Virtual Cut-through Routing Research Articles

Multidimensional Computer Interconnection Networks with the Virtual Cut–Through Routing

A theoretical model of an n-dimensional toroidal interconnection network with the virtual cut-through routing is developed. The network performance is characterized as a function of the message load for various values of the network and communication parameters. An exact analytical expression for the saturation point has been obtained. The method of statistical physics known as the mean field theory approximation has been used in order to derive analytical expressions of latency as a function of message generation rate for the full range of the network load. The saturation point has been found proportional to the number of the torus dimensions and inversely proportional to the message length and to the length of the path from the source to the destination. It was found that the transition to the saturation state is a second-order (continuous) phase transition with a critical exponent equal to 1.

Computer interconnection networks with virtual cut-through routing

This paper considers a model of a toroidal computer interconnection network with the virtual cut-through routing. The interrelationships between network parameters, load and performance are analyzed. An exact analytical expression for the saturation point and expressions for the latency as a function of the message generation rate under the mean field theory approximation have been obtained. The theoretical results have been corroborated with the results of simulation experiments for various values of network parameters. The network behavior has been found not depending on the torus linear dimensions provided that they are at least twice as large as the message path length. The saturation point has been found to be inversely proportional to the message length in good agreement with the analytical results. A good agreement with Little’s theorem has been found if the network remains in the steady state during the experiment.

Blue Gene/L torus interconnection network

The main interconnect of the massively parallel Blue Gene®/L is a three-dimensional torus network with dynamic virtual cut-through routing. This paper describes both the architecture and the microarchitecture of the torus and a network performance simulator. Both simulation results and hardware measurements are presented.

Modeling of interconnection subsystems for massively parallel computers

The analysis, design and evaluation of the interconnection subsystem for massively parallel architectures is normally carried out using computer simulation tools, requiring elevated computational costs. Moreover, in some cases, these simulation processes show serious difficulties when both experiments and results have to be reproduced by other research or design teams. This work shows the suitability of the use of formal representation methods, like DSPN (stochastic Petri nets with deterministic and exponential firing times), for the description of the message routers, focusing on two important features. Firstly, the possibility of obtaining network performance indicators through the simulation of the obtained models with a lower computational cost than using conventional techniques; in some cases, analytical results can also be obtained. And secondly, making the basic parameters of the network design relatively independent of the router implementation features, thus simplifying the method of establishing the behavior of new router structures. This approach has been successfully applied to the analysis of both symmetrical torus and asymmetrical mesh interconnection topologies, with virtual cut-through flow control, oblivious routing and random traffic. It should be noted that most modern parallel computers employ a local buffer space big enough to store at least a complete packet. Two different functional router structures have been used in each case: transit buffers located at the input or at the output router links.

Wait-free deflection routing of long messages

In order to obtain the lowest possible latency, routing algorithms should try to avoid a message waiting for resources (network links) blocked by other messages or multiplexing of more messages over one physical channel. This requirement becomes especially important in the case of long messages. The only type of protocols able to guarantee waiting free routing under heavy load are algorithms based on deflection (also called nonminimal adaptive or hot potato) routing. This paper deals with problems connected with the use of deflection algorithms. In contrast to the case of nonadaptive or partially (e.g., minimal) adaptive routing, it is very infrequent that an unrestricted deflection routing becomes deadlocked and, similarly, livelock is not a serious problem. On the other hand, there is another phenomenon, called a deflection jam, that limits throughput of deflection algorithms used to route long messages. It has been observed for many deflection heuristics, interconnection network topologies, and both virtual cut-through and wormhole routing. A deflection jam is a sudden and persistent saturation of a network which sometimes occur, after a very long period of undisturbed communication. This paper describes events that trigger this saturation which suggest ways to design improved and stable deflection routing algorithms.

