An End-to-End Approach to the Resequencing Problem
Journal of the ACM (JACM)
Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Sharp approximation models of adaptive routing in mesh networks (preliminary report)
Proc. of the international seminar on Teletraffic analysis and computer performance evaluation
The Distribution of Waiting Times in Clocked Multistage Interconnection Networks
IEEE Transactions on Computers
The Dependence of Sojourn Times in Closed Queueing Networks
Proceedings of the International Workshop on Computer Performance and Reliability
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Banyan networks for partitioning multiprocessor systems
ISCA '73 Proceedings of the 1st annual symposium on Computer architecture
Efficient schemes for parallel communication
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Randomized parallel communication (Preliminary Version)
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A conceptual approach to general purpose parallel computer architecture
A conceptual approach to general purpose parallel computer architecture
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
The representation of multistage interconnection networks in queuing models of parallel systems
Journal of the ACM (JACM)
A Markov chain approximation for the analysis of banyan networks
SIGMETRICS '91 Proceedings of the 1991 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Design and analysis of buffered crossbars and banyans with cut-through switching
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
The efficiency of greedy routing in hypercubes and butterflies
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Traffic studies of unbuffered Delta networks
IBM Journal of Research and Development
Randomized routing with shorter paths
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Randomized Routing with Shorter Paths
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Computers
Journal of the ACM (JACM)
Using the Dual Path Property of Omega Networks to Obtain Conflict-Free Message Routing
IEEE Transactions on Parallel and Distributed Systems
Partitioning Message Patterns for Bundled Omega Networks
IEEE Transactions on Parallel and Distributed Systems
Providing guaranteed rate services in the load balanced Birkhoff-von Neumann switches
IEEE/ACM Transactions on Networking (TON)
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Closed-form analysis of end-to-end network delay with Markov-modulated Poisson and fluid traffic
Computer Communications
Load balanced Birkhoff-von Neumann switches, part I: one-stage buffering
Computer Communications
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Parallel communication algorithms and networks are central to large-scale parallel computing and, also, data communications. This paper identifies adverse source-destination traffic patterns and proposes a scheme for obtaining relief by means of randomized routing of packets on simple extensions of the well-known omega networks. Valiant and Aleliunas have demonstrated randomized algorithms, for a certain context which we call nonrenewal, that complete the communication task in time O(log N) with overwhelming probability, where N is the number of sources and destinations. Our scheme has advantages because it uses switches of fixed degree, requires no scheduling, and, for the nonrenewal context, is as good in proven performance. The main advantage of our scheme comes when we consider the renewal context in which packets are generated at the sources continually and asynchronously. Our algorithm extends naturally from the nonrenewal context. In the analysis in the renewal context we, first, explicitly identify the maximum traffic intensities in the internal links of the extended omega networks over all source-destination traffic specifications that satisfy loose bounds. Second, the benefits of randomization on the stability of the network are identified. Third, exact results, for certain restricted models for sources and transmission, and approximate analytic results, for quite general models, are derived for the mean delays. These results show that, in the stable regime, the maximum mean time from source to destination is asymptotically proportional to log N. Numerical results are presented.