K. Bolding, M. Fulgham, and L. Snyder. The case for chaotic adaptive routing. IEEE Trans. on Computers, 46(12):1281--1292, December 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of a particular system. This approach offers a significant improvement in accuracy over existing techniques used to estimate the worst case. Previous studies of routing algorithms generally chose bad traffic patterns that the authors felt represented worst case or near worst case behavior [5, 12]. However, for the example presented in Section 5, the traditional techniques overestimate the worst case throughput of the ROMM routing algorithm [12] by approximately 47 . Worstcase characterization has also been approached from a theoretical perspective [1, 6, 9, 11] Despite providing strong ....

....0.278 0.255 Worst case 0.278 0.173 expect that ROMM would have better worst case performance than DOR. To test this intuition, the performance of these two algorithms was compared against uniform random traffic and two permutations that are typically relied upon to demonstrate poor performance [5, 12]: bit complement and transpose. The tornado pattern was also considered, where each node sends packets (k 1) 2 hops to the right in the lowest dimension (Figure 7) In addition to these patterns, a trial of 10 random permutation matrices was generated and the worst case throughput for both ....

K. Bolding, M. Fulgham, and L. Snyder. The case for chaotic adaptive routing. IEEE Trans. on Computers, 46(12):1281--1292, December 1997.

....of a particular system. This approach offers a significant improvement in accuracy over existing techniques used to estimate the worst case. Previous studies of routing algorithms generally chose bad traffic patterns that the authors felt represented worst case or near worst case behavior [3][4]. However, for the example presented in Section IV, the traditional techniques overestimate the worst case throughput of the ROMM routing algorithm [3] by approximately 47 . Worst case characterization has also been approached from a theoretical perspective [5] 6] 7] Despite providing strong ....

....presented in [3] one might expect that ROMM would have better worstcase performance than DOR. To test this intuition, the performance of these two algorithms was compared against uniform random traffic and two permutations that are typically relied upon to demonstrate poor performance [3][4]: bit complement and transpose. The tornado pattern was also considered, where each node sends packets (k 1) 2 hops to the right in the lowest dimension (Figure 4) In addition to these patterns, a trial of 10 random permutation matrices was generated and the worst case throughput for both ....

K. Bolding, M. Fulgham, and L. Snyder, "The case for chaotic adaptive routing," IEEE Trans. on Computers, vol. 46, no. 12, pp. 1281--1292, December 1997.

....of a particular system. This approach offers a significant improvement in accuracy over existing techniques used to estimate the worst case. Previous studies of routing algorithms generally chose bad traffic patterns that the authors felt represented worst case or near worst case behavior [3][4]. However, for the example presented in Section iV, the traditional techniques overestimate the worst case throughput of the ROMM routing algorithm [3] by approximately 47 . Worst case characterization has also been approached from a theoretical perspective [5] 6] 7] Despite providing strong ....

....presented in [3] one might expect that ROMM would have better worstcase performance than DOR. To test this intuition, the performance of these two algorithms was compared against uniform random traffic and two permutations that are typically relied upon to demonstrate poor performance [3][4]: bit complement and transpose. The tornado pattern was also considered, where each node sends packets ( 1) 2 hops to the right in the lowest dimension (Figure 4) In addition to these patterns, a trial of 10 4 random permutation ma trices was generated and the worst case throughput for both ....

K. Bolding, M. Fulgham, and L. Snyder; "The case for chaotic adaptive routing," IEEE Truns. on Computers, vol. 46, no. 12, pp. 1281 1292, December 1997.

....on improving wormholed based routers by means of different routing and deadlock avoidance recovery strategies. Little has been done, though, for virtual cut through networks. To the best of our knowledge, few proposals, apart from our own, have considered VCT 0 s impact on network behavior ([18] [5] 17] among others) the more close to our proposal are the Chaos router [18] which implements non minimal adaptive routing, and the minimal adaptive routing proposed by Cypher and Gravano [5] 3 The Bubble Router In this section we propose a minimal fully adaptive routing algorithm for ....

