C. Glass and L. Ni. The turn model for adaptive routing. J. ACM, 41:847--902, Sept. 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the other flits in the message packet remain where they are until them header flit advances. Thus, the flits of the packet wind from the current processor containing the header flit, all the way back to the source processor (much like a worm) A routing protocol needs to be simple and robust [7], and have low latency and high throughput. Latency refers to the time that it takes for a packet to travel from the source to its destination. Wormhole routing has extremely low transmission latency since a flit of a message packet does not have to wait for the entire packet to arrive at a ....

C. J. Glass and L. M. Ni, "The turn model for adaptive routing," in Proceedings of 19th Annual International Symposium on Computer Architecture, 1992, pp. 278-287.

....first to address the mapping and routing path allocation problems for tile based architectures and provide an efficient way to solve them. Although routing (especially wormhole based routing [3] has been a hot research topic in the area of direct networks for parallel and distributed systems [6][7][8] the specifics of NoC force us to re think standard network techniques and adapt them to the context of NoC architectures. In what follows, we address this issue by presenting a suitable routing technique for NoC together with an algorithm for automatic generation of the routing function. 3 ....

....To be deadlock free, the routing algorithm needs to prohibit at least one turn in each of the possible routing cycles. In addition, it should not prohibit more turns than necessary to preserve the adaptiveness. Based on this, several deadlock free adaptive routing algorithms have been proposed [7], including west first, north last and negative first. In [8] Chiu proposed the odd even turn model which restricts the locations where some types of turns can take place such that the algorithm remains deadlock free. In our algorithm, we convert the adaptiveness offered by the above algorithms ....

C. J. Glass and L. M. Ni, "The turn model for adaptive routing," Proc. ISCA, May 1992.

....the height of the tree. Deadlock free routing is achieved nonmember processor (3, 0) 0, 0) 0, 3) 0 1 345 8 7 62 up direction between siblings (b) a) Figure 3: Virtual and routing topologies: a) a virtual topology G v and (b) a routing topology G p . using a variantoftheturn model [14], called up down routing [4] with the following rule: A legal route traverses zero or more links in the upward direction until anode with a direct downwardpath is reached. This is followed by traversing zeroormore links in the downwarddirection. For the processor topology of Figure 2(b) the ....

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of the ACM,Vol. 41 No. 4, September 1994.

....tree approach is highly inefcient since a large number of links are unused, and links close to the root become congested. Instead, we propose to resort to a more sophisticated approach based on the prohibition of turns. Here, a turn is dened as a specic pair of input output links around a node [12]. The main claim is that in order to break all the cycles in a network, it is sufcient to prohibit a set of turns instead of a set of links, as is the case with spanning trees (a turn ### ## ## around some node # is prohibited if not packets can be forwarded from link ### ## to link ### ##) For ....

C. Glass and L. Ni, The Turn Model for Adaptive Routing, Journal of ACM, Vol. 5, pp. 874-902, 1994.

....ports. To be able to direct the information appropriately, a tilebased architecture requires a method of routing the data packets through the network. There are quite a few routing algorithms proposed so far. In general, they can be divided into two categories: static routing and adaptive routing [6]. For the tile based architecture, we believe that the static routing is more suitable than the adaptive routing because: 1. Compared to static routers, implementing adaptive routers requires by far more resources because of their complexity. 2. Since in adaptive routing packets may arrive out ....

....network. In a few words, for 2D mesh networks, XY routing first routes packets along the X axis. Once it reaches the column wherein lies the destination tile, the packet is then routed along the Y axis. Obviously, XY routing is a minimal path routing algorithm and is free of deadlock and livelock [6]. As we will see later, this leads to a much simpler power model compared to its macro network peer. B. The Energy Model In [7] Ye et al. propose a new model for evaluating the power consumption of switch fabrics in network routers. To this end, the bit energy (E bit ) metric is defined as ....

C. J. Glass and L. M. Ni, "The turn model for adaptive routing," Proc. ISCA, May 1992.

.... wormhole routing [1, 2] Since wormhole routing is susceptible to deadlocks considerable body of work has been dedicated to designing routing algorithms that prevent deadlocks from occurring [3 10] Existing routing strategies can be classified as deterministic [6, 9, 11, 12] and adaptive [3, 5, 8, 9, 13]. In deterministic routing the path between a source and destination is unique, whereas in adaptive routing network state is considered during routing of worms. Adaptive routing algorithms that use all permitted ports in every router are called maximal [6] Maximal adaptive routing is not fully ....

....in our approach we use the TP or Turn Prohibition algorithm [24] to prohibit a minimal or near minimal number of input output pairs of ports at various nodes of the network. Minimizing the number of prohibited turns has been shown to correlate to lower average message latency in meshes and tori [8] and in irregular graphs [10, 15] After turn prohibition, routing tables are computed based on the shortest path between source and destination pairs. All paths computed this way contain no prohibited turns. Instead of keeping just the shortest distance to the destinations, we sort distances in ....

