Decentralized Adaptive Helper Selection in Multi-channel P2P Streaming Systems

In Peer-to-Peer (P2P) multichannel live streaming, helper peers with surplus bandwidth resources act as micro-servers to compensate the server deficiencies in balancing the resources between different channel overlays. With deployment of helper level between server and peers, optimizing the user/helper topology becomes a challenging task since applying well-known reciprocity-based choking algorithms is impossible due to the one-directional nature of video streaming from helpers to users. Because of selfish behavior of peers and lack of central authority among them, selection of helpers requires coordination. In this paper, we design a distributed online helper selection mechanism which is adaptable to supply and demand pattern of various video channels. Our solution for strategic peers' exploitation from the shared resources of helpers is to guarantee the convergence to correlated equilibria (CE) among the helper selection strategies. Online convergence to the set of CE is achieved through the regret-tracking algorithm which tracks the equilibrium in the presence of stochastic dynamics of helpers' bandwidth. The resulting CE can help us select proper cooperation policies. Simulation results demonstrate that our algorithm achieves good convergence, load distribution on helpers and sustainable streaming rates for peers

Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition

AbstractThree new fully implicit methods which are based on the (5,5) Crank-Nicolson method, the (5,5) N-H (Noye-Hayman) implicit method and the (9,9) N-H implicit method are developed for solving the heat equation in two dimensional space with non-local boundary conditions. The latter is fourth-order while the others are second-order. While the implicit methods developed here, like the scheme based on the standard implicit backward time centered space (BTCS) method, use a large amount of central processor (CPU) time, the high accuracy of the new fourth-order fully implicit scheme is significant. Like the BTCS method, the new methods are also unconditionally stable

Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

AbstractThe main aim of this paper is to apply the Legendre polynomials for the solution of the linear Fredholm integro-differential-difference equation of high order. This equation is usually difficult to solve analytically. Our approach consists of reducing the problem to a set of linear equations by expanding the approximate solution in terms of shifted Legendre polynomials with unknown coefficients. The operational matrices of delay and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative examples are included to demonstrate the validity and applicability of the presented technique and a comparison is made with existing results