The turn model for adaptive routing

We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing, n-dimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing algorithms are described for 2D meshes, n-dimensional meshes, k-ary n-cubes, and hypercubes. Simulations of partially adaptive and nonadaptive routing algorithms for 2D meshes and hypercubes show that which algorithm has the lowest latencies and highest sustainable throughput depends on the pattern of message traffic. For nonuniform traffic, partially adaptive routing algorithms perform better than non-adaptive ones.

[1]  Smaragda Konstantinidou.  Adaptive, minimal routing in hypercubes , 1990 .

[2]  William J. Dally,et al.  Performance Analysis of k-Ary n-Cube Interconnection Networks , 1987, IEEE Trans. Computers.

[3]  Anoop Gupta,et al.  The directory-based cache coherence protocol for the DASH multiprocessor , 1990, ISCA '90.

[4]  Daniel H. Linder,et al.  An Adaptive and Fault Tolerant Wormhole Routing Strategy for k-Ary n-Cubes , 1994, IEEE Trans. Computers.

[5]  Lionel M. Ni,et al.  Adaptive routing in mesh-connected networks , 1992, [1992] Proceedings of the 12th International Conference on Distributed Computing Systems.

[6]  Chris R. Jesshope,et al.  Adaptive, low latency, deadlock-free packet routing for networks of processors , 1989 .

[7]  W. J. Dally,et al.  Finite-grain message passing concurrent computers , 1988, C3P.

[8]  Alain J. Martin,et al.  The architecture and programming of the Ametek series 2010 multicomputer , 1988, C3P.

[9]  Xiaola Lin,et al.  Deadlock-free multicast wormhole routing in multicomputer networks , 1991, ISCA '91.

[10]  William J. Dally,et al.  The J-Machine: System Support for Actors , 1988 .

[11]  Lionel M. Ni,et al.  Fault-tolerant wormhole routing in meshes , 1993, FTCS-23 The Twenty-Third International Symposium on Fault-Tolerant Computing.

[12]  Leonard Kleinrock,et al.  Virtual Cut-Through: A New Computer Communication Switching Technique , 1979, Comput. Networks.

[13]  Anant Agarwal,et al.  APRIL: a processor architecture for multiprocessing , 1990, ISCA '90.

[14]  Shekhar Y. Borkar,et al.  iWarp: an integrated solution to high-speed parallel computing , 1988, Proceedings. SUPERCOMPUTING '88.

[15]  Theodore R. Bashkow,et al.  A large scale, homogeneous, fully distributed parallel machine, I , 1977, ISCA '77.

[16]  William J. Dally,et al.  Deadlock-Free Message Routing in Multiprocessor Interconnection Networks , 1987, IEEE Transactions on Computers.