C. Glass and L. Ni, The Turn Model for Adaptive Routing, Journal of ACM vol. 5, pp. 874-902, 1994.

....a mesh does not have any wrap around channels. Routing algorithms for only mesh topologies are reviewed here, because wormhole routing has been used primarily on low dimension meshes and the focus of this paper is on mesh topologies. Many adaptive routing algorithms for meshes have been proposed [2, 3, 5, 8, 9, 10, 11]. Table 1 summarizes the main features of each algorithm. VCs is used as an abbreviation for number of virtual channels. Designing deadlock free routing algorithms for wormhole routing was simplified by a proof that an acyclic channel dependency graph guarantees deadlock freedom [6] Each node of ....

.... Table 1: Overview of Adaptive Routing Algorithms for Meshes Author(s) Fully VCs for Comments Adaptive 2D Mesh Partially Adaptive for Chien Kim [2] Yes 6 Higher Dimensions Daily [3] Yes 6 2D Mesh Only Daily Aoki [5] Yes 2D Mesh with x nodes Glass Ni [8] Yes 6 2D Mesh Only Glass Ni [9] No 4 Roughly Half the Adaptiveness of Fully Adaptive Jesshope, Miller Yes 8 Number of Virtual Yantchev [10] Channels is Exponential Linder Harden [11] Yes 6 in Dimension of Mesh to the set of nodes N, define an outgoing channel on which to route the message. Acyclicity of the channel ....

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C. Glass and L. Ni. The Turn Model for Adaptive Routing. In Proceedigs of the 19 Aual Itcratioal Symposium o Computer Architecture, pages 278 287, 1992.

....deadlock while using only two virtual channels [5] Sanz et al. developed the channels routing algorithm which is based on the same concept. In addition, Ni and Glass have developed a unique approach to adaptive routing which prevents deadlock without virtual channels by prohibiting turns [19]. However, this approach only works for meshes; in tori (meshes with wraparounds) additional virtual channels are required for deadlock prevention. Though each novel routing algorithm reduced the virtual channel requirements for deadlock prevention, their virtual channel requirements can have a ....

....interface bandwidth is an important factor affecting the achievable peak throughput of CR networks. CR outperforms DOR with equal resources on uniform traffic, and because CR includes adaptive routing, it would likely produce an even larger performance difference for non uniform traffic patterns [4, 19, 31]. 6.2 Fault Tolerant Compressionless Routing Performance In this section, we explore the performance of Fault tolerant Compressionless Routing (FCR) with a range of fault rates. FCR networks tolerate any transient faults. Also, as long as the network remains connected, FCR can tolerate all ....

L. Ni and C. Glass, "The turn model for adaptive routing," in Proceedings of the International 5'ympo- slum on Computer Architecture, pp. 278 87, 1992.

....with high probability of channel contention or even deadlock. Researchers have proposed schemes using virtual channels for increasing physical channel utilization [5] exploiting adaptivity [6, 16] and avoiding deadlock [2, 4, 6, 16] Routing algorithms to avoid deadlock are also investigated in [8]. Multicast represents the most complex communication pattern. It is in general NP complete and remains so even with some restrictions [10, 13] Heuristics based on finding a multicasting tr ee from a source node have been proposed for hypercubes [11, 18] and faulty hypercubes [12] These schemes ....

....22 and 25. With the above conditions, one can easily see that excluding the faulty nodes, the network remains connected. A linear path can be constructed on the mesh from left to right by including as many nodes as possible using a greedy strategy. For example, in Fig. 4(a) one possible path is [1, 2, 4, 3, 5, 7, 8, 10, 12, 14, 13, 15, 16, 18, 17, 19, 21, 23, 24, 26, 28, 27, 29, 30, 32, 31]. This path is 26 nodes long, with only 2 healthy nodes un routed. In general, no more than f healthy nodes will be unused and the path length is 2 2f. The readers are requested to refer to [1] for the embedding procedure. Lemma 4 [1] In an n cube with f ( k(nd 1) 2] faulty nodes, the e ....

C.J. Glass and L. M. Ni, "The Turn Model for Adaptive Routing," Int'l Syrup. on Computer Architecture, 1992, pp. 278-287.

....algorithms for regular communication patterns in n cubes. Preliminary experimentation on the Symult 2010 [3] has led to the observation that the processor to router channel is a bottleneck for several communication patterns. Scientific applications typically generate non uniform traffic [8]. For such traffic, there exists consumption bottleneck due to the messages queuing at the hot destination nodes. On hierarchical hypercube networks routing schemes have been proposed by [6] to reduce the hot spot contention. However, no research has been done on studying the interplay between the ....

....can proceed concurrently with S4. Figure l(b) also shows the respective message latencies with VCFC. VCFC and adaptive routing techniques use virtual channels for improved flow control and deadlock prevention, respectively. With the performance improvement suggested by adaptive routing algorithms [2, 8], future systems are more likely to support adaptive routing using virtual channels. Additional use of virtual channels for flow control (VCFC) is less likely to be used due to cost and technological constraints. 0,0) 1,0) 2,0) 3,0) 4,0) si 4 4 4 s 13 7 13 ss 17 11 6 Figure h An ....

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C.J. Glass and L. M. Ni. The turn model for adaptive routing. In Proc. of the Int'l Symp. on Computer Architecture, pp. 278d87, May 1992.

