S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, pages 21#30, June 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....This matches the known upper bound of three queues per node for deadlock free, minimal packet routing on cycle and torus networks. 1 Introduction routing in parallel and distributed architectures. A wide range of packet routing algorithms with differing properties and costs have been proposed [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20]. In this paper we Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by ....

S. Konstantinidou and L. Snyder. The Chaos router: A practical application of randomization in network routing. In Proc. nd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 21-30, 1990.

....have been derouted. Nonminimal routing allows the most flexibility in packet paths, but at a cost of more complex logic to avoid livelock, the situation in which a packet never reaches its destination because it is derouted frequently. Examples of adaptive routers include the Chaos router [BFS94, KS90, KS91] and the Ngai and Seitz router [NS89, NS91] In theory, there are many fast algorithms for static 1 routing problems on synchronous networks 2 , but all make use of large queues or information about destination addresses beyond just preferred directions. See Sections 1.1 and 1.2. An ....

....nothing to prevent a packet from being derouted frequently, resulting in a livelock situation. However, the Chaos algorithm is probabilistically livelock free: the probability that a packet has not been delivered after T time tends to zero as T tends to infinity. A proof of this can be found in [KS90] for the hypercube; the proof for the mesh is almost identical [Bol93] The Chaos router has a mechanism called virtual cut through, which allows the head of a packet to move from frame to frame (either the input frames, the output 56 frames, or the central queue) without waiting for the tail ....

S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, pages 21--30, June 1990.

....Performance of Adaptive Routers on Worst Case Permutations Donald D. Chinn Department of Computer Science and Engineering University of Washington Seattle, WA 98195 USA Abstract. Chaotic routing [4, 13, 14] is a randomized, nonminimal adaptive routing algorithm for multicomputers. An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing ....

....said to have been derouted. Nonminimal routing allows the most flexibility in packet paths, but at a cost of more complex logic to avoid livelock, the situation in which a packet never reaches its destination because it is derouted frequently. Examples of adaptive routers include the Chaos router [4, 13, 14] and the Ngai and Seitz router [16, 17] One of the simplest benchmarks for a router s performance is how it performs in the worst case on static one to one (or partial permutation) routing problems, where each processor sends at most one message and receives at most one message. The motivation ....

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S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, pages 21--30, June 1990.

....are derouted immediately, without being buffered in the node. 3 In some networks, there may be links available which take a packet neither closer nor further away from its destination. These no progress hops will be labelled deroutes as well. 18 Queueing non minimal routers [Ngai Seitz 89, Konstantinidou Snyder 90, Coates et al. 93] differ from deflection routers by the presence of a central buffer which holds packets awaiting free outgoing links. In general, packets move into a central buffer from incoming links and wait there until a preferred outgoing link (a link on a minimal path) becomes available. ....

....of a new cut through design. Finally, the new cut through chaos router is compared with other competing router designs and shown to be competitive. 2. 1 Previous Work Chaotic routing was developed by Konstantinidou and Snyder as an efficient alternative to priority non minimal adaptive routers [Konstantinidou Snyder 90, Konstantinidou 91] The chaos router presented there belongs to the queueing non minimal adaptive router class and is specific to hypercubic networks. Routing is accomplished in a store and forward manner and, thus, requires packetization of messages. 2.1.1 Conceptual Chaotic Routing The basic ....

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S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 2nd Symposium on Parallel Algorithms and Architectures, pages 21--30. ACM, 1990.

....Although algorithms that use central queues require less storage than those using edge buffers, central queues can become a bottleneck. So, algorithms that use edge buffers usually achieve a higher performance. Several researchers have proposed the use of edge buffers for multicomputer networks [22, 25]. The restriction of buffer allocation, although it avoids deadlock, can increase traffic jams, especially in heavily loaded networks. In order to avoid congested regions of the network, an adaptive routing algorithm can be used. Adaptive strategies have been shown to outperform deterministic ....

S. Konstantinidou and L. Snyder, "The Chaos router: A practical application of randomization in network routing," in Proc. 2nd ACM Symp. Parallel Algorithms Architectures, 1990.

