X. Lin, P.K. Mckinley, and L.M. Ni, "The message flow model for routing in wormhole-routed networks," IEEE Trans. Parallel and Distributed Systems, 6(7): 755--760, July, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... one another in a number of ways, a common feature of these algorithms is that they all ensure freedom from deadlock by imposing a partial ordering on the set of channels using mechanisms such as channel dependency graphs [5] extended channel dependency graphs [6] or the message flow methodology [10]. An important question therefore is to determine the theoretical upper bound on the number of faults that can be tolerated using this partial ordering approach, or equivalently, the lower bound on the number of resources that must remain non faulty. This paper resolves this question by ....

....routing algorithm allows a message owning channel u to wait for channel v if v is owned by another message. 4 Dally and Seitz show [5] that a deterministic routing algorithm is deadlock free if and only if there is no cycle in the corresponding channel dependency graph. Duato [6] and Lin et al. [10] independently generalize this model by decoupling the last two conditions above. Specifically, these generalizations allow a message to be routed along available channels for which it might not be allowed to wait. A common feature of all of these models is that deadlock freedom is ensured by ....

[Article contains additional citation context not shown here]

X. Lin, P. K. McKinley, and L. M. Ni. The message flow model for routing in wormholerouted networks. In Proc. of the 1993 International Conference on Parallel Processing, volume I, pages 294--297, 1993.

....CH1 CH2 direct dependency indirect dependency (b) a) n3 n0 n1 Figure 7: a) Network for the example, b) its extended channel dependency graph. Alternative theoretical formulations of necessary and sufficient conditions for deadlock free adaptive routing are proposed by Lin, McKinley, and Ni [49] and Schwiebert and Jayasimha [63] 4.3 Performance Evaluation Routing algorithms are evaluated primarily by measures of average message latency and average system throughput. The hardware requirements in terms of the buffer size required per node and the number of virtual channels per physical ....

X. Lin, P. K. McKinley, and L. M. Ni, "The message flow model for routing in wormhole-routed networks," Int. Conf. on Parallel Processing, vol. I, pp. 294-297, 1993.

....implementing escape paths as dedicated virtual channels. Additionally, there has been a considerable interest on these issues. Several researchers developed alternative theories of deadlock avoidance, proposing sufficient conditions [1, 23, 31, 19] and necessary and sufficient conditions [15, 16, 29, 24] for deadlock free adaptive routing. Recently, several switch based interconnects like Autonet [28] Myrinet [3] and ServerNet [20] have been proposed to build networks of workstations for costeffective parallel computing. Typically, these switches support networks with irregular topologies. Such ....

X. Lin, P. K. McKinley and L. M. Ni, "The message flow model for routing in wormhole-routed networks," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 7, pp. 755--760, July 1995.

....11] and the Cray T3E router [30] are based on these techniques, implementing escape paths as dedicated virtual channels. Additionally, there has been a considerable interest on these issues. Several researchers developed alternative theories of deadlock avoidance, proposing sufficient conditions [1, 23, 31, 19] and necessary and sufficient conditions [15, 16, 29, 24] for deadlock free adaptive routing. Recently, several switch based interconnects like Autonet [28] Myrinet [3] and ServerNet [20] have been proposed to build networks of workstations for costeffective parallel computing. Typically, these ....

X. Lin, P. K. McKinley and L. M. Ni, "The message flow model for routing in wormhole-routed networks," in Proceedings of the 1993 International Conference on Parallel Processing, August 1993.

....Dally and Seitz [17] proved that an acyclic channel dependency graph is a necessary and sufficient condition for nonadaptive routing algorithms, determining what constitutes a necessary and sufficient condition for adaptive routing algorithms has remained an open problem. Lin, McKinley, and Ni [65] propose a proof technique based on the observation that a routing algorithm is deadlock free if none of the channels in the network can be held forever. If every message that uses a given channel is guaranteed to reach its destination, no matter which subsequent path (of those allowed by the ....