....than the fully adaptive algorithm of Linder and Harden, but requires only a constant number of virtual channels, regardless of the network dimension. For example, in a k ary n cube without wrap around connections, only three virtual channels for each physical link are required. The turn model [10] prevents some of the transitions between dimensions: this scheme requires only a virtual channel per physical channel, is non minimal, and partially adaptive. However it only works for meshes; tori require additional virtual channels for deadlock prevention. The turn model can be used in ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing. In Proceedings of the 19th Annual Symposium on Computer Architecture, pages 278--287, May 1992.

....packetization on two types of routers. First, we examine packetization in dimension order routers, similar to those in most existing multicomputer networks. Second, we extend our study to next generation networks which are likely to incorporate advanced routing techniques such as adaptive routing [12, 2] and virtual lanes 3 Chittor and Enbody studied the Symult 2010 system[13] in which long messages are split into packets of 256 bytes. 7] The remainder of the paper is organized as follows. In Section 2, we describe the simulation models and metrics used for the exploration. In Section 3, ....

....impact of packetization on the performance of advanced routing networks. 4 Packetization and Multipath Networks Several routing techniques that eliminate the intermessage interference in wormholerouted networks have been proposed. For example, multipath routing techniques such as adaptive routing [12, 2] and virtual lanes [7] reduce intermessage interference by circumnavigating congestion and multiplexing resources respectively. In this section, we investigate the impact of packetization on the advanced routing networks which incorporate both adaptive routing and virtual lanes. In such networks, ....

L. Ni and C. Glass. The turn model for adaptive routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....than the fully adaptive algorithm of Linder and Harden, but requires only a constant number of virtual channels, regardless of the network dimension. For example, in a k ary n cube without wrap around connections, only three virtual channels for each physical link are required. The turn model [15] prevents some of the transitions between dimensions, and generalizes to multidimensional meshes and binary n cubes. This scheme requires only a virtual channel per physical channel, is non minimal, and partially adaptive. However it only works for meshes; tori require additional virtual channels ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing. In Proceedings of the 19th Annual Symposium on Computer Architecture, pages 278--287, May 1992.

....activity. From such a complex range of sources, we anticipate new range of network communication workloads with a wide variety of traffic patterns and message size distributions. However, to date much of the study of multicomputer network performance is based on uniform message size distributions [14, 2, 24]. While presuming uniform traffic simplifies simulations and the interpretation of results, these traffic loads are not representative of the actual communication workloads. It is also important to study the interaction of messages of different sizes, examining the impact of hybrid traffic loads. ....

L. Ni and C. Glass. The Turn Model for Adaptive Routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....tree approach is highly inefficient since a large number links are unused, and links close to the root become congested. Instead, we propose to resort to a more sophisticated approach based on the prohibition of turns. Here, a turn is defined as a specific pair of input output links around a node [12]. The main claim is that in order to break all the cycles in a network, it is sufficient to prohibit a set of turns instead of a set of links, as is the case with spanning trees (a turn (a, b, c) around some node b is prohibited if not packets can be forwarded from link (a, b) to link (b, c) For ....

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of ACM, Vol. 5, pp. 874-902, 1994.

....routing if blocked by a packet with a lower number of reversals. Updating reversal counts and making routing decisions on that basis may increase router complexity significantly. Recently, Glass and Ni have described a deadlock free adaptive router based on prohibiting turns which cause cycles [29]. Direct comparison is difficult as descriptions of their approach leave open many design choices which may affect both performance and implementation complexity critically. For example, routing can be minimal or non minimal. Minimal adaptive routing algorithms developed by Duato [16] and Sanz ....

L. Ni and C. Glass. The turn model for adaptive routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....and tangible benefits, adaptive routers have yet to gain acceptance in many commercial machines. Recently, adaptive routing and virtual lanes have been touted as practical approaches for improving network performance. A number of dramatically simpler adaptive routing algorithms have been proposed [28, 22, 5]. This breakthrough makes adaptive routing feasible, but not without cost. Deciding whether or not to incorporate adaptive routing into a router is still a complex costperformance tradeoff with the cost side of the equation still largely undefined. Virtual lanes have been proposed as a mechanism ....

....designs, this is the maximum operation rate. For synchronous designs, it is the maximum clock rate. In both cases, this is the primary determinant of the channel clock rate. Most previous studies of router enhancements have focused on channel utilization, a measure of performance improvement [28, 22, 15, 5, 6]. One reason for this is that channel utilization can be studied independent of implementation issues. In this paper, we focus on the cost of adaptive routing and how it affects the router setup latency and achievable clock rate. Increases in setup latency and achievable clock period can also be ....

L. Ni and C. Glass. The turn model for adaptive routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....because of its complex scheme of deadlock prevention. Several approaches have shown that the hardware cost for deadlock prevention is reduced by restricting adaptivity to some extent. A good example of the partially adaptive routing algorithm is the Turn model introduced by Ni and Glass in [41]. They observed that prohibiting some turns on k ary n cube networks allows adaptive routing without causing any channel dependency cycles. Figure 3.2 illustrates an application of the Turn model to two dimensional networks. Among all of the possible turns (dashed or solid lines) solid lines ....