....avoidance recovery strategies. Little has been done, though, for virtual cut through networks. To the best of our knowledge, few proposals, apart from our own, have considered VCT 0 s impact on network behavior ( 18] 5] 17] among others) the more close to our proposal are the Chaos router [18], which implements non minimal adaptive routing, and the minimal adaptive routing proposed by Cypher and Gravano [5] 3 The Bubble Router In this section we propose a minimal fully adaptive routing algorithm for k ary n cube networks using virtual cutthrough switching. After an informal ....

K. Bolding, M. Fulgham, and L. Snyder, "The Case of Chaotic Adaptive Routing", IEEE Trans. on Computers, vol. 46, no. 13, pp. 1281-1292, December 1997.

....the worst case throughput of a particular system. This approach can offer a significant improvement in accuracy over existing techniques. Previous studies of routing algorithms generally chose bad traffic patterns that the authors felt represented worst case or near worst case behavior [3][4]. However, for the example presented in Section 5, the traditional techniques overestimate the worstcase throughput of the ROMM routing algorithm [3] by approximately 47 . Worst case characterization has also been approached from a theoretical perspective [5] 6] 7] and while providing strong ....

....presented in [3] one might expect that ROMM would have better worst case performance than DOR. To test this intuition, the performance of these two algorithms was compared against uniform random trafficand two permutations that are typically relied upon to demonstrate poor performance [3][4]: bit complement and transpose. The tornado pattern was also considered, where each node sends packets (k1) 2 hops to the right in the lowest dimension (Figure 7) In addition to these patterns, a trial of 10 4 random permutation traffic patterns was generated and the worst case throughput ....

K. Bolding, M. Fulgham, and L. Snyder, "The case for chaotic adaptive routing," IEEE Trans. on Computers, vol. 46, no. 12, pp. 1281--1292, December 1997.

....the main paradigms are: # minimal routing versus non minimal routing; # optimal routing versus shortest path routing. Minimal routers allow packets to choose only minimal cost paths, while non minimal algorithms allow choices among all the available paths following some heuristic strategies #Bolding, Fulgham, Snyder, 1994#. Optimal routing has a network wide perspective and its objective is to optimize a function of all individual link #ows #usually this function is a sum of link costs assigned on the basis of average packet delays# #Bertsekas Gallager, 1992#. Shortest path routing has a source destination ....

Bolding, K., Fulgham, M. L., &Snyder, L. #1994#. The case for chaotic adaptive routing. Tech. rep. CSE-94-02-04, Department of Computer Science, UniversityofWashington, Seattle.

....underlying control protocol. Virtual circuit networks do not exhibit re ordering problems and their #lower# sensitivity to routing tables updates strictly depends on the circuits creation rate and holding time. Adaptive routers can be broken down in two broad categories: minimal and non minimal #Bolding, Fulgham, Snyder, 1994#. Minimal routers allow packets to choose only minimal cost paths, while non minimal algorithms allowchoosing among all the available paths following some heuristic strategies. Examples of non minimal routers are de#ection routers, hierarchical routers, cut through routers, queuing routers #see ....

....routers allow packets to choose only minimal cost paths, while non minimal algorithms allowchoosing among all the available paths following some heuristic strategies. Examples of non minimal routers are de#ection routers, hierarchical routers, cut through routers, queuing routers #see for example #Bolding et al. 1994# and #Bertsekas Gallager, 1992# for descriptions and references#. Oblivious and minimal adaptive routing algorithms are the most widely used routing paradigms #at least taking in consideration wide area communication networks#. Considering di#erent perspectives in minimal length paths ....

Bolding, K., Fulgham, M. L., & Snyder, L. #1994#. The case for chaotic adaptive routing. Tech. rep. CSE-94-02-04, Department of Computer Science, UniversityofWashington, Seattle.

....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 [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 ....

....for nonminimal algorithms. We can explore the difference between minimal adaptive algorithms and nonminimal adaptive algorithms in the worst case setting by running permutations constructed in the lower bound (hereafter called CLT permutations) on nonminimal adaptive algorithms. Chaotic routing [BFS94, KS91, KS94] is a randomized, nonminimal adaptive algorithm that is competitive with state of the art oblivious routers. Recall that a packet is said to be derouted if it makes a move that places it farther from its destination. In the Chaos algorithm, a node deroutes packets when it becomes ....

