Models For Interconnection Networks Research Articles

Partial line directed hypergraphs

AbstractThe partial line digraph technique was introduced in [7] in order to construct digraphs with a minimum diameter, maximum connectivity, and good expandability. To find a new method to construct directed hypergraphs with a minimum diameter, we present in this paper an adaptation of that technique to directed hypergraphs. Directed hypergraphs are used as models for interconnection networks whose vertices are linked by directed buses. The connectivity and expandability of partial line directed hypergraphs are studied. Besides, we prove a conjecture by J‐C. Bermond and F. Ergincan about the characterization of line directed hypergraphs. © 2002 Wiley Periodicals, Inc.

Rules for robust generation of accurate reduced-order models for high-speed coupled interconnections

Recently, robust algorithms have been established for passive order reduction of electrical models of complex interconnection networks. However, very little is known about the way the order of the reduced model should be chosen to ensure accuracy in subsequent transient simulation studies. In this paper, a rule is derived for the selection of the order of the reduced model for interconnections modeled as transmission lines. It is shown that pulse rise time, interconnection length, and physical properties impact the order of the reduced model. The proposed rule is validated through numerical studies involving both analytic and numerical results from the frequency- and time-domain response of multiconductor transmission line circuits.

Complete Rotations in Cayley Graphs

As it is introduced by Bermond, Pérennes, and Kodate and by Fragopoulou and Akl, some Cayley graphs, including most popular models for interconnection networks, admit a special automorphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, some optimal gossiping algorithms can be easily designed by using a complete rotation, and the constructions of the best known edge disjoint spanning trees in the toroidal meshes and the hypercubes are based on such an automorphism. Our purpose is to investigate such Cayley graphs. We relate some symmetries of a graph with potential algebraic symmetries appearing in its definition as a Cayley graph on a group.

Avaliacao de desempenho da arquitetura Wolf

Performance analysis of interconnection networks for Wolf architecture is provided. Based on communication requirements, an optical interconnection network model for the architecture, an architectural modification, a new model for the Wolf architecture were suggested to investigate the possibilities for performance gain. Both architecture models were simulated with SAW simulator. SAW is a time-driven simulator that implements the Wolf characteristics. Parameters such as load distribution and execution time were dealt with so that performance of the architecture might be investigated. Results by simulations showed that the new model of Wolf architecture gives better results for the parameters investigated

Rotational Cayley Graphs on Transposition Generated Groups

Abstract As it is introduced by Bermond, Kodate, and Prennes, some Cayley graphs, in cluding most popular models for interconnection networks admit a special automorphism, called complete rotation. Such anautomorphism is often used to derive algorithms or properties of the underlying graph For example, optimal gossiping algorithms can be easily designed, and the constructions of the best known edge disjoint spanning trees in the toroidal meshes and the hypercubes are based on such an automorphism. Our purpose is to characterize among Cayley graphs defined a group generated by transpositions, which admit a complete rotation.

A finite automata approach to modeling the cross product of interconnection networks

This paper describes a modeling technique, finite state automata (FA) model, for the cross product of interconnection networks. The primary purpose of the proposed modeling technique is to provide a mechanism for developing efficient routing and novel embedding algorithms, which we refer to as node-independent algorithms, for product networks. In contrast to the current embedding algorithms which are node dependent (their output is a set of adjacent node labels which forms the desired topology), the embedding algorithms developed in this paper are rule-based. That is, they generate a set of rules (input sequences to the FA model of the network) which can be used by any node for mapping a desired topology into the network. Furthermore, a new interconnection topology, called Ring Connected Cycles (RCC), is introduced. The main objective of introducing RCC networks is to illustrate the use of the FA model to develop node-independent embedding as well as routing algorithms. In addition, to demonstrate the generality of the proposed technique, FA models of several popular interconnection networks (such as n-cubes and n-star graphs) are presented. The RCC networks are proposed in this paper as a possible communication network for parallel multicomputers or as an alternative to the ring topology for local area networks. An RCC network can execute grid, mesh and ring algorithms as efficiently as the grid, mesh, and ring networks. It is shown in Section 6 that this significant amount of computational versatility offered by RCC networks comes at no additional VLSI area cost over the same size ring, grid, or mesh networks.

A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections

A new, computationally efficient, discrete model is presented for passive model order reduction of high-speed interconnections. The proposed discrete model is based on the use of the theory of compact finite differences for the development of the discrete approximation to the transmission line equations that govern wave propagation on the interconnections. Thus result in a discrete model that utilizes only a few unknowns per wavelength and yet provides highly accurate waveform resolution. In addition to improved computational efficiency, the generated discrete model is passive, and compatible with the passive reduced-order interconnect modeling algorithm (PRIMA). Thus, it is suitable for the development of passive reduced-order models of interconnection networks of high complexity. Numerical experiments from the simulation and model order reduction of coupled interconnections are used to illustrate the validity and efficiency of the proposed model.