....all of the westbound messages are routed in a deterministic way. However, all of the eastbound messages are routed in a fully adaptive way. This algorithm is called west first. The Turn model may or may not allow misrouting. Although a livelock prevention mechanism was not presented in [41], the Turn model is capable of allowing misrouting on wormhole routed networks. In contrast to other wormhole routed adaptive algorithms, it does not require any virtual channels for deadlock prevention. However, since the Turn model resolves deadlocks in an irregular fashion, it may cause uneven ....

[Article contains additional citation context not shown here]

L. Ni and C. Glass. The Turn Model for Adaptive Routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....of research has been devoted to either preventing or resolving network deadlock. Deadlock can be prevented by ordering the acquisition of resources in such a way that static dependencies among packets cannot form a cycle. This can be achieved by restricting the routing such as in the Turn model [16] or by splitting the traffic into two or more virtual channels so that cyclic dependencies are eliminated [10] There are multiple proposals of adaptive wormhole routers based on these approaches [21, 8] Common drawbacks of these proposals are the high hardware complexity of the resulting device ....

C. J. Glass and L. M. Ni, "The Turn Model for Adaptive Routing, " Proceedings of the 19th Annual International Symposium on Computer Architecture, May 1992.

....tree approach is highly inefficient since a large number links are unused, and links close to the root become congested. Instead, we propose to resort to a more sophisticated approach based on the prohibition of turns. Here, a turn is defined as a specific pair of input output links around a node [11]. The main claim is that in order to break all the cycles in a network, it is sufficient to prohibit a set of turns instead of a set of links, as is the case with spanning trees (a turn (a; b; c) around some node b is prohibited if not packets can be forwarded from link (a; b) to link (b; c) For ....

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of ACM, Vol. 5, pp. 874-902, 1994.

....than the fully adaptive algorithm of Linder and Harden, but requires only a constant number of virtual channels, regardless of the network dimension. For example, in a k ary n cube without wrap around connections, only three virtual channels for each physical link are required. The turn model [17] prevents some of the transitions between dimensions, and generalizes to multidimensional meshes and binary n cubes. This scheme requires only a virtual channel per physical channel, is non minimal, and partially adaptive. The approach for two dimensional meshes works by disallowing two of the ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing. In Proceedings of the 19th Annual Symposium on Computer Architecture, pages 278--287, May 1992.

....cost effective facilities to alleviate the blocking [8] 9] 4] Nevertheless, a number of virtual channels still cost too much to accept. So one of the technical trends of wormhole routed interconnection networks is to find high performance designs using less virtual channels [16] 23] 7] 20] [14]. Adaptive routing algorithm has been proved important in fully utilizing the virtual channel resources [16] An adaptive routing algorithm actually consists of two parts, a routing function and a selection function [10] The routing function supplies a set of routable paths, and the selection ....

....for his family of algorithms. Schwiebert compared a number of routing policies for the opt y routing algorithm [20] and identified the best policy for the algorithm [21] In fact, many authors have tried to optimize the routing policy implicitly in their routing algorithm design [16] 23] [14] [20] These routing policies are specific to certain routing algorithms. Feng evaluated three commonly used routing policies by extensive simulations, namely, the dimension ordered, the diagonal, and the random policies [13] It observed that none of them is always best for all traffic ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing, Proceedings of the 19 th Annual International Symposium on Computer Architecture, pp. 278-287, May 1992.

....tree approach is highly inefficient since a large number links are unused, and links close to the root become congested. Instead, we propose to resort to a more sophisticated approach based on the prohibition of turns. Here, a turn is defined as a specific pair of input output links around a node [11]. The main claim is that in order to break all the cycles in a network, it is sufficient to prohibit a set of turns instead of a set of links, as is the case with spanning trees (a turn (a, b, c) around some node b is prohibited if not packets can be forwarded from link (a, b) to link (b, c) For ....

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of ACM, Vol. 5, pp. 874-902, 1994.

....which limits the application of the theory. Classic routing algorithms based on CDG are X Y algorithm for 2D meshes and e cube algorithm for n D meshes. They are of low cost employing only one virtual channel. However, as deterministic routing schemes, their performance is not high. Turn model [11] introduces routing adaptivity for meshes having one virtual channel. Nevertheless, the performance improvement is limited. Linder and Harden tried to maximize the network performance with enough virtual channels. Their fully adaptive minimal routing algorithm for n D meshes uses 2 n 1 virtual ....

....number unchanged, we will enhance its adaptivity considerably to n dimensions. 3. Scheme Design 3.1. Basic idea of VBMAR for 2D meshes VBMAR features load balance and full adaptivity in 2D meshes. Full adaptivity is reached based on the concept of complementary turn models. As described in [11] the turn model is a deadlock avoidance methodology based on CDG. It avoids deadlock by prohibiting some turns of messages. It is not fully adaptive as a routing model. In some region of the network, it allows fully adaptive routing. In the rest region, it only allows deterministic routing. The ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing, Proceedings of the 19 th Annual International Symposium on Computer Architecture, pp. 278-287, May 1992.