....and Aoki [4] Duato [6] Konstantinidou [17] Ngai and Seitz [24] and Pifarr e et al. 26] among others. A survey of adaptive routing for binary cubes can be found in [7] Deterministic, adaptive routing is used on the Connection Machine models CM 1, CM 2, and CM 200 [9] The Chaos router [18] is a randomized, adaptive router, which allows messages to follow random shortest paths from source to destination, but will misroute messages when congestion occurs. A prototype of the Chaos router has been implemented [2] However, questions about the effectiveness of adaptive routing, in ....

S. Konstantinidou and L. Snyder. The Chaos Router: A Practical Application of Randomization in Network Routing. In Proc. of the 2nd Annual ACM Symp. on Parallel Algorithms and Architectures, pages 21--30. ACM Press, July 1990.

....wires, full utilization of the data wires can be achieved with duplex channels. 2.1.2 Simulation Results Simulations were performed to gauge the performance of simplex and duplex channels. The reported results are based on simulations of 256 node torus networks using Chaotic adaptive routing [Konstantinidou Snyder 90, Bolding 93] with a uniform random traffic load. Throughput results are normalized to the theoretical maximum throughput constrained by the bisection bandwidth of the network. Latency figures reported do not include source queueing. The routing node modeled has an internal delay of 3 cycles, but ....

S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 2nd Symposium on Parallel Algorithms and Architectures, pages 21--30. ACM, 1990.

....The arbiter selects the next flits to be sent on the physical channels. There are several well known routing algorithms for massively parallel computers. We can include: Random Routing [Val81] Fluent Machine [Ran85] Adaptive Minimal routing [Kon90] Fully Adaptive Routing [Dal86] Chaos [Kon90b], Exchange Model [Nga89] Routing by Sorting [Nas81] and others. Further information about these and other approaches can be found in [Fel91] and [Ni93] a) b) c) Figure 2. Basic structure of routers (a) oblivious 4x4, b) mesh (c) cut through and packet switching [Li94a] 5. Real Time systems ....

KONSTANTINIDOU, S.; SNYDER, L "The chaos router: a practical application of randomization in network routing". 2nd. Annual ACM SAAP, pp. 21-30. 1990.

....routing algorithms. These techniques can be divided into two classes, namely those which require only central queues [10, 12, 16, 18, 22, 25, 28, 29] and those which require that each node have queues (often called buffers) that are associated with each edge that is incident to the node [9, 15, 19]. Algorithms in the first class often require less storage than those in the second class. However, the central queues can become sequential bottlenecks, so algorithms in the second class may offer better performance. In addition, it should be noted that deadlockfree wormhole routing algorithms ....

S. Konstantinidou and L. Snyder. The Chaos router: A practical application of randomization in network routing. In Proc. 2nd. Annual ACM Symposium on Parallel Algorithms and Architectures, pages 21-- 30, 1990.

....route messages and to guarantee the three essential properties of every router, i.e. freedom from deadlock, livelock and starvation. Other alternative routing algorithms such as randomized routers [VaBr 81] minimal adaptive routers [Kons 90] non minimal adaptive routers [Hill 85] chaos router [KoSn 90] are also suggested in many articles. Routing can also be classified according to the methods that implement it, self routing and using special routing table are the two popular ones. Self routing [NaSa 81] also called digital controlled routing, is most suitable for symmetric, multistage ....

S. Konstantinidou and L. Snyder, "The Chaos Router: A Practical Application of Randomization in Network Routing", ACM 1990, pp. 79-88

....and Advanced Applications Group, IBM Argentina, Buenos Aires, Argentina 1 Introduction This paper studies the problem of deadlock free packet routing in parallel and distributed architectures. A wide range of packet routing algorithms with differing properties and costs have been proposed [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24]. In this paper we will focus on a particularly simple and important class of routing algorithms which we will call buffer reservation algorithms. A buffer reservation algorithm consists of rules that specify to which buffers a packet may move based solely on the buffer currently holding the ....

S. Konstantinidou and L. Snyder. The Chaos router: A practical application of randomization in network routing. In Proc. 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 21-- 30, 1990.

....randomization have been proposed by Dally and Aoki [6] Duato [9] Konstantinidou [38] Ngai and Seitz [57] and Pifarr e et al. 58] among others. A survey of adaptive routing for binary cubes can be found in [15] Deterministic, adaptive routing is used on the CM 2 200 [18] The Chaos router [2, 39] is a randomized, adaptive router, which allows messages to follow random shortest paths from source to destination, but will misroute messages when congestion occurs. ROMM (Randomized, Oblivious, Minimal, Multi Phase) routing is a routing technique that combines minimality with randomization for ....