....directions. The message then switches to the second set of virtual channels and routes 48 first in all remaining positive directions and then all negative directions, waiting for busy channels when necessary. A fully adaptive hypercube routing algorithm has been proposed by several authors [23, 44, 65, 94]. This routing algorithm requires two virtual channels per physical channel. A message routes in dimension order along the first set of virtual channels. Each message also has the possibility of routing in any dimension that moves the message closer to the destination along the second set of ....

[Article contains additional citation context not shown here]

X. Lin, P. K. McKinley, and L. M. Ni. The Message Flow Model for Routing in Wormhole-Routed Networks. In International Conference on Parallel Processing, volume I, pages 294--297, 1993. 210

....Dally and Seitz proved that an acyclic channel dependency graph is a necessary and sufficient condition for nonadaptive routing algorithms [9] determining what constitutes a necessary and sufficient condition for adaptive routing algorithms has remained an open problem. Lin, McKinley, and Ni [23] propose a proof technique based on the observation that a rout3 ing algorithm is deadlock free if none of the channels in the network can be held forever. If every message that uses a given channel is guaranteed to reach its destination, no matter which path (of those allowed by the routing ....

....graph describes the order in which channels can be used. From Definition 12, however, it is clear that any deadlock configuration is based on the waiting channels, rather than the channels a message could use. The idea of waiting channels was introduced independently by Lin, McKinley, and Ni [23], however, the methodology presented in this paper is novel. The routing algorithm may allow a message to use a channel when the channel is free, even if the message is not permitted to wait for this channel when the channel is busy. This is our motivation for using the CWG, since it ignores ....

[Article contains additional citation context not shown here]

X. Lin, P. K. McKinley, and L. M. Ni. The Message Flow Model for Routing in WormholeRouted Networks. In International Conference on Parallel Processing, volume I, pages 294-- 297, 1993.

....Dally and Seitz proved that an acyclic channel dependency graph is a necessary and sufficient condition for nonadaptive routing algorithms [8] determining what constitutes a necessary and sufficient condition for adaptive routing algorithms has remained an open problem. Lin, McKinley, and Ni [22] propose a proof technique based on the fact that a routing algorithm is deadlock free if none of the channels in the network can be held forever. If every message that uses a given channel is guaranteed to reach its destination, no matter which path (of those allowed by the routing algorithm) the ....

....livelock free. 5 Necessary and Sufficient Condition Most techniques for proving that routing algorithms for wormhole routing are deadlock free require that the channel dependency graph be acyclic in some manner. The idea of waiting channels was introduced independently by Lin, McKinley, and Ni [22], however, the methodology used in this paper is novel. The channel dependency graph describes the order in which channels can be used. However, from definition 12, it is clear that any deadlock configuration is based on the waiting channels, rather than the channels a message could use. The ....

[Article contains additional citation context not shown here]

X. Lin, P. K. McKinley, and L. M. Ni. The Message Flow Model for Routing in WormholeRouted Networks. In International Conference on Parallel Processing, volume I, pages 294-- 297, 1993.

....adaptive and deterministic. Messages originate from adaptive channels. Once a message is on a deterministic channel, the message must be routed in dimension order and cannot re enter any adaptive channel. Actually, their method relies on a stronger constraint than Duato s algorithm. Lin et al.: [23] proposed a message flow model in wormhole routed networks, and applied it to develop adaptive routing algorithms. Any routing algorithm under this message flow model can be guaranteed to have deadlock freedom. In [13, 30] Gaughan and Yalamanchili proposed a misrouting backtracking protocol under ....

X. Lin, P. K. McKinley, and L. M. Li, "The message flow model for routing in wormhole-routed networks, " in Proc. of Int. Conf. on Parallel Processing, vol. 1, pp. I294--I297, Aug. 1993.

....acyclic channel dependency graph guarantees deadlock freedom was originally proposed as a necessary and sufficient condition for deadlock free routing algorithms. As previously mentioned, Duato showed that this claim does not hold for adaptive routing algorithms, however, it was generally believed [7, 8, 12, 15, 17] that an acyclic channel dependency graph was required for deadlock free oblivious routing. A counter example is shown in this paper, by presenting a deadlock free oblivious routing algorithm with cyclic dependencies. Finding a necessary and sufficient condition for deadlock free routing remained ....