....routing allows the density of network interconnection to be taken 1 advantage of. Messages have several routing choices at each node and the path choices are made based on the local information available at the node. Adaptive routing can help in increasing the achievable network throughput [9, 10, 11]. Many new routing schemes have been proposed in recent research [3, 5, 8, 10, 12, 13, 16] A detailed survey of various routing schemes in wormhole networks can be found in [14] One disadvantage of adaptive routing in wormhole networks, however, is that it increases the likelihood of deadlocks. ....

....advantage of. Messages have several routing choices at each node and the path choices are made based on the local information available at the node. Adaptive routing can help in increasing the achievable network throughput [9, 10, 11] Many new routing schemes have been proposed in recent research [3, 5, 8, 10, 12, 13, 16]. A detailed survey of various routing schemes in wormhole networks can be found in [14] One disadvantage of adaptive routing in wormhole networks, however, is that it increases the likelihood of deadlocks. Thus, preventive measures have to be taken in the routing algorithm to avoid deadlocks. ....

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C.J. Glass and L.M. Ni, "The Turn Model of Adaptive Routing", Proceedings of the 19th Annual Symposium on Computer Architecture, May 1992, pp. 278-287. 6

.... topology makes it difficult to avoid deadlock among multiple packets traveling simultaneously [1, 2, 4, 5, 6] Up down routing algorithm prevents deadlock by restricting the sequences of turns in the routing paths [1] the idea of which was originally suggested for a regular mesh topology [7]. Routing complexity directly affects the communication performance which is the most critical factor in assessing the overall system performance in the switch based cluster systems. Especially, collective operations need more attention than the operations with point to point communication since ....

....two opposite unidirectional Eulerian trails. The Eulerian trails are determined based on some heuristics during initialization. However, not every network topology has such Eulerian trails [38] Here we assume the routing scheme based on the up down routing which is a variant of the turn model [7]. Upon startup of a cluster system, a node in each switch starts the configuration 3 Virtual cut through routing pipelines message transmission across multiple routers. In the absence of contention, it is the same as the wormhole routing. However, when a packet is blocked, it is removed from the ....

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of the ACM, Vol. 41 No. 4, September 1994.

....a concrete cost and speed model. We instantiate our parametric model, using a 0.8 micron gate array technology and produce specific constants for all aspects of the model. This model is then used to compare a selection of routing algorithms: dimension order [14] planar adaptive [8] turn model [28], and channels [6] The comparison produces a variety of insights about the relative latency and achievable clock rate of these routers. In particular, we find that all of the adaptive routers we consider are significantly slower (longer setup latency and lower clock speeds) than deterministic ....

....be small, allowing routers to be extremely small and fast. The obvious disadvantage is that by allowing a message to retain the buffers and channels, wormhole routing increases the possibility of resource cycles which cause deadlock. A number of schemes have been developed which solve this problem [10, 28]. 2.2 Adaptive Routing Adaptive routing has been proposed as a means of improving network throughput and performance robustness. A wide variety of adaptive routing algorithms have been proposed [24, 12, 16, 8, 28, 6] However to date, most evaluations of adaptive routing algorithms use register ....

[Article contains additional citation context not shown here]

L. Ni and C. Glass. The turn model for adaptive routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....algorithms for n dimensional mesh networks. The virtual channel requirements for Dally and Aoki s scheme are omitted as they depend on the number of dimension reversals permitted reversal counts and making routing decisions on that basis may increase router complexity significantly. Recent work [10] proposes another mechanism, prohibiting certain turns, for providing deadlock free routing. In many ways, the basic idea is similar to planar adaptive routing limiting adaptivity to prevent deadlock. Thus far, the technique has been studied primarily in two dimensional networks. A table ....

L. Ni and C. Glass. The Turn Model for Adaptive Routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....this communication pattern each node sends messages only to the node that has the reversed bit string as identifier. The negative impact of the internal conflicts can be alleviated by adaptive algorithms. Several examples already exists for the more common topologies, as the class of k ary n cubes [91, 7, 62, 13, 17, 27, 38, 48, 57, 64, 104]. Alternatively, interconnection topologies can be provided with many redundant paths and simpler routing algorithms [44] But this kind of solution is more expensive in terms of wiring complexity. External conflicts are the result of a poor program development or compilation process. An external ....

....right turns allowed in figure 3.8(a) are equivalent to the prohibited left turn in figure 3.8(b) and, symmetrically, the three left turns allowed in figure 3.8(b) are equivalent to the prohibited right turn in figure 3.8(a) Thus, both cycles exist and deadlock is still possible. The turn model [64] prevents some of the transitions between dimensions, and generalizes to multidimensional meshes and binary n cubes. These schemes require only a virtual channel per physical channel, are non minimal, and partially adaptive. The approach for two dimensional meshes works by disallowing two of the ....

C. J. Glass and L. M. Ni. The Turn Model for Adaptive Routing. In Proceedings of the 19th Annual Symposium on Computer Architecture, pages 278--287, May 1992. BIBLIOGRAPHY 139

....example of the deadlock cycles and a combination of the escape candidates. In this case, the messages A, B, C and D are the escape candidates because they are trying to advance along x dimension. We can limit the escape candidates to the messages B and C using the similar idea of North last routing[11], although this limitation does not reduce the number of VCs. A B D C Figure 2. Deadlock recovery. A torus cycle, which is a cyclic channel dependency introduced by a wraparound channel, can be broken by using two VCs[10] One method is switching the VC when a message passes a dateline link. ....

