Showing papers on "Destination-Sequenced Distance Vector routing published in 1991"

A framework for adaptive routing in multicomputer networks

Abstract: Message-passing concurrent computers, also known as multicomputers, such as the Caltech Cosmic Cube [47] and its commercial descendents, consist of many computing nodes that interact with each other by sending and receiving messages over communication channels between the nodes. The communication networks of the second-generation machines, such as the Symult Series 2010 and the Intel iPSC2 [2], employ an oblivious wormhole-routing technique that guarantees deadlock freedom. The network performance of this highly evolved oblivious technique has reached a limit of being capable of delivering, under random traffic, a stable maximum sustained throughput of ~~45 to 50% of the limit set by the network bisection bandwidth, while maintaining acceptable network latency. This thesis examines the possibility of performing adaptive routing as an approach to further improving upon the performance and reliability of these networks. In an adaptive multipath routing scheme, message trajectories are no longer deterministic, but are continuously perturbed by local message loading. Message packets will tend to follow their shortest-distance routes to destinations in normal traffic loading, but can be detoured to longer but less-loaded routes as local congestion occurs. A simple adaptive cut-through packet-switching framework is described, and a number of fundamental issues concerning the theoretical feasibility of the adaptive approach are studied. Freedom of communication deadlock is achieved by following a coherent channel protocol and by applying voluntary misrouting as needed. Packet deliveries are assured by resolving channel-access conflicts according to a priority assignment. Fairness of network access is assured either by sending round-trip packets or by having each node follow a local injection-synchronization protocol. The performance behavior of the proposed adaptive cut-through framework is studied with stochastic modeling and analysis, as well as through extensive simulation experiments for the 2D and 3D rectilinear networks. Theoretical bounds on various average network-performance metrics are derived for these rectilinear networks. These bounds provide a standard frame of reference for interpreting the performance results. In addition to the potential gain in network performance, the adaptive approach offers the potential for exploiting the inherent path redundancy found in richly connected networks in order to perform fault-tolerant routing. Two convexity-related notions are introduced to characterize the conditions under which our adaptive routing formulation is adequate to provide fault-tolerant routing, with minimal change in routing hardware, The effectiveness of these notions is studied through extensive simulations, The 2D octagonal-mesh network is suggested; this displays excellent fault-tolerant potential under the adaptive routing framework. Both performance and reliability behaviors of the octagonal mesh are studied in detail. A number of

Switching networks with expansive and/or dispersive logical clusters for message routing

Abstract: A class of switching networks is comprised of expansive logical clusters and/or dispersive logical clusters. These clusters are of low degree. The class of networks include multibutterfly networks as well as multi-Benes networks. These networks provide for fault tolerance and routing and for efficient routing. Moreover, routing is provided in a non-blocking fashion.

Neural network implementation of the shortest path algorithm for traffic routing in communication networks

Abstract: A neural network computation algorithm is introduced to solve for the optimal traffic routing in a general N-node communication network. The algorithm chooses multilink paths for node-to-node traffic which minimize a certain cost function. Unlike the algorithm introduced earlier in this area, knowledge of the number of links between each origin-destination pair is not required by the algorithm, therefore it can be applied to variable-length path routing problems. The neural network structure for implementing the algorithm is a modified form of the one used by the traveling salesman algorithm. Computer simulation in a nine- and sixteen-node grid network showed that the algorithm performs extremely well in single and multiple paths. >

Message-routing apparatus

Abstract: Message-routing apparatus is known for routing messages between a plurality of communications networks. Typically, the known apparatus comprises a respective network interface card for each communications network and a shared, processor-based, routing manager with which the cards communicate through a backplane bus system. In order to overcome the bandwidth limitations of such known apparatus, the present invention provides a local routing manager on each card and high-speed, point-to-point, links interconnecting the local routing managers in a closed loop. Each local routing manager recognizes whether a message passed to it is for outward transmission over the associated network; if this is not the case, the message is passed to the local routing manager of the next card. Any messages which the local routing managers are unable to route, are diverted to a shared routing manager.

Deadlock-free multicast wormhole routing in multicomputer networks

Abstract: Efficient routing of messages is the key to the performance of multicomputers. Multicast communication refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. Wormhole routing is the most promising switching technique used in new generation multicomputers. In this paper, we present multicast wormhole routing methods for multicomputers adopting 2D-mesh and hypercube topologies. The dual-path routing algorithm requires less system resource, while the multipath routing algorithm creates less traffic. More import antly, both routing algorithms are deadlock-free, which is essential to wormhole networks.

