is generally believed that bursty phenomena appears apparently and enormously in cellular data traffic series which is closely related to people’s daily life. In this section, we have a brief look at the burstiness of application-level cellular data traffic at different time scales and validate this intrinsic characteristics.\n\n**Remark 2.** _There widely exists self-similarity in application-level cellular data traffic in terms of IM, Web browsing, and video services. Specifically, for IM and web browsing service, most traffic series exhibit a moderate degree of self-similarity while video service shows weaker self-similarity compared with the other two services under study_.\n\nIn general, the parameter _H_ is known as the Hurst parameter with the value ranging from 0.5 to 1.0 and has a positive correlation with the degree of self-similarity. That is to say, _H_ =0.5 indicates the lack of self-similarity whereas large value for _H_ (i.e., close to 1.0) indicates a large degree of self-similarity. Generally, graphical methods such as variance-time plot, R/S plot are used to test for self-similarity (see the following Figures).\n\n<img src=\"stable/图片1-003.png\" alt=\"图片1-003\" style=\"zoom:50%;\" />\n\n**Remark 3**. _According to the minor fitting errors, beside the MIM (WeChat/WeiXin), $\\alpha$-Stable models are suitable to characterize all the other application-level data traffic in cellular networks._\n\nIn summary, we have demonstrated the universal existence of burstiness and self-similarity and their great significance in social mobile data traffic series. To capture these characteristics, $\\alpha$-Stable distribution has been taken to model traffic series. The minor fitting errors for different service types verify the validity of $\\alpha$-Stable models and the estimated parameter can reflect the characteristics of traffic series well.\n\n* * *\n\n**Related references:**\n\n1. Rongpeng Li, Zhifeng Zhao, Chen Qi, Xuan Zhou, Yifan Zhou, and Honggang Zhang. “**Understanding the Traffic Nature of Mobile Instantaneous Messaging in Cellular Networks: A Revisiting to $\\alpha$-Stable Models**,” IEEE Access, vol. 3, pp. 1416-1422, 2015. \n\n2. Rongpeng Li, Zhifeng Zhao, Jianchao Zheng, Chengli Mei, Yueming Cai, and Honggang Zhang, “**The Learning and Prediction of Application-level Traffic Data in Cellular Networks**,” IEEE Trans. Wireless Communications, March 2017.\n\n3. Zhifeng Zhao, Meng Li, Rongpeng Li, and Yifan Zhou, “**Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,”** IET Communications, August 2017.\n\n4. Chen Qi, Zhifeng Zhao, Rongpeng Li, and Honggang Zhang, “**Characterizing and Modeling Social Mobile Data Traffic in Cellular Networks,”** 2016 IEEE 83rd Vehicular Technology Conference (VTC-Spring 2016), Nanjing, May 2016.\n\n# Dependence Between Base Stations Deployment and Traffic Spatial Distribution\n\n## Background\n\nBase stations (BSs) deployment and traffic spatial distribution play crucial roles in network design and resource management. Actually, the BSs deployment and traffic spatial distribution are dually coupled, since BSs are built up to fulfill the traffic demand while data traffic is transmitted to mobile users through BSs. Thus it is imperative to fully understand BSs and traffic spatial distribution as well as statistical relationship between them.\n\n## Data Description\n\nThe data used in this paper is obtained from a commercial mobile operator in China. The dataset, collected from two kinds of networks (i.e., 2G and 3G cellular networks), includes traffic and BSs information. The data traffic is measured in the unit of bytes that each BS transmits to the covered users in one-hour interval. BSs information mainly involves geographic location (i.e., longitude, latitude, etc.) and BS type (i.e., macrocell or microcell). Specifically, we convert the longitude and latitude values of each BS to X, Y coordinates, and plot the actual geographic location on an 2D coordinate plane as shown in Fig. 1 and Fig. 2.\n\n<img src=\"stable/QQ截图20160316093615.jpg\" alt=\"QQ截图20160316093615\" style=\"zoom:100%;\" />\n\n\n\n## Spatial Distribution of BSs and Traffic\n\nConsidering the real situations that heavy-tailed phenomenon does exist in BSs and traffic spatial distributions, we take $\\alpha$-Stable distribution as the fitting candidate. The parameters of $\\alpha$-Stable model are firstly estimated and the results are listed in Table II. Afterwards, we use the $\\alpha$-Stable model, produced by the aforementioned estimated parameters, to generate some random variable, and compare the induced PDF with the exact (empirical) one. Therefore, as shown in Fig. 3 and Fig. 4, after fitting an $\\alpha$-Stable distribution to BSs density and traffic spatial density in City A, they both better obey the $\\alpha$-Stable distributions obviously. In City B, $\\alpha$-Stable distribution is also applicable.