Algorithms for Constructing Overlay Networks For Live Streaming

We present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. We construct networks consisting of three stages of nodes. The nodes in the first stage are the entry points that act as sources for the live streams. Each source forwards each of its streams to one or more nodes in the second stage that are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage that act as sinks and are located in edge networks near end-users. As the packets in a stream travel from one stage to the next, some of them may be lost. A sink combines the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. Our primary contribution is an algorithm that constructs an overlay network that provably satisfies capacity and reliability constraints to within a constant factor of optimal, and minimizes cost to within a logarithmic factor of optimal. Further in the common case where only the transmission costs are minimized, we show that our algorithm produces a solution that has cost within a factor of 2 of optimal. We also implement our algorithm and evaluate it on realistic traces derived from Akamai's live streaming network. Our empirical results show that our algorithm can be used to efficiently construct large-scale overlay networks in practice with near-optimal cost

Exact two-terminal reliability of some directed networks

The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even when nodes do not fail and all edges have the same reliability p. We consider here a directed, generic graph of arbitrary size mimicking real-life long-haul communication networks, and give the exact, analytical solution for the two-terminal reliability. This solution involves a product of transfer matrices, in which individual reliabilities of edges and nodes are taken into account. The special case of identical edge and node reliabilities (p and rho, respectively) is addressed. We consider a case study based on a commonly-used configuration, and assess the influence of the edges being directed (or not) on various measures of network performance. While the two-terminal reliability, the failure frequency and the failure rate of the connection are quite similar, the locations of complex zeros of the two-terminal reliability polynomials exhibit strong differences, and various structure transitions at specific values of rho. The present work could be extended to provide a catalog of exactly solvable networks in terms of reliability, which could be useful as building blocks for new and improved bounds, as well as benchmarks, in the general case

Implementing an approximation scheme for all terminal network reliability

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaf 50).by Ray P. Tai.M.Eng