K. Bolding, M. Fulgham, and L. Snyder. The case for chaotic adaptive routing. Technical Report TR 94-02-04, University of Washington Department of Computer Science and Engineering, March 1994.

....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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K. Bolding, M. Fulgham, and L. Snyder. The case for chaotic adaptive routing. Technical Report TR 94-02-04, University of Washington Department of Computer Science and Engineering, Mar. 1994.

....the assumption is not likely to be a significant factor in the results since it is uniform across all the designs. We use two communication patterns: random and hotspot. For the random load, all destinations are equally probable. For the hot spot load, we use a similar scheme to that described in [3]: four destinations are four times as likely as the others. The load is presented in terms of the expected number of flits injected per node per cycle. We prefer this measure to that of fraction of overall capacity in that it forces separate evaluation for each communication pattern. We use two ....

....wh 2 6 bi vct 2 6 bi vct 2 12 bi wh 4 6 bi wh 4 12 bi vct 4 6 bi vct 4 12 hot 24 mesh wh 2 6 spot mesh wh 2 12 mesh wh 2 24 bi vct 2 48 bi wh 4 24 bi wh 4 48 bi vct 4 48 Table 8: Cost effective designs in Figure 4. router [4] and the SGI Spider [12] A network that uses VCT is the Chaos router [3]. Innumerable RTL simulators have been created for these and other studies; however comparatively few studies have accounted for hardware implementation. Of particular note are those by Chien [5] and by Aoyama and Chien [1] 6 Conclusions and Work in Progress In this work we have endeavored to ....

Bolding, K., Fulgham, M., and Snyder, L. The case for Chaotic Adaptive Routing. IEEE Trans. on Computers C-46, 12 (1997), 1281--1292.

....main paradigms are: ffl minimal routing versus non minimal routing; ffl optimal routing versus shortest path routing. Minimal routers allow packets to choose only minimal cost paths, while non minimal algorithms allow choices among all the available paths following some heuristic strategies (Bolding, Fulgham, Snyder, 1994). Optimal routing has a network wide perspective and its objective is to optimize a function of all individual link flows (usually this function is a sum of link costs assigned on the basis of average packet delays) Bertsekas Gallager, 1992) Shortest path routing has a source destination ....

Bolding, K., Fulgham, M. L., & Snyder, L. (1994). The case for chaotic adaptive routing.

....underlying control protocol. Virtual circuit networks do not exhibit re ordering problems and their (lower) sensitivity to routing tables updates strictly depends on the circuits creation rate and holding time. Adaptive routers can be broken down in two broad categories: minimal and non minimal (Bolding, Fulgham, Snyder, 1994). Minimal routers allow packets to choose only minimal cost paths, while non minimal algorithms allow choosing among all the available paths following some heuristic strategies. Examples of non minimal routers are deflection routers, hierarchical routers, cut through routers, queuing routers (see ....

....allow packets to choose only minimal cost paths, while non minimal algorithms allow choosing among all the available paths following some heuristic strategies. Examples of non minimal routers are deflection routers, hierarchical routers, cut through routers, queuing routers (see for example (Bolding et al. 1994) and (Bertsekas Gallager, 1992) for descriptions and references) Oblivious and minimal adaptive routing algorithms are the most widely used routing paradigms (at least taking in consideration wide area communication networks) Considering different perspectives in minimal length paths ....

Bolding, K., Fulgham, M. L., & Snyder, L. (1994). The case for chaotic adaptive routing.

....studies of mesh, torus, and hypercube networks were presented in [Fulgham Snyder 93] which explored the performance of several types of nonuniform traffic such as transpose, bit revesal, complement, hot spot, and others in chaotic and oblivious routing. All of this work is summarized in [Bolding et al. 94] The VLSI implementation of the Chaos Router Chip was detailed in [Bolding et al. 93] and [Bolding 93a] Implementation of a high performance, clock skew tolerant version of a channel is discussed in [Wille 92] The fault tolerant aspects of chaotic routing were presented in [Bolding Snyder ....