C.J. Glass and L.M. Ni: "The Turn Model for Adaptive Routing ", Proc. 19th ISCA, pp.278--287 (May 1992).

....a proper VC balance[21] and little degradation of the router s operation speed. We first clarify the influence of the VC based on a typical router design for the twodimensional mesh and torus networks. 2.2. Adaptive Routing We have designed several adaptive routers based on the turn model[13]. The turn model is unique which does not use the VCs to prevent deadlocks. The original algorithm supports both minimal and non minimal adaptive routing. The non minimal routing enhances fault tolerance, however it requires livelock prevention. This complicates the router logic and may sacrifice ....

....a physical network into a set of independent ones[23] They proposed a method to design an adaptive routing network by using the virtual networks. Linder and Harden generalized the adaptive routing algorithms for k ary n cubes by using the virtual networks[17] Glass and Ni proposed the turn model[13]. It allows the maximum number of turns which do not introduce cycles on the channel dependency graph. These routers are classified in a group of deadlock avoidance routers. The routers which we considered in this paper, such as the double x and double xy, belong to this group. One contribution of ....

C.J. Glass and L.M. Ni: "The Turn Model for Adaptive Routing", Proc. 19th ISCA, pp.278--287 (May 1992).

....adapts itself to the traffic congestion by providing alternate paths. Adaptive routing algorithms are classified as partially adaptive or fully adaptive. Partially adaptive routing algorithms use only a subset of the available physical paths between the source and the destination. Turn model [2] [3], direction restriction model [4] and planar adaptive routing [5] are examples of partially adaptive algorithms. Examples of fully adaptive algorithms include the routing schemes proposed by Linder and Harden [6] Duato [7] Su and Shin [8] Boura and Das [9] and Schwiebert and Jayasimha [10] ....

....all of the virtual paths, if virtual channels are used) The region of adaptivity of a routing algorithm is the region of adaptivity of a source node at the center of the network. Consider a 2D mesh network as shown in Fig. 2a. With node (3, 1) as the source node, under the East First algorithm [3], all the messages directed toward any of the nodes in the shaded region can be routed fully adaptively, while messages to any node outside this region would be routed deterministically. We refer to the shaded region as the region of adaptivity of the node (3, 1) under the East First algorithm. ....

[Article contains additional citation context not shown here]

C.J. Glass and L.M. Ni, "The Turn Model for Adaptive Routing," J. ACM, pp. 874--902, Sept. 1994.

....networks. In this respect, various types of interconnection networks, such as complete networks, hypercubes, meshes, rings, tori, irregular switch based, stack graphs, and hypermesh have been proposed and some of them have been implemented [46, 124, 108] Meanwhile, many routing algorithms [47, 56, 12] have been proposed for such networks. 4 In parallel processing systems, the ability to efficiently communicate and share data between processors is very critical to obtaining high performance. In essence, parallel computers require extremely short communication latencies such that network ....

....as hypermesh) 117] The routing algorithm determines which routes messages should follow through the network to reach their destinations. There are many different routing algorithms with different guarantees and performance such as Duato s adaptive routing [47] Glass and NI s turn model routing [56], and up down routing [12] The flow control mechanism determines when the message, or packet, or portion of a message should move along its route. Packets or flits may be blocked, buffered, discarded or detoured to an alternate route based on the flow control mechanism. 24 3.1.1 Message ....

C. J. Glass and L. M. Ni, "The Turn Model for Adaptive Routing", Proceedings of the 17th International Symposium on Computer Architecture, 1992, pp. 278-287.

....the new network. In this paper we consider non adaptive routing, not taking the sizes of corresponding message queues into account. 1. Introduction The problems of fault detection (testing) and fault location (diagnosis) have been mostly studied under the general area of system level diagnosis [7,21,29]. System level diagnosis techniques model the system as a test graph, whose vertices denote the nodes and an edge or test link (p i ,p j ) from node p i to node p j indicates that p i tests p j . While the test graph in is a subgraph of the system graph, it generally contains as many vertices as ....

....problem for link testing is related to the problem of determining the point covering number of the system graph G. A vertex and an edge in G cover each other if they are incident, and the size of the smallest set of vertices that covers all the edges in G is called the point covering number (G) [7]. Clearly, M = G) and the processors in the smallest cover are selected as monitors. A set of vertices in G is independent if no two of them are adjacent. Let (G) be the size of the maximum independent set for G. The maximum independent set can be constructed using a simple procedure described ....

[Article contains additional citation context not shown here]

C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Proc. of the 19th Annual Int. Symp. on Computer Architecture, pp. 278-286, May 1992.

....of this author no systematic study of the subject exists. There are some attempts at analytical modeling of wormhole switched networks [32, 39, 87] They are all characterized by imposing crude assumptions about stochastic independence. Otherwise, studies are based on simulation experiments [6, 13, 34, 35, 50, 88, 102, 103, 105, 106]. Unfortunately, the random nature of output data is often neglected in these cases. Usually little or nothing is said about the experimental design, hence it is hard to put confidence in the results. Combining the fact that analytical work rests on stochastic independence with the fact that ....