An analytical performance model for multistage interconnection networks with finite, infinite and zero length buffers

Multistage Interconnection Networks (MINs) with crossbar switches have been used to interconnect processors and memory modules in parallel multiprocessor systems. They also play an increasingly important role in the development of Asynchronous Transfer Mode (ATM) networks. In this paper we analyze the general case of MINs, made of k × k switches with finite, infinite or zero length buffers (unbuffered). The exact solution of the steady-state distribution of the first stage is derived for all cases. We use this to get an approximation for the steady-state distributions in the second stage and beyond. In the case of unbuffered switches we reach the known exact solution for all the stages of the MIN. Our results are validated by extensive simulations.

Performance analysis of buffering schemes in wormhole routers

Wormhole switched input-buffered and middle-buffered routers with virtual channels are analyzed in this paper. Middle buffering refers to the placement of virtual channels between the demultiplexers and multiplexers of a crossbar switch. An analytical model for multistage interconnection networks using middle-buffered switches is developed. In addition, extensive simulation is conducted to assess the performance of the two buffering techniques in different network topologies. The study demonstrates that middle buffering with virtual channels provides better performance than input buffering with virtual channels in multistage interconnection networks, two-dimensional meshes, and hypercubes.

Nearly optimal one-to-many parallel routing in star networks

Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and the running time of our algorithm is bounded by O(n/sup 2/). More specifically, given a node s and n-1 other nodes {t/sub 1/, t/sub 2/, ..., t/sub n-1/} in the n-star network, our algorithm constructs n-1 node-disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-1/, where P/sub i/ is a path from s to t/sub j/ of length at most dist(s, t/sub j/)+6 and dist(s, t/sub j/) is the distance, i.e., the length of a shortest path, from s to t/sub j/, for i=1, 2, ..., n-1.The best bound on the path length by previously known algorithms for the same problem is 5(n-2)/spl ap/10/spl Delta//sub n//3, where /spl Delta//sub n/=max{dist(s, t)} is the diameter of the n-star network.

Vertex-symmetric digraphs with small diameter

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric (△, D) digraphs, that is large digraphs with a given maximum out-degree △ and diameter at most D. The digraphs are derived from a certain family of digraphs on alphabets, proposed by Faber and moore (1988), with new construction techniques that generalize previous result from conway and Guy (1982). With these families we have made important updates in the table of largest known vertex-symmetric (△, D) digraphs.

ON LARGE VERTEX SYMMETRIC 2-REACHABLE DIGRAPHS

We are interested in the construction of the largest possible vertex symmetric digraphs with the property that between any two vertices there is a walk of length two (that is, they are 2-reachable). Other than a theoretical interest, these digraphs and their generalizations may be used as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. On the other hand, a message sent from any vertex reaches all vertices, including the sender, in exactly two steps. In this work we present families of vertex symmetric 2-reachable digraphs with order attaining the upper theoretical bound for any odd degree. Some constructions for even degree are also given.

Performance analysis of synchronous multibuffered packet-switching networks

In this paper, a general mathematical method for analysis of synchronous multibuffered packet-switching interconnection networks in multiprocessor systems is presented. The proposed mathematical method is general in that he analyzed synchronous interconnection networks under uniform and nonuniform traffic. The existing methods for analysis of buffered interconnection networks have assumed either single or infinite buffers at each output (or input) port of a switch, as well as uniform traffic pattern of the networks. Recently, H. Yoon et al. [1] have presented an analytical model of buffered delta networks, assuming finite buffers at each input port and uniform traffic. Firstly, in the paper, a general model of synchronous buffered switching element, using output buffering, under assumption of finite buffer size for a very general class of traffic, is presented. Traffic can be uniform or nonuniform. It is assumed that the subsequent stages of the network are nearly independent and a model is extended for entire network under this assumption. Analytical results obtained with proposed model are then compared with each other, and it is shown that the proposed mathematical method is more general then the known models of interconnection networks.

New methods for using Cayley graphs in interconnection networks

A number of researchers have proposed Cayley graphs and Schreier coset graphs as models for interconnection networks. New algorithms are presented for generating Cayley graphs in a more time-efficient manner than was previously possible. Alternatively, a second algorithm is provided for storing Cayley graphs in a space-efficient manner (log 2(3) bits per node), so that copies could be cheaply stored at each node of an interconnection network. The second algorithm is especially useful for providing a compact encoding of an optimal routing table (for example, a 13 kilobyte optimal table for 64,000 nodes). The algorithm relies on using a compact encoding of group elements known from computational group theory. Generalizations of all of the above are presented for Schreier coset graphs.

