Markov-based Models For P2P Systems

With the development of network and information technology, there are more and more various applications and innovations based on computer networks. Recently, P2P (Peer-to-Peer) and IPTV (Internet Protocol Television) are those famous research and application fields of the current network technology. They are both stochastic systems due to the frequent accesses of their nodes or users. And they are generally integrated with many other services and cover a large range of Internet. Therefore, each of them may have a distributed and hierarchical structure and there exist many complicated factors constraining each other in system performances. The performance bottlenecks and optimizations have been become the key problems currently on research, design and implementation of these application systems. Some of them can be solved by direct technical reconstruction or update, which is generally not low-cost. From the view of system theory, some of them can also be solved by using modern optimization and control theories and methods. Especially, the models based on Markov processes can also be applied in order to avoid constructing and identifying the accuracy mathematical descriptions with complicated physical backgrounds.Considering the hierarchical structure and switching problem for a class of hierarchical unstructured P2P systems. According to some given principle, these systems are divided to many groups with lots of nodes and elect a supper node for one group. Each supper node indexes the nodes and resources in its own group. A normal node has to search resources via the super node's location service, which consists of the internal search engine in group and the one between groups. These systems actual have a two-layered structure: one is the single group around its supper node, the other is the subsystem between groups, which is a pure P2P and uses flooding-like search. Since the system scale and distribution of nodes varies dynamically, the partitioning has to be adaptive to maintain the system's overall performance. In this paper, a Markov switching-space model is introduced to describe their behavior of dynamic grouping. The state process under each partitioning is characterized as a Markov process with a special state space. The controls of grouping behavior correspond to the actions of Markov switching-space model, which are selected according to some given policy. It can be proved that the Markov switching-space model is equivalent to a Markov decision process or a parameterized Markov reward process. Therefore, the optimal policies for dynamic grouping can be given by applying policy iterations and gradient methods, which are verified by some simulations in this paper.A kind of P2P-enhanced distributed VoD (Video on Demand) system in a practical project has a global centralized directory server to index all the data of segment caches on edge service nodes and to provide location service for them. This solution has poor scalability and suffers from single point of failure problem. Therefore, a hybrid search which combines random walk and the existent global service is proposed. And models based on Markov processes are introduced to characterize and discuss this hybrid location service. In order not to extend the large state space, event is used in models. And also state clustering is applied to reduce computational complexity. Then, a simplified single location model is placed to discuss its effect, search efficiency and control problem of search costs. Considering the close relation between admission control and location service, a more complicated model combined with admission control is also discussed.