Communicating sequential processes
Communicating sequential processes
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Performance Analysis of Multibuffered Packet-Switching Networks in Multiprocessor Systems
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On the communication throughput of buffered multistage interconnection networks
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Performance Analysis of Finite Buffered Multistage Interconnection Networks
IEEE Transactions on Computers
Communication Throughput of Interconnection Networks
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
On the Semantics of Multistage Interconnection Networks
SOFSEM '96 Proceedings of the 23rd Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Banyan networks for partitioning multiprocessor systems
ISCA '73 Proceedings of the 1st annual symposium on Computer architecture
Virtual Shared Memory: A Survey of Techniques and Systems
Virtual Shared Memory: A Survey of Techniques and Systems
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Multistage interconnection networks (MINs) have a number of applications in many areas, for example in parallel computing systems or high-speed communication networks. In the paper we define Markov chains describing several models of packet flow through the buffered MIN with a butterfly interconnection structure and 2×2 switching elements. We develop a notation together with a mathematical framework enabling to prove certain results relating the models. Moreover, we show that all considered Markov chains are ergodic and discuss relationships between stationary distributions. The important novelty is that our approach is compositional, which allows to keep the complexity of description of a very complicated network's behaviour on a reasonable and tractable level. Considerations are mostly independent of specific network topology and routing protocol, hence we expect our method to be applicable also in other contexts for stochastic models of massively parallel systems.