....prove that an unreachable configuration can occur only when at least two of the dependencies in a configuration require the simultaneous use of some channel in the interconnection network. For this reason, they refer to unreachable configurations as false resource cycles. Lin, McKinley, and Ni [12] propose a proof technique based on the observation that a routing algorithm is deadlock free if none of the channels in the network can be held forever. If every message that uses a given channel is guaranteed to reach its destination, then that channel is called a deadlock immune channel. Since ....

LIN, X., MCKINLEY, P. K., AND NI, L. M. The Message Flow Model for Routing in Wormhole-Routed Networks. IEEE Transactions on Parallel and Distributed Systems 6, 7 (July 1995), 755--760.

....for a channel occupied by packet p j . All these proof techniques provide only a sufficient condition for deadlock free adaptive wormhole routing. Determining what constitutes a necessary and sufficient condition for adaptive routing algorithms has remained an open problem. Lin, McKinley, and Ni [22] propose a proof technique based on the fact that a routing algorithm is deadlock free if none of the channels in the network can be occupied forever. This proof technique was proposed as a necessary and sufficient condition, although Duato points out that only sufficiency is proved [12] ....

....We define a waiting buffer to be a buffer that a packet can wait to acquire when all the output buffers permitted by the routing relation are unavailable. A packet may have multiple waiting buffers. The idea of waiting channels was also introduced independently by Lin, McKinley, and Ni [22] for wormhole routing, however, the methodology used in this paper is novel. The buffer waiting graph (BWG) for a given routing algorithm is a directed graph, BWG = G(B;E) The vertices of the BWG are the buffers and the edges of the BWG are pairs of buffers (q 1 ; q 2 ) where a packet that ....

[Article contains additional citation context not shown here]

X. Lin, P. K. McKinley, and L. M. Ni. The Message Flow Model for Routing in Wormhole-Routed Networks. In International Conference on Parallel Processing, volume I, pages 294--297, 1993.

....2.4 Deadlock Deadlock is another important consideration in designing a network system, and one that has been the subject of numerous studies. Various avoidance techniques have been proposed, such as in Y in X in X out CPU M E M O R Y Routing Y out Buffers Flit Figure 1: Structure of a Node [LMN93, SS93, CK92, GN92b, SJ93, LH91, LGS92]. In general, deadlock avoidance is achieved either by restricting routing or by the addition of hardware such as virtual channels, as proposed in [DS87] A recent study describing a new model of deadlock freedom can be found in [Dua93] The issue of deadlock, however, is orthogonal to that of ....

X. Lin, P. K. McKinley, and L. M. Ni. The message flow model for routing in wormholerouted networks. In Proc. Int. Conf. on Parallel Processing, pages I294--I297, 1993.

....are allowed to hold many resources while requesting others. Designing deadlock free routing algorithms using few hardware facilities is a major problem for wormhole routed networks. Many papers have been devoted to the crucial problem of deadlock avoidance in wormholerouted networks. References [20, 21, 23, 25, 26, 27, 29, 30, 49, 52, 53, 69, 70] is a non exhaustive list of papers giving necessary and sufficient conditions for deadlock avoidance. Even if all these papers deal with wormhole routing, the hypotheses slightly differ from one paper to another. In particular, the routing function is not exactly defined in the same way in all ....

....sufficient conditions for a routing function to be deadlock free. These tools can be applied to other problems as multicasting (see [27, 53] All these conditions hold for any routing function which depends on the current node and the destination. Lin, McKinley and Ni independently produced in [52] other sufficient conditions based on the notion of deadlock immuneness for channels. All authors pointed out that the channel dependency graph of an adaptive and deadlockfree routing function can contain cycles. Duato then improved in [29] his results by enlarging the class of adaptive routing ....