\n\n\n\n\n\n\n\n## Linear Dependence Between BSs Density and Traffic Spatial Density\n\nTo ease illustration, Urban1 is taken as an representative example. With the sampling window size being 3x3 km^2^, 5x5 km^2^, 7x7 km^2^, then fitting results are depicted in Fig. 5. Evidently, BSs density and traffic spatial density exhibit strong linearity regardless of the BS type. Besides the visual observation, R- square value is also adopted as a performance metric to evaluate the goodness of fit. The closer is the value to 1, the better is the goodness of fit. According to Table III, we find that linear regression model is reasonable to characterize the spatial correlation between BSs deployment and traffic spatial distribution, which can be stated as follows:\n\n$ {\\lambda_{rm{BS}}} = {k}{\\lambda_{rm{TR}}+{t}}. $\n\nHere, ${k}$ is a linear slope value that represents the needed number of BSs per unit spatial traffic.\n\n\n\n\n\nOn one hand, linear regression model keeps better fitting effect no matter the sample region is urban or rural. On the other hand, the key parameter slope k is closely associated with the BS type, without dependence on the sampling window size. These findings indicate that BSs deployment is deeply influenced by the subscribers’s demand as well as the corresponding traffic dynamics over the space, and imply that BSs density and traffic spatial density have almost identical heterogeneity feature.\n\n## Cellular Networks Evolution Trend\n\nBy comparing the fitted parameters in 2G and 3G scenes carefully, we discover that the ${k_{2G,microcell}}$ is greater than the ${k_{2G,microcell}}$ regardless of region type. The computed results are listed in Table IV. These experimental results demonstrate that an upgraded BS in 3G own more capacity and higher transmission rate than that in 2G.\n\n\n\nGenerally, some technological bottlenecks would be inevitable in cellular networks evolution for each generation.Therefore, new and advanced technologies have been explored to solve the confronted problems, thus achieving success in network upgrading and optimization. Particularly, in view of the difference of slope k in various cellular network scenarios, a reasonable assumption can be stated as follows:\n\n${k_{2G}} > {k_{3G}}>{k_{4G}}.$\n\nIn actual situations, however, with the increase of traffic load, it is impossible for the number of BSs to grow linearly and infinitely, due to the physical and performance constraints of each generation cellular network. Consequently, there should be a certain critical state for each generation cellular network. That is, the available service capability is pre-determined, and if traffic demand increases continuously, the network evolution would go through a network transition (i.e., upgrading from 2G to 3G, then to 4G). In that regard, an explanatory outline about how cellular network architecture evolves is illustrated in Fig. 6.\n\n\n\nWhether it is a 2G era, 3G era or 4G era, linear dependence between BSs density and traffic spatial density always exists but with different slope k. Surely, the performance improvement of network expects BSs with larger capacity to supply more traffic demand meanwhile requires operators to implement less BSs to serve more subscribers in certain area.\n\n**Related references:**\n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, \"**The Stochastic Geometry Analyses of Cellular Networks with alpha-Stable Self-Similarity**,\" arxiv.org/abs/1709.05733v1, September 2017. \n\n* Zhifeng Zhao, Meng Li, Rongpeng Li, and Yifan Zhou, “**Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,”** IET Communications, August 2017.\n\n* Meng Li, Zhifeng Zhao, Yifan Zhou, Xianfu Chen, and Honggang Zhang, “**On the Dependence Between Base Stations Deployment and Traffic Spatial Distribution in Cellular Networks,”** 23rd International Conference on Telecommunications, Thessaloniki, Greece, May 2016. \n\n# The Emergence of Scaling Law, Fractal Patterns and Self-Similarity in Wireless Networks\n## Background\n\nCellular networks have been undergoing a long history of evolution and gradually accumulated unique spatial distribution pattern, as BSs are continually deployed to provision the ever-increasing mobile traffic in hotspots accompanied by the global popularity of smart phones and tablets. Accordingly, by taking advantage of realistic traffic records from cellular networks, we can leverage the theory of complex networks to answer what is the intrinsic evolved nature in cellular networks? We first create a spatial traffic correlation model of BSs by regarding BSs as nodes and the traffic correlation between BSs as edges. Then, we analyze the structure and properties of this spatial traffic correlation model and derive the corresponding results in the networks. Interestingly, we discover that there exist three key properties, i.e., scale-free pattern, fractality, self-similarity, and small-world.