Evaluation and Extension of Mathematical Models of P2P Systems

Inhaltsverzeichnis (Table of Contents)

• 1 Introduction and Motivation for the Thesis
• 1.1 Field of Research
• 1.2 Contribution and Outline of this Thesis
• 1.3 Model Definition and Classification
• 2 Related Work for Existing Mathematical P2P Models
• 3 The New Mathematical Model of P2P Systems
• 3.1 Overlay Parameters
• 3.1.1 The Basic Notations
• 3.1.2 Overlay Functionality
• 3.1.3 Routing in P2P Overlays
• 3.1.4 The Random Walk Search Algorithm
• 3.1.5 The Service Capacity
• 3.1.6 The Identifier Space
• 3.1.7 The Super Peer Network Design
• 3.2 The Characteristics of Participating Peers
• 3.2.1 The Basic Notations
• 3.2.2 The Delay Experienced by Peers
• 3.2.3 The Request Processing
• 3.2.4 The Peers' Heterogeneity
• 3.3 The Resource and Service Characteristics
• 4 Extending the Mathematical Model to the Application Layer
• 5 P2P System Layers
• 5.1 Introduction
• 5.2 P2P Reference Architectures
• 5.3 User Level
• 5.4 Application Layer
• 5.5 P2P Service Layer
• 5.6 Key-Based Routing
• 5.7 Overlay Network
• 5.8 Network Layer
• 6 Case Study: Modeling the GLOBASE.KOM Overlay
• 6.1 Introduction
• 6.2 Basic Notations
• 6.3 The Overlay Tree Structure
• 6.4 Interconnections and Their Effect on Overlay's Performance
• 6.5 GLOBASE.KOM Operations
• 7 Conclusion
• 7.1 Summary and Results of This Thesis
• 7.2 Future Work
• 7.3 Contribution in the Related Research Area
• A GLOBASE.KOM Implementation

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This master's thesis aims to evaluate and extend existing mathematical models of peer-to-peer (P2P) systems. The work focuses on developing a new mathematical model and applying it to real-world P2P applications.

• Mathematical Modeling of P2P Systems
• Analysis of Existing P2P Models
• Development of a New P2P Model
• Application of the Model to Real-World Systems (Skype, Joost, KaZaA)
• Case Study: GLOBASE.KOM Overlay

Zusammenfassung der Kapitel (Chapter Summaries)

1 Introduction and Motivation for the Thesis: This chapter introduces the field of research, focusing on mathematical modeling of P2P systems. It outlines the thesis's contributions and provides a classification of existing models. The chapter sets the stage for the subsequent chapters by defining the scope and objectives of the research, highlighting the importance of accurate P2P system modeling for understanding their behavior and performance.

2 Related Work for Existing Mathematical P2P Models: This chapter reviews existing mathematical models of P2P systems, exploring various approaches like those related to query popularity and file replication in Gnutella, random walk search algorithms, stochastic fluid theory for streaming, and service capacity analysis. The chapter critically assesses the strengths and weaknesses of these models, laying the groundwork for the development of a novel model proposed in the next chapter. The discussion covers different aspects of P2P network behavior, like search efficiency and resource allocation, highlighting existing limitations and potential areas for improvement.

3 The New Mathematical Model of P2P Systems: This chapter presents a new mathematical model for P2P systems, detailing its parameters, including notations, functionality, routing algorithms (like random walk), service capacity, identifier space, and super peer network design. The model considers the characteristics of participating peers, such as delay experienced, request processing, and heterogeneity. This chapter forms the core of the thesis, introducing a novel framework for modeling the intricacies of P2P networks.

4 Extending the Mathematical Model to the Application Layer: This chapter extends the mathematical model to the application layer by applying it to several real-world P2P applications: Skype, Joost, and KaZaA. It analyzes user behavior, network operators, and participating peers within each application, demonstrating the model's versatility and applicability to different P2P architectures. The chapter showcases the practical relevance of the developed model by showing how it can be used to analyze various types of P2P applications.

5 P2P System Layers: This chapter provides an overview of the layered architecture of P2P systems, discussing reference architectures such as JXTA and presenting a structured model that considers user, application, service, and network layers. The chapter establishes a foundational understanding of the different components and functionalities within a P2P system, providing context for the model's application and analysis in subsequent chapters.

6 Case Study: Modeling the GLOBASE.KOM Overlay: This chapter presents a case study focusing on the GLOBASE.KOM overlay network. It describes the overlay's tree structure, explores the impact of interconnections on its performance, and analyzes the results of simulations and analytical modeling. This detailed analysis of a specific P2P network demonstrates the practical application and validation of the mathematical model developed earlier in the thesis.

Schlüsselwörter (Keywords)

Peer-to-Peer (P2P) systems, mathematical modeling, overlay networks, random walk algorithms, service capacity, network performance, GLOBASE.KOM, Skype, Joost, KaZaA, P2P applications, super peers, resource allocation.

Frequently Asked Questions: A Comprehensive Language Preview of a Master's Thesis on Mathematical Modeling of P2P Systems

What is the main topic of this Master's thesis?

This master's thesis focuses on the mathematical modeling of peer-to-peer (P2P) systems. It aims to evaluate existing models, develop a new, more comprehensive model, and apply this model to real-world P2P applications.

What are the key objectives of the thesis?

The key objectives include analyzing existing mathematical P2P models, developing a novel mathematical model incorporating various parameters (overlay parameters, peer characteristics, resource characteristics), extending this model to the application layer by applying it to real-world P2P applications (Skype, Joost, KaZaA), and conducting a case study on the GLOBASE.KOM overlay network.

What aspects of P2P systems are covered in the model?

The model covers various aspects of P2P systems, including overlay parameters (notations, functionality, routing algorithms like random walks, service capacity, identifier space, super peer network design), characteristics of participating peers (delay, request processing, heterogeneity), and resource and service characteristics. The model is further extended to encompass the application layer, considering user behavior and network operators.

Which real-world P2P applications are analyzed?

The thesis applies the developed mathematical model to three real-world P2P applications: Skype, Joost, and KaZaA. This analysis demonstrates the model's applicability and versatility across different P2P architectures.

What is the role of the GLOBASE.KOM case study?

The GLOBASE.KOM case study serves as a practical application and validation of the developed mathematical model. It involves analyzing the overlay's tree structure, the impact of interconnections on performance, and the results of simulations and analytical modeling for this specific P2P network.

What are the key components of the thesis structure?

The thesis is structured into several chapters: an introduction setting the context and objectives; a literature review of existing models; the presentation of the new model; its extension to the application layer; an overview of P2P system layers; the GLOBASE.KOM case study; and finally, a conclusion summarizing the findings and outlining future work.

What are the key keywords associated with this thesis?

Key terms include: Peer-to-Peer (P2P) systems, mathematical modeling, overlay networks, random walk algorithms, service capacity, network performance, GLOBASE.KOM, Skype, Joost, KaZaA, P2P applications, super peers, and resource allocation.

What are the contributions of this thesis to the field of research?

The thesis contributes a novel mathematical model for P2P systems, its application to real-world scenarios, and a detailed case study on GLOBASE.KOM. It also provides a comprehensive analysis of existing P2P models and identifies areas for future research.

Where can I find more information about the GLOBASE.KOM implementation?

The thesis includes an appendix (Appendix A) detailing the GLOBASE.KOM implementation.

What are the limitations of the thesis?

While not explicitly stated, inherent limitations might include the scope of real-world applications analyzed, the assumptions made in the mathematical model, and the specific characteristics of the GLOBASE.KOM network used in the case study. Further research could address these limitations.