....and high performance, and a rendezvous interface for flexibility. To minimize software overhead, Cranium is directly accessible by user level programs. Protection for user level message passing is implemented by mapping user level handles into physical node identifiers and buffer addresses. ffl [Bolding et al. 94] UW CSE 94 02 04.PS.Z) Chaotic routers are randomizing, nonminimal adaptive packet routers designed for use in the communication networks of parallel computers. Chaotic routing is reviewed along with other contemporary network routing approaches, including the state of the art oblivious ....

K. Bolding, M. Fulgham, and L. Snyder. The case for chaotic adaptive routing. Technical Report CSE-94-02-04, University of Washington, February 1994.

....current wormhole routers, because they provide extra buffering. In the simulations, each packet consists of 20 flits where the first flit is the header of the message. The channels between nodes are shared bi directionally. The details of the simulation methodologies have been described before [36]. The traffic patterns considered have been used previously in the literature and are generally thought to be difficult, useful or both. Following is a description of the traffic patterns simulated. Let the binary representation of the source node be an Gamma1 an Gamma2 : a 0 , and let 0 = 1 ....

....creates so many difficulties, and since the addition of only a few extra links to create a torus doubles the bisection bandwidth and halves the network diameter, we will concentrate on the torus for the remaining discussion. Simulation results for mesh networks can be found in the appendices of [36]. For torus networks, saturation almost always occurs earlier using oblivious routing than when using chaotic routing. One exception to this is the complement permutation, which achieves an unusually high throughput under oblivious routing when compared to the other nonuniform traffic patterns. ....

[Article contains additional citation context not shown here]

Kevin Bolding, Melanie Fulgham, and Lawrence Snyder, "The case for chaotic adaptive routing," Tech. Rep. CSE-94-02-04, University of Washington, Feb. 1994.

....in each direction, an injection and a delivery buffer, in addition to a central queue with 5 buffers, for a total of 15 buffers per node. The node latencies to make a routing and selection decision are three cycles for the oblivious and four cycles for the more complex adaptive algorithms [BFSar] Although the adaptive algorithms appear quite complex to describe, the additional calculations required beyond that of the oblivious router are actually easy to compute. The computation determines, in parallel, the dimension and direction of all of the minimal routes, the lowest dimension ....

K. Bolding, M.L. Fulgham, and L. Snyder. The case for chaotic adaptive routing. IEEE Transactions on Computers, to appear.

....algorithm is similar to the modified packet Triplex algorithm described earlier in Chapter 4. The only difference is the Duato algorithm introduces a slightly larger bubble between consecutive messages on a channel. The results are comparable though. Additional comparisons can be found elsewhere [BFS94] and include hypercube networks [FS93] and deflection routing [Bol93b] Table 6.1: Summary of the design differences between the packet routing algorithms simulated. Router Node Latency Adaptivity Buffers per Node Oblivious 3 none 34 Duato 4 min adaptive 26 Chaos 4 non min adaptive 15 6.1.1 ....

....addition of only a few extra links to create a torus doubles the bisection bandwidth and halves the network diameter, we will concentrate on the torus for the remaining discussion. Simulation results for mesh networks which include both uniform and non uniform traffic can be 92 found elsewhere [BFS94] For torus networks, saturation almost always occurs earlier when using oblivious routing than when using minimal adaptive or chaotic routing. One exception to this is the complement permutation, which achieves an unusually high throughput under oblivious routing when compared to the other ....

[Article contains additional citation context not shown here]

K. Bolding, M.L. Fulgham, and L. Snyder. The case for chaotic adaptive routing. Technical Report TR CSE-94-02-04, University of Washington, Seattle, WA, 1994.

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K. Bolding, M. L. Fulgham, and L. Snyder, "The Case for Chaotic Adaptive Routing, " Technical Report UW-CSE 94-02-04, University of Washington, Department of Computer Science and Engineering, Seattle WA, February 1994.

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