Method and apparatus for dynamic detection and routing of non-uniform traffic in parallel buffered multistage interconnection networks

Abstract: A method and apparatus for routing processor-memory data traffic in a shared-memory multiprocessor computer system employs an interconnection network including two buffered multistage switching networks. Each of these networks can be used to route the data from any processing element to any memory element. Depending on the nature of the processor-memory traffic, two distinct routing schemes are used to distribute the traffic among the two networks. The first method distributes the memory accesses evenly among the two networks and maximizes performance when the memory accesses are uniformly distributed among the memory modules. However, when the traffic is highly non-uniform, a second routing method is used to confine the non-uniform part of the traffic to one network and the remaining part to the other network. The routing method is selected based on the prevailing traffic conditions. A distributed feedback mechanism detects the change in traffic conditions and changes the routing method accordingly. A traffic monitoring circuit within each memory module monitors the traffic into the memory module continuously and senses a change in the traffic condition. The condition is conveyed to the processing elements by means of a status flag associated with each response message from the memory module to processing elements. The processing elements respond to a change in traffic condition by switching to the alternate routing method.

Deadlock-free adaptive routing algorithms for multicomputers: evaluation of a new algorithm

Abstract: A new theory for the design of deadlock-free adaptive routing algorithms for wormhole and store-and-forward routing as well as two design methodologies have been proposed previously. In this paper, a new adaptive routing algorithm, obtained from the application of the former theory to the binary n-cube, is evaluated under different load conditions and compared with other algorithms. The results show that the new design methodology supplies faster routing algorithms, at least for those networks with a high connectivity. >

Brownian networks with discretionary routing

Abstract: Motivated by scheduling problems that arise in flexible manufacturing systems, we develop a heuristic procedure to obtain effective flow control sequencing, routing, and input control policies for multiclass queueing networks. The procedure employs a Brownian model of J. M. Harrison that approximates a multiclass queueing network with dynamic scheduling capability, if the total load imposed on each station in the queueing network is approximately equal to that station's capacity. In this paper, each customer class may be served at any of several different stations, and thus dynamic routing decisions are added to the sequencing and input control decisions already present in Harrison's model. Using previous heavy traffic results as a guide, we observe that, under heavy traffic conditions, a queueing network routing its customers to the queue where they will incur the shortest expected delay behaves very much like the reduced queueing network formed by pooling the appropriate servers. This observation leads to a proposed reduction of a Brownian network with discretionary routing to a simpler Brownian network without discretinary routing. Computational results indicate that combining this reduction with previous analysis of Brownian networks without discretionary routing leads to effective flow control policies for many moderately sized queueing network scheduling problems.

A general greedy channel routing algorithm

Abstract: A general approach for the channel routing problem is presented as a framework for a class of heuristic routing algorithms. The algorithm is shown to possess a backtracking capability that increases the chance of completing the routing with a minimum number of tracks. Since the concepts described are general, they can be applied to other channel problems, such as switchbox routing, three-layer routing, and multilayer routing, or even to the overlap model, with only a few modifications. It is shown that track-oriented greedy algorithms can be modified to solve other channel routing problems. As examples, the algorithm is modified to solve the Manhattan switch-box problem and channel routing problems in the overlap and knock-knee models. Preliminary results show that the modified algorithms have good performance and show strong potential to outperform existing algorithms. Applying the algorithm MCRP-ROUT to the benchmark Deutsch's difficult problem and Burstein's difficult problem, routing solutions of 19 tracks and six tracks, respectively, were obtained. >

Multiterminal global routing: A deterministic approximation scheme

Abstract: We consider the problem of routing multiterminal nets in a two-dimensional gate-array. Given a gate-array and a set of nets to be routed, we wish to find a routing that uses as little channel space as possible. We present a deterministic approximation algorithm that uses close to the minimum possible channel space. We cast the routing problem as a new form of zero-one multicommodity flow, an integer-programming problem. We solve this integer program approximately by first solving its linear-program relaxation and then rounding any fractions that appear in the solution to the linear program. The running time of the rounding algorithm is exponential in the number of terminals in a net but polynomial in the number of nets and the size of the array. The algorithm is thus best suited to cases where the number of terminals on each net is small.

New algorithm for over-the-cell channel routing using vacant terminals

Abstract: In this paper, we present a new algorithm, called WISER, for over-the-cell channel routing in the standard cell design technology using the two-layer routing model. The novelty of our approach lies in use of “vacant” terminals for over-the-cell routing. Furthermore, we consider longest paths in the vertical constraint graph as well as channel density as a basis for choosing nets to route over the rows of standard cells. Our approximation algorithm for net selection produces provably good results. Algorithm WISER has been tested on several benchmark examples, and experimental results show that WISER reduces the channel height by an average of 29% as compared to conventional channel routers. In addition, it reduces the total number of vias by 32% in the average case.

Application of fuzzy sets theory to the saving based vehicle routing algorithm

Abstract: The basic input data for any vehicle routing models are travel time, distances, and cost between nodes in the network. Information on these basic data is not always accurate, since many fa...

Channel routing by sorting

Abstract: A novel approach for the channel routing problem based on sorting is described. A router based on the bubble-sort for routing two point nets across a channel is presented. A lower and an upper bound on the channel width and an upperbound on the number of vias are given. The router is extended for handling multiterminal nets and single-sided connections. Results for multilayer channel routing are presented. The high-speed and predictable performance of these channel routing algorithms makes them valuable in assessing the difficulty of routing a particular configuration of logic blocks. This makes then suitable for use when calculating a cost metric in an iterative placement algorithm. >

Constant queue routing on a mesh

Abstract: Packet routing is an important problem in parallel computation since a single step of inter-processor communication can be thought of as a packet routing task. In this paper we present an optimal algorithm for packet routing on a mesh-connected computer.

Fully-adaptive routing: packet switching performance and wormhole algorithms

Abstract: In thts paper, a strnulatton study on the performance of some new algorithms for deadlock- and lwelock-free adaptive routing is reported. Packetswztchcd fully -adaptive minzmal routing on the mesh and the hypercube as ezplored for dt~erent tn~ection models: stattc and dynamic. The algorithms stmu lated in this paper are the jirst known to be !ivelockand deadlock-free fully -adaptive minimal that requzre a moderate amount of hardware. These techniques need only two central queues per routing node. The performance of these schemes IS measured for dtfferent irafic models: random, complement, transpose, bit-reversal and leveied permutations. Several machine sizes are trted and critical parameters indicating the performance of the routing algorithms are measured such as throughput, maximum and average latency, effective tn~ectaon, and saturation point. In the case of the mesh network, the new method w compared to an obltvzous scheme based on a simtlar routing node model. In the present versaon of thts paper, stm u!atton results are reported for hypercubes up to 16K nodes and for meshes of 11{ nodes. Ftnallyl a fu!iy-adaptwe minzmal worm-hole routing algorathm for the torus network wiil be presented. This technique is dead!ock- and hvelock-free and requuvs only 8 vzrtual channels per physzcal bzdzrectzonal link for zts implementation. Szmu!ations are currently being performed to determme the practical performance of this routing method.

A Fault-Tolerant Routing Algorithm for Star Graph Interconnection Network.

Abstract: This paper presents a fault tolerant routing algorithm for the star graph. The suggested algorithm is based on the concept of unsafety vectors, originally proposed for hypercubes. In this algorithm, each node starts by computing a first level unsafety set, composed of the set of unreachable neighbors. It then performs some exchanges with its neighbors to determine the unsafety nodes. After that, all nodes have the addresses of all faulty nodes. Based on the information gathered in each node, faulttolerant routing between a source node and a destination node is realized. We conducted a performance comparison between the star and hypercube graph using the unsafety vectors routing algorithm under different working conditions. The results obtained through simulation experiments reveal that the hypercube is of superior performance compared to the star graph in the presence of low fault rates. But its performance under high fault rates falls short of that of the star graph.

Algorithms for three-layer over-the-cell channel routing

Abstract: The authors present a novel algorithm for three-layer, over-the-cell channel routing of standard cell designs. The novelty of the proposed approach lies in the use of 'vacant' terminals for over-the-cell routing. Furthermore, the authors consider both the maximum cliques in the horizontal constraint graph and the longest paths in the vertical constraint graph as a basis for choosing the nets to route over the cells. They prove that their net selection algorithm is guaranteed to produce a solution within 68% of the optimum. The proposed algorithm has been implemented and tested on several benchmark examples. For the entire PRIMARY 1 benchmark, they reduce the total routing height by 76% as compared to a two-layer channel router, which leads to a 7% reduction in chip height. >

A simple adaptive routing scheme for congestion control in ShuffleNet multihop lightwave networks

Abstract: The authors describe a simple adaptive routing scheme for datagram (connectionless) and virtual circuit (connection-oriented) transmission that relieves congestion resulting from nonuniform traffic patterns and network failures. The authors describe a fixed-routing algorithm for dedicated channel ShuffleNets. Based on the fixed routing algorithm, an adaptive routing scheme for datagram transmission is presented followed by performance results for uniform and nonuniform traffic patterns and fault tolerance. The adaptive routing of datagrams uses only the local queue size information available at the network interface units (NIUs) and redistributes the load as congestion develops. Since datagrams are individually routed through the network, they may not arrive at their destination in the order they were generated and may need to be resequenced. The authors compute an upper estimate on the resequencing buffer size for stream traffic. A virtual circuit version of the adaptive routing algorithm eliminates the need for resequencing buffers. >