....is to find an appropriate routing scheme. In general, routing is a more critical design factor for wormhole switched networks than for buffered networks. Accordingly, a large number of algorithms have been pro16 16 posed [114] Adaptive routing is a central issue for wormhole switched networks [5,6,35,40,49, 50,88,104,105]. The objective is either to avoid blocking or to recover from it. Another way to deal with blocking is in terms of virtual channels as proposed by [33, 34, 37] The idea is to equip the switches with parallel flit buffers, also called multi lane buffers. Then a suspended packet can be decoupled ....

GLASS, C., AND NI, L. The turn model for adaptive routing. In Proc. of the 19th IEEE International Symposium on Computer Architecture (1992), pp. 278-- 287.

....output selection function is a key to the good adaptive routing performance. In this paper, we examine output selection functions for SP like, bidirectional multistage interconnection networks (BMIN) Previous studies on output selection functions have focused on the mesh and torus networks [22, 13, 14, 29, 30, 11, 4]. To the best of our knowledge, output selection functions for BMINs or MINs have not been studied to this date. We introduce six output selection functions. The performance of adaptive routing under the proposed output selection functions is studied with extensive simulations. There are a number ....

....adaptive route for di erent SP networks. Note that the 64 node network has a relatively irregular topology which results in the 4 routes per destination being dissimilar most of the time and therefore not as many 4 routes can be combined. Likewise, the turn restrictions used for deadlock avoidance [23, 2, 14, 20, 19] in 256 node and 512 node networks result in fewer percentage of routes that can be combined into adaptive in comparison to other networks. Table 3 compares the execution time of of fully adaptive (Sec. 5.1) and partially adaptive algorithms for di erent system sizes. Figure 20 compares ....

[Article contains additional citation context not shown here]

C.J. Glass and L. M. Ni. The turn model for adaptive routing. J. Assoc. Comp. Machinery, 41(5):874-902, 1994.

....to route a message along X direction at a particular router means that the message can choose either of the two channels going along X out of that router. The effect of adaptivity on average and standard deviation of latencies has been studied by using partially adaptive (for example, West first [9]) and fully adaptive (for example, Opt y [13] routing algorithms. West first has roughly half the adaptiveness of a fully adaptive routing algorithm. Opt y has been proved to be optimal in the number of virtual channels required and in the number of restrictions placed on the use of these ....

....is able to reduce it effectively. Opt y also leads to an improvement in performance at high network traffic. However, the performance of West first is similar to that of X Y at low traffic, but is much worse at high traffic this is consistent with the observations made by Glass and Ni in [9]. 7.3.2 Considering router design complexity 0 10 20 30 40 50 60 0 1 2 3 4 5 6 Traffic (flits ns) XY:1 VCS West First XY:2 VCS XY:3 VCS Opt y 0 10 20 30 40 50 60 0 1 2 3 4 5 6 Traffic (flits ns) XY:1 VCS West First XY:2 VCS XY:3 VCS Opt y Figure 8: Latency Measures ....

C. Glass and L. M. Ni. The Turn Model for Adaptive Routing. In Proceedings of the 19 th Annual International Symposium on Computer Architecture, pages 278--287, 1992.

.... Finite Buffering Fault Detection but not Fault Tolerance Arbitrary delivery order means that the transmission order of messages between a particular source and destination are not preserved. This may arise because messages pass each other in the network (multipath routing (adaptivity) [9, 20], and virtual channels [7] or because the network state may be swapped and resumed in a way that does not preserve transmission order (timesharing [10] and process migration) Finite buffering in networks and machines means that flow control is generally necessary for correct execution. Most ....

....As we have seen in this study, some features which produce improved routing performance may incur unacceptable software costs. For example, a number of designs have proposed out of order delivery in order to improve network routing performance (randomization [18, 1] or adaptive routing [20, 7, 9]) Our results show clearly that a significant cost can be incurred for packet sequencing and reordering, so the benefits of out of order delivery for the network must be weighed against the software costs of such behavior. Because the software overhead is generally much larger than the hardware ....

L. Ni and C. Glass. The turn model for adaptive routing. In Proceedings of the International Symposium on Computer Architecture, 1992.

....communication operations, its development has been along a different direction than the conventional development of wormhole routed systems. In the past, wormhole routed systems started with e cube routing [12] Recently in the literature, various adaptive routing schemes have been proposed [5, 8, 11, 13, 15, 16, 19, 24, 31, 34]. Though today s commercial and experimental systems (Intel Paragon, Cray T3D, Ncube 3, Stanford DASH) use only e cube routing, a natural extension for these machines in the near future will be to go for adaptive routing. 1 In order to implement Hamiltonian path based routing, these machines need ....

....before, it consists of multiple destinations and gets routed in a piece wise manner from the source to the final destination. Let us assume the network supports a deadlock free routing scheme R for unicast message passing. This routing R could be e cube [12] planar adaptive [11] turn model [16], fully adaptive [13] or any other routing scheme. We identify R as the base routing. In order to build up the BRCP model, let us introduce the following definition. Definition 1 A path p is defined as a sequence of virtual channels (v 1 ffi v 2 ffi : ffi v i ) from a source node to a ....