S. Konstantinidou and L. Snyder. The Chaos Router: A Practical Application of Randomization in Network Routing. In Proc. of the 2nd Annual ACM Symp. on Parallel Algorithms and Architectures, pages 21--30. ACM Press, July 1990.

....include wide area or even local area networks of workstations. To date, the primary thrust of work on the Chaotic Routing Project has been in the areas of design, simulation, and implementation of the Chaos Router. The design and theory behind the chaotic routing concept was first introduced in [Konstantinidou Snyder 90] and a proposed architecture for a chaos router was presented in [Konstantinidou Snyder 91] Konstantindou s dissertation provides more in depth details on the proposed design and architecture [Konstantinidou 91] A more concise version of Konstantinidou s dissertation work can be found in ....

.... Snyder 93] UW CSE 93 06 01.PS. Z) The Chaos router is a nonminimal adaptive packet router that is both deadlock free and probabilistically livelock free [Konstantinidou 91] Unlike its predecessors [Ngai 89] the Chaos router uses randomization to provide an efficient way to avoid livelock [Konstantinidou Snyder 90] The Chaos router has been compared in software simulation studies to the state of the art oblivious routers (i.e. dimension order routers) on the hypercube topology [Konstantinidou Snyder 91] and the mesh and torus topologies [Bolding Snyder 92] The results, based on simulations of two ....

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S. Konstantinidou and L. Snyder. The Chaos Router: A practical application of randomization in network routing. In Proc. Symp. on Parallel Algorithms and Architectures, pages 21--30, 1990.

.... University of Washington July 23, 1993 Abstract Chaos router is a nonminimal adaptive packet router that is both deadlock free and probabilistically livelock free [Kon91] Unlike its predecessors [Nga89] the Chaos router uses randomization to provide an efficient way to avoid livelock [KS90]. The Chaos router has been compared in software simulation studies to the state of the art oblivious routers (i.e. dimension order routers) on the hypercube topology [KS91] and the mesh and torus topologies [BS92] The results, based on simulations of two different workloads, one uniform and one ....

....livelock free, nonminimal adaptive packet router for dynamically injected network traffic [Kon91] It was introduced as a practical alternative to oblivious and priority routers. Unlike its predecessors [Nga89] the Chaos router uses randomization to provide an efficient way to avoid livelock [KS90]. Using a simplified functional design, the Chaos router has been compared in software simulation studies to the state of the art oblivious routers (i.e. dimension order routers) on the hypercube topology [KS91] and the mesh and torus topologies [BS92] The results demonstrate a general ....

[Article contains additional citation context not shown here]

S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proc. of the 2nd ACM Symp. on Parallel Algorithms and Architectures, pages 21--30, 1990.

....two or more packets may desire the same outgoing link. One packet will be given its desired link, while the other packets are assigned one of the remaining links. Thus, the losing packets are derouted immediately, without being buffered in the node. Queueing non minimal routers [Ngai Seitz 89, Konstantinidou Snyder 90, Coates et al. 93] differ from deflection routers by the presence of a central buffer which holds packets awaiting free outgoing links. In general, packets move into a central buffer from incoming links and wait there until a preferred outgoing link (a link on a minimal path) becomes available. ....

....becomes more complicated due to the necessity of comparing priorities when derouting. Also, the timestamp or battle scar must be transmitted in the header of the packet consuming bandwidth that could provide other crucial routing information. The third solution is randomization. Chaotic routers [Konstantinidou Snyder 90] choose randomly among queued packets when selecting a packet to deroute. By introducing randomness into the network in this manner, the very regular cycles, typical of livelock, decay with time. Livelock freedom is provided only in a probabilistic sense: the probability a packet is in the ....

[Article contains additional citation context not shown here]

S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 2nd Symposium on Parallel Algorithms and Architectures, pages 21--30. ACM, 1990.

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S. Konstantinidou and L. Snyder. The chaos router: A practical application of randomization in network routing. In Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, pages 21#30, June 1990.

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