[Article contains additional citation context not shown here]

X. Lin, P. McKinley, and L. Ni, The message flow model for routing in wormhole-routed networks, IEEE Transactions on Parallel and Distributed Systems, 6 (1995), pp. 755--759.

....acyclic channel dependency graph is necessary and sufficient for deadlock freedom [3] Much of the early research on wormhole routing has focused on the design of deadlock free routing algorithms using this result. The idea of channel waiting was introduced independently by Lin, McKinley, and Ni [10]. Nonadaptive routing algorithms can be characterized by functions of the form R : C Theta N Theta N C, where the input channel, belonging to the set of channels C, and the current and destination node, belonging to the set of nodes N , define an output channel on which to route the message. ....

X. Lin, P. K. McKinley, and L. M. Ni. The Message Flow Model for Routing in Wormhole-Routed Networks. IEEE Transactions on Parallel and Distributed Systems, 6(7):755-- 760, July 1995.

....Irregular switch interconnects make the problem even harder. Three philosophies have been used to develop deadlock free routing algorithms. One is based on deadlock prevention which never allows the formation of a cycle and is quite conservative. Another approach allows the existence of cycles [14, 15], but does provide a path to escape from the cycle. The third and more aggressive approach is based on deadlock detection [16] Practical, convincing, and meaningful quantitative evidence is needed to demonstrate the superiority of one approach over other approaches. For regular topologies like ....

X. Lin, P. McKinley, and L. Ni, "The message flow model for routing in wormhole-routed networks, " IEEE Transactions on Parallel and Distributed Systems, pp. 755 -- 760, July 1995.

....the CDG alone is of limited use in the development of deadlock free adaptive routing algorithms. Alternative methods have been developed to prove that certain adaptive unicast routing algorithms are deadlock free even though their CDGs contain cycles [7, 1] A new method, the message flow model [19], is used to prove that the deadlock free property holds for 1 PM routing and the algorithms described in later sections. It is assumed that every destination node can consume any incoming message. For a given routing algorithm, a channel (u; v) is deadlock immune if and only if, for any message ....

Lin, X., McKinley, P. K., and Ni, L. M. The message flow model for routing in wormholerouted networks. In Proc. of the 1993 International Conference on Parallel Processing (1993), vol. I, pp. 294--297.

....resources. Because blocked wormhole routed messages are not buffered and therefore cannot be removed from the network, cyclic dependencies with respect to channel usage must be avoided in order to avoid deadlock. Numerous deadlock free adaptive unicast routing methods have also been proposed [17, 18, 19, 20, 21, 22, 23]. One class of algorithms requires additional (virtual) channels [24] to support the adaptive routing [17, 18, 22] In this method, the multicomputer network is partitioned into several disjoint acyclic subnetworks, with each subnetwork containing channels that form all of the shortest paths from ....

....into several disjoint acyclic subnetworks, with each subnetwork containing channels that form all of the shortest paths from one node to some other nodes. Recently, several groups have developed adaptive routing algorithms that use only a modest number of virtual channels per physical channel [19, 21, 23]. Another method for adaptive unicast wormhole routing is the turn model [20] which involves analysis of the cycles that can be formed when messages change direction. Cycles are avoided by prohibiting certain turns, producing a partially adaptive routing algorithm that does not require virtual ....

X. Lin, P. K. McKinley, and L. M. Ni, "The message flow model for routing in wormholerouted networks," in Proc. of the 1993 International Conference on Parallel Processing, vol. I, pp. 294--297, 1993.

No context found.

X. Lin, P.K. Mckinley, and L.M. Ni, "The message flow model for routing in wormhole-routed networks," IEEE Trans. Parallel and Distributed Systems, 6(7): 755--760, July, 1995.

No context found.

X. Lin, P.K. Mckinley and L.M. Lin, The message flow model for routing in wormhole-routed networks, Proc. International Conference on Parallel Processing, pp. 294-297, 1993.

No context found.

X. Lin, P.K. McKinley, L.M. Ni, "The Message Flow Model for Routing in Wormhole-Routed Networks," IEEE T-Par. and Dist. Sys., Vol. 6, No. 7, July 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC