Double-loop Networks Research Articles

Reliabilities of Double-Loop Networks

A double-loop network G(h1, h2) has n nodes represented by the n residues modulo n and 2n links given by i ↦i + h1, i ↦ i + h2, i = 0,1,…,n – 1.We consider the reliability model where each link fails independently with probability p, the nodes always work, and the network fails if it is not strongly connected. There exists no known polynomial time algorithm to compute the reliabilities of general double-loop networks. When p is small, the reliability is dominated by the link connectivity. As all strongly connected double.loop networks have link connectivity exactly 2, a finer measure of reliability is needed. In this paper we give such a measure and show how to use it to obtain the most reliable double-loop networks.

Tolerance of double-loop computer networks to multinode failures

The reliability of double-loop networks is examined along with their fault tolerance in cases when more than two nodes break down. It is demonstrated that double-loop structured networks are very desirable with respect to the measure of fault tolerance introduced.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Diameters of weighted double loop networks

Let n, h 1 and h 2 be positive integers such that h 1, h 2 < n and w 1, w 2 be positive real numbers. We define the weighted double loop network G( n, h 1, h 2; w 1, w 2), as the directed graph with vertex set Z/ nZ = {0,1,…, n − 1 and weighted edges i → w 1 i + h 1 ( mod n), i → w 2 i + h 2 ( mod n) for i ϵ Z nZ .Suppose that n, h 1 and h 2 are relatively prime. The weight of a directed path is the sum of weights on the edges. The distance d( x, y) between two vertices x and y is defined as the minimum weight of directed paths from x to y. The weighted diameter of this network, is defined as the maximum d( x, y) among all x and y. In this paper, we obtain an O(log n) algorithm for computing the diameter.

Double loop networks with minimum delay

Double loop networks have been widely studied as practical and reliable computer networks. Let N denote the number of stations in a double loop network. The literature has proposed a topology which yields the diameter 2√ N. In this paper we give a heuristic method which finds a topology with diameter roughly √3 N for large N. We also give several infinite classes of values of N for which topologies are found that achieve the lower bound ⌈√3 N⌉ − 2 for the diameter.

A survey of multi-connected loop topologies for local computer networks

Abstract Loop network architectures are an attractive topology for local computer networks because they require simple interfaces and control. Single loop networks tend to become unreliable when the number of nodes in the network becomes large. Multiconnected loop topologies have been proposed for improved reliability and performance. There are several double loop networks based on forward loop backward hop topology, with a loop in the forward direction connecting all the neighboring nodes, and a backward loop connecting nodes that are separated by a distance h. This paper presents a systematic study of single and double loop networks and also discusses various other loop networks with higher connectivities.

Performance evaluation of a simulated data-flow computer with low-resolution actors

In the ambition to go beyond a single-processor architecture, to enhance programmability, and to take advantage of the power brought by VLSI devices, data-flow systems and languages were devised. Indeed, due to their functional semantics, these languages offer promise in the area of multiprocessor systems design and will possibly enable the development of computers comprising large numbers of processors with a corresponding increase in performance. Several important design problems have to be surmounted and are described here. We thus present a “variable-resolution” scheme, where the level of primitives can be selected so that the overhead due to the data-flow mode of operation is reduced. A deterministic simulation of a data-flow machine with a variable number of processing elements was undertaken and is described here. The tests were performed using various program structures such as directed acyclic graphs, vector operations, and array handling. The performance results observed confirm the advantage of actors with variable size and indicate the presence of a trade-off between overhead control and the need to control parallelism in the program. We also look at some of the communication issues and examine the effect of several interconnection networks (dual counter-rotating rings, daisy chain, and optimal double loop network) on the performance. It is shown how increasing communication costs induce a performance degradation that can be masked when the size of the basic data-flow actor is increased. The asociative memory cycle time is also changed with similar conclusions. Finally, the lower-resolution scheme is applied to the array handling case; the observations confirm the advantage of a more complex actor at the array level.

Double Loop Network Architectures--A Performance Study

Single loop networks tend to become unreliable and suffer from poor performance when the number of nodes in the network becomes large. One approach to increasing reliability and improving performance is to use a double loop. In this paper, the performance (using analytical and simulation models) of a class of highly reliable double loop network architectures is presented. The richer topology of double loop networks allows more sophisticated routing algorithms to be used. Several routing algorithms are studied, including: fixed, adaptive to failure, and fully adaptive to failure and traffic load conditions.

Reliable Loop Topologies for Large Local Computer Networks

Single-loop networks tend to become unreliable when the number of nodes in the network becomes large. Reliability can be improved using double loops. In this paper a highly reliable and efficient double-loop network architecture is proposed and analyzed. This network is based on forward loop backward hop topology, with a loop in the forward direction connecting all the neighboring nodes, and a backward loop connecting nodes that are separated by a distance ⌊√N⌋where N is the number of nodes in the network. It is shown that this topology is optimal, among this class of double-loop networks, in terms of diameter, average hop distance, processing overhead, delay, throughput, and reliability. The paper includes derivation of closed form expressions for diameter and average hop distance, throughput, and number of distinct routes between two farthest nodes. For fault-tolerance study, the effect of node and link failures on the performance of the network is analyzed. A simple distributed routing algorithm for reliable loop network operation is also presented.

MIKE: A Network Operating System for the Distributed Double-Loop Computer Network

This paper presents the framework and model of a network operating system (NOS) called MIKE for use in distributed systems in general and for use in the Distributed Double-Loop Computer Network (DDLCN) in particular. MIKE, which stands for Multicomputer Integrator KErnel, provides system-transparent operation for users and maintains cooperative autonomy among local hosts.

Optimal loop topologies for distributed systems

Double loop network architectures offer higher performance and reliability than single loop networks. In this paper, a double loop network which is optimal among all double loops is described. This network topology consists of a loop in the forward direction connecting all the neighboring nodes, and a backward loop connecting nodes that are separated by a distance @@@@@@@@ N @@@@, where N is the number of nodes in the network. We show that this network is optimal in terms of hop distance between nodes, delay, throughput, and terminal reliability. The paper includes derivation of closed form expressions for the maximum and average hop distance between nodes, number of distinct routes between two farthest nodes, and throughput. The effect of node and link failures on network performance is also considered.