L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for DeadlockFree Wormhole Routing. Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 channel are also used in comparing ....

L. Schwiebert and D. N. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing," Jou. of Parallel and Distributed Computing, 32, pp. 103-117, 1996.

....along with the condition that messages are not preempted makes cyclic dependencies and deadlock possible. 2.1 Depicting Deadlocks We use channel wait for graphs (CWGs) 6] to model resource dependencies within interconnection networks. Although similar to dependency graphs used in previous work [3, 7, 8], these graphs depict network state reflecting resource allocations and requests existing at a particular point in time, not the resource allocations allowed by the routing algorithm. Hence, in this context, CWGs depicting the entire network state are not necessarily connected. Figures 1 through 4 ....

....of true deadlocks. In contrast, our work presents frequencies of actual deadlock as well as their characteristics as they relate to key network parameters. CWGs and similar constructs have previously been used to statically represent connections allowed by deadlock avoidance based algorithms [3, 8]. In contrast, we use these graphs to model dynamic resource allocation in unrestricted routing, and to precisely define and detect deadlocks. A summary of work characterizing deadlocks as knots in generalized resource graphs intended to describe deadlocks in operating systems is presented in [9] ....

Loren Schwiebert, D.N. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing", Journal of Parallel and Distributed Computing, 32, 103-117 (1996).

....The analysis work presented in this paper assumes the followings: ffl a wormhole routing network using a deadlock free routing that guarantees no cycle of link dependency. No cycle of link dependency is a sufficient, but not necessary, condition for deadlock free routing, as discussed in [12, 13]. ffl source routing. Routing is made by the source host and cannot be changed by switches (i.e. no deflection or adaptive routing) ffl only one finite size buffer at each input port of a switch. Also, worms cannot share a link through interleaving (i.e. multiple virtual channels are not ....

L. Schwiebert and D.N. Jayasimha. "A Necessary and Sufficient Condition for Deadlock-free Wormhole Routing". Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.

....network is needed. We use channel wait for graphs (CWGs) for this purpose [8] Channel wait for graphs are used to depict network state reflecting resource allocations and requests existing at a particular point in time as opposed to resource allocations allowed by the routing algorithm as in [3, 9, 10]. In this context, channel wait forgraphs are not necessarily connected. Figures 1 through 3 show examples of messages being routed in k ary n cube wormhole networks, along with the corresponding CWGs. In the network illustrations (Figures 1a, 2a, and 3a) the source and destination nodes of ....

Loren Schwiebert, D.N. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing", Journal of Parallel and Distributed Computing, 32, 103-117 (1996).

.... can be expressed in terms of the space needed to maintain the channel wait for graph, cycle list, and deadlock list as follows: 5 Related Work Static channel dependency and wait for graphs which represent connections allowed by routing algorithms have been presented in previous work [7, 8, 12]. In contrast, the channel wait for graphs presented in this work are dynamic and represent the state of resource allocations and requests existing within a network at a given point in time. While the dependency and wait for D C M c cwg size Max vc c 1 ( Max m c 2 ( Max fr c ....

Loren Schwiebert, D.N. Jayasimha, "A Necessary and Sufficient Condition for DeadlockFree Wormhole Routing", Journal of Parallel and Distributed Computing, 32, 103-117 (1996).

No context found.

L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for DeadlockFree Wormhole Routing. Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.

....that relies on routing restrictions to prevent deadlock. The use of the channel waiting graph simplifies the task of proving deadlock freedom. We first describe the proof technique as it applies to wormhole routing. The application of our proof technique to wormhole routing is to be published in [90]. In Section 4.1, we present definitions used in the proofs and discussion of our technique. In Section 4.2, we briefly explain why livelock and deadlock are independent. We then present a simple sufficient condition for deadlock freedom in Section 4.3. The necessary and sufficient condition is ....

L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing. Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.

....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 ....

....among these dependencies. This is possible because the actual dependencies at any instance rely on the dynamic interaction among messages in the network at that time, but the channel dependencies are static, in that they are determined by the routing algorithm. Schwiebert and Jayasimha [15, 17] 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 ....

[Article contains additional citation context not shown here]

SCHWIEBERT, L., AND JAYASIMHA, D. N. A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing. Journal of Parallel and Distributed Computing 32, 1 (January 1996), 103--117.

....to demonstrate the ease with which our proof technique can be applied. 2 Previous Work We briefly review the existing techniques for proving deadlock freedom. For nonminimal routing, the issue of livelock freedom also arises, however, livelock freedom and deadlock freedom are independent issues [28]. For store and forward routing, most routing algorithms have used the proof technique proposed by Gunther [19] to prove deadlock freedom. This methodology requires an acyclic ordering of the buffers. Toueg and Steiglitz [30] have shown that this is necessary and sufficient for nonadaptive ....

....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] Recently, we have proposed a necessary and sufficient condition for a rich class of wormhole routing algorithms [28]. Duato [12] has independently proposed a necessary and sufficient condition for a restricted class of adaptive wormhole routing algorithms. In this paper, we propose a necessary and sufficient condition for deadlock freedom that can be applied regardless of the switching technique employed. 3 ....

[Article contains additional citation context not shown here]

L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing. Technical Report OSU-CISRC-4/94-TR22, The Ohio State University, April 1994. Revised December 10, 1994. Accepted for publication in the Journal of Parallel and Distributed Computing.

....mechanisms. The previous work done by two authors of this paper provides the most general solution proposed so far. The solution, which works for routing relations of the form R : C Theta N Theta N P (C) introduces two new notions: the channel waiting graph (CWG) and False Resource Cycles [SJ96]. The CWG, which is derived on the basis of waiting instead of channel usage, omits most channel dependencies that cannot lead to a deadlock configuration. Consequently, the proofs of deadlock freedom become natural and straightforward. The CWG is a static graph, however, and the dependencies ....

....output channel m i could use at this node is busy. For any output channel available to m i that is also available to the source, assume the source has injected a message that is occupying this channel. If RA is not suffix closed (the notions of suffix closure and prefix closure are defined in [SJ96], however, it is possible that some of the output channels available to m i can be used only by messages arriving on the input channel used by m i . For these output channels, assume that a previous message, m j , used this input channel and was forwarded on one of the output channels. In ....

L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing. Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.

....mechanisms. Previous work done by two authors of this paper provides the most general solution proposed so far. The solution, which works for routing functions of the form R : C Theta N Theta N P (C) introduces two new notions: the channel waiting graph (CWG) and False Resource Cycles [19]. The CWG, which is derived on the basis of channel waiting instead of channel usage, omits most channel dependencies that cannot lead to a deadlock configuration. Consequently, the proofs of deadlock freedom become natural and straightforward. The CWG is a static graph, however, and the ....

....output channel m i could use at this node is busy. For any output channel available to m i that is also available to the source, assume the source has injected a message that is occupying this channel. If RA is not suffixclosed (the notions of suffix closure and prefix closure are defined in [19]) however, it is possible that some of the output channels available to m i can be used only by messages arriving on the input channel used by m i . For these output channels, assume that a previous message, m j , used this input channel and was forwarded on one of the output channels. In ....

L. Schwiebert and D. N. Jayasimha. A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing. Journal of Parallel and Distributed Computing, 32(1):103--117, January 1996.

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