\n\n## Data Acquisition and Preparation\n\nWe acquire the real measurement data from one of the biggest commercial mobile operator in China, which contains the information of traffic and BSs from a second-generation (2G) cellular network in City A and the counterpart from a third-generation (3G) cellular network in City B. Specifically, the traffic data is measured in the unit of bytes that each BS transmits to the serving users. The related traffic for City A and City B lasts 7 days and 1 day, with one-hour and half-hour granularity, respectively. Therefore, for one BS, the traffic series for City A and City B could be regarded as a vector of 168 entries and 48 entries, respectively. Meanwhile, we plot the BS deployment with the geographical landforms in Fig. 1. Moreover, the BS related information such as BS type, location area and geographic location is available as well and more details are summarized in Table I.\n\n<img src=\"stable/1.png\" style=\"zoom:100%;\" />\n\n<img src=\"stable/3.png\" style=\"zoom:100%;\" />\n\nFig. 1. An illustration of the deployment of base stations in two typical cities with geographical landforms, namely City A, B, respectively.\n\n## Box-covering Algorithm\n\nAs a widely used technique for characterizing fractal networks and calculating their fractal dimensions, box-covering algorithm has experienced a number of distinct versions since the generalized box-covering algorithm was introduced by Song . The random sequential (RS) box-covering algorithm is not suitable in our work due to its low efficiency in finding the minimum number of boxes among all the possible tiling configurations. Therefore, we adopt a slightly improved algorithm and detailed steps is shown in Algorithm. 1.\n\n<img src=\"stable/5.png\" style=\"zoom:100%;\" />\n\n## Analysis of Degree Distribution\n\n### Degree Distribution\n\nThe spatial traffic correlation model is built in terms of the traffic loads and contributes to understanding the underlying relationship of BSs, which can not be directly observed from brief information such as locations (e.g., longitude and latitude) or BS types. We provide the fitting results of the degree distributions of City A and City B. In general, the spatial traffic correlation model points to the property of scale-free and help us to know which BSs have higher degree values. The scale-free property from the traffic load correlation model clearly demonstrates that the minority of BSs with larger degree are highly correlated with plenty of other BSs, while the other remaining BSs are only correlated with a few number of BSs.\n\n<img src=\"stable/6.png\" style=\"zoom:100%;\" />\n\n### Identifying Influential Base Stations\n\nCellular networks have already employed macrocell BS as the signaling node, so the macrocell BSs are more suitable to be influential nodes due to their greater coverage capability and being more easily to predict the tendency of BS traffic loads. As a result, it is imperative to pick out the most important BSs so as to assign them more functions such as signaling control. Based on the theory of influence maximization in complex networks, we further employ the CI algorithm for localizing the most influential BSs.\n\n<img src=\"stable/11.png\" alt=\"11\" style=\"zoom:75%;\" />\n\nFig. 3. Performance of CI in correlation model compared with heuristic methods (HD, HDA).\n\nAfterwards, according to the optimal set of nodes found by the CI algorithm, we display the locations of the most influential 500 base stations of City A in the map and color codes each BS's degree in Fig. 4 and Fig. 5. From the two figures, we observe that among the most influential base stations extracted by the CI algorithm, a large number of low-degree BSs even exhibit a greater influence than some high-degree BSs. That is to say, we should pay more attention to those influential BSs even with low-degree, comparing with the high-degree BSs with less influence.\n\n<img src=\"stable/61.png\" style=\"zoom:100%;\" />\n\n<img src=\"stable/7.png\" alt=\"27\" style=\"zoom:100%;\" />\n\n## Structural Properties of the Traffic Load Correlation Model\n\n### Fractal Patterns\n\nOne important property that exists in many complex and real-world networks is fractality. In fractal geometry, box-covering is widely used to approximately evaluate the fractal dimension of a fractal object.\n\n<img src=\"stable/13.png\" alt=\"11\" style=\"zoom:100%;\" />\n\nFig. 6. Fractal patterns of City A and City B with the same threshold K 0.54.\n\n### Skeleton Features\n\nBasically, skeleton is thought to be a maximum spanning tree. Thus, the skeleton of our correlated BSs network is a spanning tree connected by the most close links, whose topology can be regarded as the core of the correlated BSs network.\n\nAfter tiling the skeletons with the box-covering algorithm, the number of boxes needed to cover the networks is almost identical with the original networks. The box-covering analysis results of the original network, the skeleton and the random spanning tree are provided in Fig. 7. According to the curves, the relevant results express that although the random spanning tree possesses a different statistics, the fractal dimensions of the random spanning tree and the original network are just the same. Meanwhile, the fractality of the skeleton matches the fractality of the original correlation model very well. Hence, understanding the properties of the skeleton is of great importance for analyzing the original model.\n\n<img src=\"stable/23.png\" alt=\"2\" style=\"zoom:100%;\" />\n\n### Further Exploration On Small-World\n\nThe small-world property usually coexists with scale-free networks. Specically, small-world property refers to the average distance d scales logarithmically with the network size N . Another indispensable characteristic of small-world networks is their high clustering coeffcient.\n\n<img src=\"stable/32.png\" alt=\"3\" style=\"zoom:100%;\" />\n\nWe have demonstrated that the spatial traffic correlation model of BSs expresses scale-free, fractal and small-world properties simultaneously, which will further facilitate the performance analysis of complex cellular networks as well as the design of efficient networking protocols. Moreover, for a topological structure with fractality, we can find some regularities from its special topology and irregularity, which contributes to more effective resource assignment based on dynamic BSs management. Finally, the discovery of small-world property means that, despite the large-scale feature of the traffic load correlation model, the traffic association on base stations is very compact.\n\n* * *\n\n**Related references:**\n\n* Chao Yuan, Zhifeng Zhao, Rongpeng Li, M. Li, and Honggang Zhang, “**The Emergence of Scaling Law, Fractal Patterns and Small-World in Wireless Networks**,” IEEE Access, March 2017. \n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, “**The Stochastic Geometry Analyses of Cellular Networks with α-Stable Self-Similarity**,\" IEEE Trans. on Communications, March 2019.\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**Study on Base Station Topology in National Cellular Networks: Take Advantage of Alpha Shapes, Betti Numbers, and Euler Characteristics**,\" IEEE Systems Journal, Q3/Q4 2019.\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology**,\" IEEE Wireless Communications Letters, April 2019.\n\n* Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, \"**The Stochastic Geometry Analyses of Cellular Networks with alpha-Stable Self-Similarity**,\" arxiv.org/abs/1709.05733v1, September 2017.\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**On the Capacity of Wireless Networks With Fractal and Hierarchical Social Communications**,” arxiv.org/abs/1708.04585, August 2017.\n\n* Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “**On the Capacity of Fractal Wireless Networks With Direct Social Interactions**,” arXiv:1705.09751, May 27, 2017.\n\n* Rongpeng Li, Zhifeng Zhao, Jianchao Zheng, Chengli Mei, Yueming Cai, and Honggang Zhang, “**The Learning and Prediction of Application-level Traffic Data in Cellular Networks**,” IEEE Trans. Wireless Communications, March 2017. \n\n* Zhifeng Zhao, Meng Li, Rongpeng Li, and Yifan Zhou, “**Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,”** IET Communications, August 2017.\n\n* Chen Qi, Zhifeng Zhao, Rongpeng Li, and Honggang Zhang, “**Characterizing and Modeling Social Mobile Data Traffic in Cellular Networks,”** 2016 IEEE 83rd Vehicular Technology Conference (VTC-Spring 2016), Nanjing, May 2016. ","tags":["highlights"],"categories":["research"]},{"title":"He visited Supelec (Rennes, France) as a doctoral visiting student.","url":"/2013/12/19/visitsupelec/","content":"\n<img src=\"visitsupelec/20110311101912813901.jpg\" style=\"zoom:50%;\" />\n\nFrom September to December 2013, Mr. Li visited Supélec (Rennes, France) as a doctoral visiting student. During the visit, he continued the study over the green cellular networks and exchanged thoroughly with the researchers there.\n\nInformation on Supélec (Excerpt from the Official Site of Supélec)\n\n<img src=\"visitsupelec/2011031110191281390.jpg\" style=\"zoom:15%;\" />\n\nSupélec has a very special position among the leading engineering institutes. It is the reference in its field - electric energy and information sciences. Internationally, with classes of 440 engineers graduating each year, Supelec is on a par with the best departments of electrical and computer engineering of the top American or European universities. _More information on Supelec could be found in [http://www.supelec.fr/388\\_p\\_12054/brief-introduction.html](http://www.supelec.fr/388_p_12054/brief-introduction.html) ._","tags":["highlights"],"categories":["news"]},{"title":"世界，你好！","url":"/2013/07/18/hello-world/","content":"\n11年的时候，心血来潮在Godaddy上注册了rongpeng.info的域名，然后时不时做着被哪家叫rongpeng的公司收购，赚得人生第一桶金，结局是意料之中的，两年多过去了，域名还在我手里。发财的美梦终究破灭了，但域名总要利用起来，在orgfree上面申请了免费的空间，然后慢慢的自己搭建好了[rongpeng.info/](http://rongpeng.info/) 的子站点，把一些学术信息放在了上面，虽然访问的人数一直寥寥无几，但程序员嘛，有时候得瑟的就是自己的内心。\n\n搭建这个博客的初衷是因为有时候写文章的时候，会上网查一些技巧，杂七杂八的。零零碎碎的东西，时间长了，久不整理，也就忘记了；再加上本来就有点达则兼济天下的幻想，索性把这个域名更充分地利用起来，也没什么不好。\n\n总之吧，这里就是一个大杂烩，什么都有，祈祷他山之石可以攻玉吧。","categories":["blog"]}]