Hypercube communication delay with wormhole routing

We present an analytical model for the performance evaluation of hypercube computers. This analysis is aimed at modeling a deadlock-free wormhole routing scheme prevalent on second generation hypercube systems. Probability of blocking and average message delay are the two performance measures discussed. We start with the communication traffic to find the probability of blocking. The traffic analysis can capture any message destination distribution. Next, we find the average message delay that consists of two parts. The first part is the actual message transfer delay between any source and destination nodes. The second part of the delay is due to blocking caused by the wormhole routing scheme. The analysis is also extended to virtual cut-through routing and random wormhole routing techniques. The validity of the model is demonstrated by comparing analytical results with those from simulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fully adaptive minimal deadlock-free packet routing in hypercubes, meshes, and other networks: algorithms and simulations

This paper deals with the problem of packet-switched routing in parallel machines. Several new routing algorithms for different interconnection networks are presented. While the new techniques apply to a wide variety of networks, routing algorithms will be shown for the hypercube, the two-dimensional mesh, and the shuffle-exchange. Although the new techniques are designed for packet routing, they can be used alternatively for virtual cut-through routing models. The techniques presented for hypercubes and meshes are fully-adaptive and minimal. A fully-adaptive and minimal routing is one in which all possible minimal paths between a source and a destination are of potential use at the time a message is injected into the network. Minimal paths followed by messages ultimately depend on the local congestion encountered in each node of the network. All of the new techniques are completely free of deadlock situations. >

Storage-efficient, deadlock-free packet routing algorithms for torus networks

We present two new packet routing algorithms for parallel computers with torus interconnection networks of arbitrary size and dimension. Both algorithms use only minimal length paths, are fully adaptive in the sense that all minimal length paths may be used to avoid congestion, and are free of deadlock, livelock and starvation. Algorithm 1 requires only three central queues per routing node. It is the first known minimal length packet routing algorithm for torus networks which requires a constant number of queues per node, regardless of the size and dimension of the torus. In fact, the requirement of three queues per node is optimal, as no such algorithm is possible when all nodes have two or fewer queues. Algorithm 2 requires only that each node have two input buffers per edge. It is the first known minimal-fully-adaptive packet routing algorithm for torus networks which does not require central queues and which does not require any node to have more than two input or two output buffers per edge. Both algorithms are simple and appear to be well-suited to VLSI implementation. They can be used with either store-and-forward or virtual cut-through routing. >

Fault tolerant wormhole routing in hypercube multicomputers

The communication latency between nodes of the distributed memory multicomputers (DMMPs) is a vital factor to the performance of whole the system. Up to date, researches have been proposed to show that wormhole routing always takes the least time latency for data communication in a DMMPs. Unlike store-and-forward and virtual cut-through routing strategies, wormhole routing is sensitive to deadlocks. No efficient methods for deadlock free, fault tolerant and adaptive wormhole routing in an hypercube multicomputers have been proposed yet. In this paper, two distributed fault tolerant wormhole routing strategies is proposed. One is deterministic and the other is adaptive. Both can tolerate n-1 faults and are shown to be deadlock free. The routing algorithm and examples which demonstrate the routing procedures are also given.

Performance analysis of virtual cut-through switching in HARTS: a hexagonal mesh multicomputer

The authors present a formal analysis of virtual cut-through in a C-wrapped hexagonal mesh multicomputer, called the HARTS (hexagonal architecture for real-time systems). In virtual cut-through, packets arriving at an intermediate node are forwarded to the next node in the route without buffering if a circuit can be established to the next node. The hexagonal mesh is first characterized using a combinatorial analysis to determine the probability that a packet will establish a cut-through at an intermediate node. Given this parameter the probability distribution function for packet delivery times in HARTS is derived. The delivery times obtained from the analytic model are then compared against results collected from a simulator of the routing hardware designed for use in HARTS. The results from both the analytic model and the simulator further reinforce the choice of the virtual cut-through routing scheme for use in HARTS. >