[Article contains additional citation context not shown here]

C. J. Glass and L. Ni. The Turn Model for Adaptive Routing. In Proceedings of the International Symposium on Computer Architecture, pages 278--287, 1992.

....removed to resolve deadlock, the WARRP router implements some amount of selectivity by allowing only eligible packets to access deadlock buffers and route on the recovery lane. In addition to blockage and token capture, packet eligibility is also determined by two routing criteria: westward turns [13] and dateline [4] crossings. Previous work [4, 13] has shown that restricting turns made in routing and restricting routes over the dateline (e.g. wraparound links in tori) can prevent the formation of cyclic dependencies necessary for deadlock. It follows that, for deadlock to form, at least ....

....some amount of selectivity by allowing only eligible packets to access deadlock buffers and route on the recovery lane. In addition to blockage and token capture, packet eligibility is also determined by two routing criteria: westward turns [13] and dateline [4] crossings. Previous work [4, 13] has shown that restricting turns made in routing and restricting routes over the dateline (e.g. wraparound links in tori) can prevent the formation of cyclic dependencies necessary for deadlock. It follows that, for deadlock to form, at least one packet involved must make a turn or dateline ....

C. Glass and L. Ni, "The turn model for adaptive routing ", in Proceedings of the 19th Int'l Symposium on Computer Architecture, pages 278-287, May 1992.

....scheme requires n communication startups using single dimensional paths. Based on this approach, we present algorithms for both one to all and all to all broadcasting under singleand multiple port models. The scheme is shown to work on systems supporting both e cube and minimal adaptive routing [3, 5, 8, 10]. Using multiple dimensional paths, we show that the number of startups can be reduced further. The paper is organized as follows. We define single and multiple dimensional paths in Section 2 and show their differences with Hamiltonian path. Section 3 presents algorithms for one to all ....

C. J. Glass and L. Ni. The Turn Model for Adaptive Routing. In Proceedings of the International Symposium on Computer Architecture, pages 278--287, 1992.

....problem has two parts. First, to figure out a graph that represents the topology of the network and second, given a topology, to compute routes. We refer to the first problem as the mapping problem. There has been a lot of work in computing routes with specific properties from network topologies [73, 67, 22, 38]. One of the most important properties is that routes should be deadlock free. In this section we present a new method for solving the mapping problem, and we discuss how to solve the problem of deadlock free routes. In the following paragraphs we discuss some related work in solving the mapping ....

C. J. Glass and L. M. Ni. The turn model for adaptive routing. Journal of the ACM, 41(5):874--902, Sept. 1994.

....experimental results are provided in [33] The algorithms described so far use virtual channels to break deadlocks. An alternate approach is to simply restrict the number of paths available to packets, which in turn, reduces the number of virtual channels. The turn model, due to Glass and Ni [39], provides a systematic methodology for accomplishing this. The turn model eliminates deadlock by first identifying the turns a packet can make while traversing the network and the associated simple cycles, and then prohibiting one turn in each cycle. With cycles eliminated, packets can follow any ....

C. Glass and L. Ni, The Turn Model for Adaptive Routing, Journal of the ACM, 41(5):874--902, September 1994.

....transient loops and cause traffic deadlock while reprogramming the routers. When computing the new routing tables, the key problem is to avoid introducing potential routing loops that could lead to deadlock. We use the turn method and a combination of approaches similar to the ones described in [Glass92], Glass96] Vounckx94] and [Vounckx95] to guarantee that the routing is deadlock free. Although this approach is able to produce a deadlockfree rerouting for many of the common failure cases, a general solution is still an open research issue. Certain interconnect configurations that could ....

....to reflect the loss of memory lines cached either shared or exclusive in the failed portion of the machine. Deadlock free routing in the presence of failures Static table based wormhole routing based on the avoidance of routing cycles in the interconnection graph is a well understood topic [Glass92][Glass96] Unfortunately, routing in the presence of failures is still an open research issue. The difficulty arises from the fact that failures may change the interconnect topology. Vounckx94] and [Vounckx95] present an approach for rerouting around failed areas that can handle certain limited ....

C. Glass, and L. Ni. "The Turn Model for Adaptive Routing." In Proceedings of the 19th Annual International Symposium on Computer Architecture, pp.278-287, May 1992. 138

No context found.

C. Glass and L. Ni. The turn model for adaptive routing. J. ACM, 41:847--902, Sept. 1994.

No context found.

C.J. Glass and L.M. Ni. The turn model for adaptive routing. J. ACM, 41:847--902, Sept. 1994.

No context found.

C. J. Glass and L. M. Ni, "The turn model for adaptive routing," in 19th International Symposium on Computer Architecture,, May 1992, pp. 278--287.

No context found.

Glass, C. J. and Ni, L. M., "The turn model for adaptive routing, " in Proc. of 19th International Symp. on Computer Architecture, pp. 278--287, 1992.

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C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Journal of ACM, Vol. 41, No. 5, pp. 874--902, September 1994.

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Glass, C.; Ni, L. The Turn Model for Adaptive Routing. Journal of the Association for Computing Machinery, v. 41(5), Sep. 1994, pp. 874-902.

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