Nash equilibria in bandwidth allocation for non-cooperative peer-to-peer networks

Abstract

In peer-to-peer networks, peers act as clients and servers, i.e., they can download files from others and allow others to download from them, at the same time. Since the bandwidth of a peer acting as server is shared among all its clients, the download rate experienced by a peer depends on the server choices of the other peers.

We focus our investigation on the bandwidth allocation among the peers and model this system with non-cooperative game theory. We assume that peers are rational players that maximize their utility, corresponding to minimize their download time. We study the existence of Nash equilibrium points under a very simple server selection policy and show that it is efficiency from the point of view of the bandwidth utilization.

Introduction

In the last years, peer-to-peer (P2P) applications have obtained an unexpected success in the Internet users’ community. The novelty of P2P paradigm relies on the two main concepts: cooperation among users and sharing of network resources. Users of the same P2P community provide services to the other users, while obtaining services from the community; in other words, each user (called peer) acts at the same time as client and server. This paradigm has been shown to provide many beneficial effects on the global system performances as: higher service capacity, reliability and flexibility [1].

Performance of P2P systems are influenced by many aspects. If we focus on the point of view of a user, two aspects are important: availability of the searched contents and the latency experienced before the content is available locally at the user. The availability of some particular content depends not only on its popularity and diffusion among the other peers, but also on the level of contribution of each peer with that content available. Because of the voluntary (and often free) joining to a P2P network, many users tend just to exploit the shared resources without any contribution: this behavior is called “free-riding” and is prevalent in many P2P communities, as pointed out in [2]. Given that the wanted content is available uncorrupted at some peers, the user experiences the latency between the time he starts to search a content and the time the content is available locally. This latency depends mainly on (i) the time required to find the peer who owns the content (search phase), (ii) the time to download the content (download phase), (iii) the dynamical behavior of the peers who can disconnect from the community at any time and abort all the services provided to the network.

Among all these aspects, we focus our investigation only on the download time, because of its time scale is much larger than the search time and at the same time, it is not related to the user behavior (which is difficult to model). The download time depends on the bandwidth available from the source to the peer; the bandwidth depends mainly on the packet network topology, the network congestion and on the transport protocol considered: in our case, TCP/IP. We essentially model the dynamics driven by the user selfishness who wants to minimize the download latency by choosing (and also changing in real-time) the source with the highest rate available. In this content, we are interested in understanding whether the overall system converges to some equilibrium and how efficient this equilibrium is.

In our investigation we neglect the search phase, which depends on the particular implementation of the P2P network and its effects on the performance are independent from the download phase. Hence, we initially assume that any content searched by a peer is available in any other peer, even if we will relax this assumption later on. In our model we neglect also the dynamical behavior of the peers, independent from the bandwidth allocation under study. We also assume that all the peers are cooperating and always provide the content requested, thanks to some cooperation mechanism present in the network.