An analysis of deflection routing in multi-dimensional regular mesh networks

Abstract: A Markov Chain based analysis for deflection routing in n-dimensional regular mesh networks is presented. Detailed analyses are given for the 2D mesh, and a generalization to higher dimensions is outlined. Analytic results are shown to agree very closely with simulations. A basic routing scheme in which all packets have equal priority and a priority scheme in which packets with fewer alternative routes are given priority are proposed and analyzed. Results show that the priority scheme gives higher maximum throughput and lower average packet delay than the basic scheme by reducing average deflections under heavy loads. With the priority scheme, the network performance is almost identical to that of the optimal diagonal routing scheme. By doubling the number of links the throughput is always more than doubled. The authors conclude that in the 2D case, bidirectional links are more cost-effective than unidirectional ones assuming the cost is the number of optical transceivers. >

The effect of model uncertainty on some optimal routing problems

Abstract: The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included. >

Modeling wormhole routing in a hypercube

Abstract: An analytical model for the performance evaluation of asynchronous hypercubes is presented. 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 discussed. The communication traffic to find the probability of blocking is the starting point. The traffic analysis can capture any message destination distribution. The average message delay that consists of two parts is found. The analysis is extended to virtual cut-through routing and random wormhole routing techniques. The validity of the model is demonstrated. >

Simultaneous pin assignment and global wiring for custom VLSI design

Abstract: The problem of determining the interconnections among component modules for top-down VLSI layout design is discussed. Two main steps, pin assignment and global routing, are attacked simultaneously. They are integrated and formulated into one special Steiner minimal tree problem. An algorithm is then presented to solve it. Also, the local resident effect of many interconnection nets on a layout is considered. A strategy based upon this effect is proposed to speed up this algorithm. The strategy finds a smaller area called a critical routing area for a net to be passed through. Experimental results show that the performance is increased without reducing the routing quality. >

Channel/switchbox definition for VLSI building-block layout

Abstract: A study is made of the problem of routing region definition and ordering in VLSI building-block layout design. An algorithm to decompose the routing area into straight channels and rectangular switchboxes corresponding to line segments in the routing structure of the placement such that the number of switchboxes is minimized, is presented. The algorithm is based on a graph-theory approach that makes use of an efficient polynomial time algorithm for computing minimum clique covers of triangulated graphs. Experimental results indicate that the algorithm performs well. For all the test problems considered, the algorithm consistently outperformed a previous known greedy algorithm, and it produced optimal solutions in all but one case. >

A parallel textured algorithm for optimal routing in data network

Abstract: A textured decomposition-based algorithm is developed to solve the optimal routing problem in data networks. The idea of the algorithm is to decompose the large-scale network into several smaller-scale subnetworks; then these subnetworks are organized systematically into several levels. Each level contains mutually independent subnetworks. When the external flows to a level are frozen, one can concurrently compute the optimal solution of the subnetworks at the level. The proposed parallel-oriented algorithm will converge to the global optimal solution when some conditions are satisfied. The authors use a few examples to illustrate the convergence conditions of the textured algorithm. A numerical example to demonstrate the potential speedup of the algorithm is also provided. >

A minimum interference routing algorithm for a linear lightwave network

Abstract: A routing algorithm for setting up point to point connection is proposed for a linear lightwave network (LLN). The overall problem of routing is decomposed into the subproblems of physical path allocation, checking for violations of some of the special constraints (MISC (mutually independent sources combining) and color clash) of the LLN on the allocated physical path and the allocation of an appropriate channel. It is shown that the problem of finding a physical path that does not violate the MISC constraint of the LLN is NP-complete. >

The 60° grid: routing channels in width d/√3.

Abstract: The 60" grid consists of vertical columns and diagonal tracks running at slopes of 2 30". This model offers a potentially large reduction in channel width, without resorting to wire overlap. For a channel routing problem with density d, the availability of the diagonal tracks leads to a lower bound of $: We present two nearoptimal channel routing algorithms. The first uses 5

Flexible, fault-tolerant routing criteria for circuit-switched hypercubes

Abstract: A set of routing criteria is proposed for circuit-switched hypercubes that exploit the flexibility provided by the hypercube. The routing criteria are provably deadlock-free and route messages along shortest paths. The number of shortest paths allowed by the routing criteria is more than one for most source-destination pairs. It is shown that the flexibility provided by the routing criteria can be used to limit the negative effects due to component-failures. The exact number of disrupted source-destination pairs are derived in the presence of a single faulty link or a single faulty node. It is shown that these numbers can be minimized using the relabeling techniques proposed. It is shown that the criteria, if used effectively, lead to a significant improvement in performance over the e-cube routing strategy for non-uniform traffic. >