Graphs on alphabets as models for large interconnection networks

Graphs on alphabets are constructed by labelling the vertices with words on a given alphabet, and specifying a rule that relates pairs of different words to define the edges. They have proved to be quite suitable to model large interconnection networks since their structure usually provides efficient routing algorithms. The aim of this paper is to present several infinite families of such graphs with a large number of vertices for given values of their diameter and maximum degree.

Shrinking stability regions and voltage collapse in power systems

The dynamic process of voltage collapse is analyzed based on three mechanisms: on-load tap-changing, load dynamics, and generator excitation limiting. The interaction among these mechanisms and how the voltage collapse takes place are thoroughly investigated in a general interconnected network model under the assumption that system frequency remains unchanged. It is found that, so long as an equilibrium exists, there is a maximal equilibrium. It is also established that there is a region in the state space corresponding to a monotonic fall of system voltages. When the reactive capability of generator(s) is reached, this region expands, whereas the voltage stability region shrinks. The system trajectory may eventually exit the stability region, whereupon the voltage begins to drop monotonically. It is shown that locking the tap-changers at an appropriate time helps the system voltage to reach a steady state, and therefore avoid the collapse. Numerical examples for a realistic power system are given to illustrate the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modeling and performance analysis of file transfer in a satellite wide area network

The authors consider the network modeling and performance analysis of multimedia file transfer between workstations connected to remotely located local area networks (LANs). The LANs are linked by a satellite wide-area network (SWAN) with a high bandwidth and high path delay. Four areas are addressed: (1) development of a fairly accurate interconnection network model using measured delay values for different network elements; (2) derivation of tight upper and lower bounds for the network throughput for both error-free and error-prone channels using mean value analysis; (3) validation of the model using computer simulation; and (4) analysis of the SWAN performance using numerical results for a wide range of parameters (file sizes, window size, link speed, number of workstations, etc.) for the case of a multimedia SWAN. Based on the analyses, performance bottlenecks for different operating conditions that could be used to evolve design criteria for better overall system performance are identified.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analytic models for multistage interconnection networks

Central to all parallel architectures is a switching network which facilitates the communication between a machine's components necessary to support their cooperation. Multistage interconnection networks (MINs) are classified and analytic models are described for both packet-switched and circuit-switched MINs with asynchronous transmission mode. Under strong enough assumptions, packet switching can be modeled by standard queuing methods, hence providing a standard against which to assess approximate models. We describe one such approximate model with much weaker assumptions which is more widely applicable and can be implemented more efficiently. To model circuit switching requires a different approach because of the presence of passive resources, namely multiple links through the MIN which must be held before a message can be transmitted and throughout its transmission. An approximate analysis based upon the recursive structure of a particular MIN topology which yields accurate predictions when compared with simulation is described.

MVAMIN: Mean value analysis algorithms for multistage interconnection networks

A new approach to the modeling of multistage interconnection networks (MIN) based on queueing theory is presented in this paper. The network operates in an asynchronous, decentralized packet-switched mode and has buffers at each queueing center. The analytical approach involves basically three steps, namely, the building of a closed multiclass queueing model for the MIN system, the derivation of input parameters for the model, and finally solving the model using a heuristic mean value analysis algorithm. Networks operating in both tightly coupled and loosely coupled environments are analyzed. Separate networks are assumed for packets from processors to memories and from memories to processors in the case of a tightly coupled system. We derive a set of routing equations corresponding to the probabilities of memory requests through which systems with arbitrary memory reference patterns can be analyzed. Here, N is the number of processors or memories with n = log 2 N number of stages. An approximate technique of aggregation is also developed to significantly reduce the computational complexity of the above analysis while maintaining the accuracy of the model. The accuracy of our models has been verified by comparing the analytical results with those obtained from simulation. The simulations are based on 95% confidence level with a relative confidence interval width of 0.005.

A robust protocol for distributed query processing on a local area network

Fault tolerant distributed databases use replicated data (e.g. record or relation) to handle failures of one or more nodes in a computer network. In this paper, the binary hypercube, a popular model for fault tolerant interconnection networks, has been studied as a model for interconnection in a local area network. It has been shown that in a local area network with 2′ nodes, based on a binary hypercube, where every relation is replicated r times, in the absence of faults, any arbitrary sequence of database operations R 1 ⊙ R 2 ⊙ … ⊙ R n (where ⊙ is any binary database operation) may be performed by repeatedly executing r database operations in a distributed fashion using r edge disjoint paths from r selected sites of database operations to r arbitrary sites containing a target relation each. This protocol also solves the problem of materialisation of relations. In the presence of up to r-2 faults, the protocol still guarantees N edge disjoint paths to arbitrary sites. The value of N is determined by the number of faulty nodes. The protocol is also applicable in a generalized architecture called “supercube” where there is no restriction on the number of nodes in the network.