Peer-to-Peer (P2P) file distribution systems can efficiently disseminate massive contents, such as disk images of operating systems, from a server to many users in a piece-by-piece manner. In particular, the BitTorrent protocol optimizes each peer's download speed by applying the tit-for-tat (TFT) strategy, where each peer preferentially uploads piece(s) to peer(s) from which it can download missing pieces faster. To the best of our knowledge, however, the optimality of TFT-based P2P file distribution has not been studied sufficiently. In this paper, we aim to understand the optimal scheduling in TFT-based P2P file distribution. First, we develop a discrete-time model of TFT-based P2P file distribution and formulate its optimal scheduling as a two-step integer linear programming problem. The first step is to minimize the average file retrieval time among peers, and the second step is to improve fairness among peers. We analyze the optimal solution obtained by the existing solver and reveal the characteristics of the optimal scheduling. Specifically, we show that it is crucial to distribute pieces from the server indirectly to peers with large upload capacity via those with small upload capacity.

Light trail architecture is attracting attention as a new optical wavelength-division multiplexing network architecture that can be built with currently available devices and can achieve bandwidth allocation with granularity finer than a wavelength. Because a light trail is a shared medium, we need a medium access control (MAC) protocol to prevent collisions. Although MAC protocols using token passing can prevent collisions, the bandwidths of links that are located upstream of the token holding node are kept idle. We first propose a dynamic light trail splitting method for increasing throughput of a light trail by using such idle bandwidths. Our method splits a trail into upstream and downstream trails at the token holding node, and independent data transmission on the two trails are permitted. As a result, we expect that the split trail architecture will achieve higher throughput than the original non-split trail architecture. The degree of performance improvement with the split trail architecture depends on how appropriately we determine the upstream and downstream token holding times of every transmission node. Thus, we formulate a problem in which we optimize the token holding times to accommodate requested traffic volume as a linear programming problem. We then derive the throughput of the split trail architecture by solving the problem using the NUOPT solver and investigate the degree of improvement over the original architecture. In addition, we evaluate the end-to-end delay of the split trail architecture by simulation. According to numerical examples, the split trail architecture achieves 1) almost the same throughput as the original one for the worst-case traffic pattern where every transmission node sends data to the terminating node of the trail only, 2) about 1.6 times higher throughput for a uniform traffic pattern where every node pair requests the same traffic volume and an extremely unbalanced traffic pattern where only a few node pairs request huge traffic volume, 3) about 1.9 time higher throughput for the split trail architecture's good-case traffic pattern where every transmission node sends data to its adjacent downstream node only, and 4) the end-to-end delay enough to satisfy any application's QoS requirement according to ITU-T Recommendation Y.1541.

In this letter we present an electronic circuit based on a neural net to compute the discrete Walsh transform. We show both analytically and by simulation that the circuit is guaranteed to settle into the correct values.