Optimizing Data Intensive Flows for Networks on Chips

Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple method to determine when and how much load to distribute to processors. We also propose a rigorous mathematical proof about the flow matrix optimal solution existence and that the solution is unique. The methodology introduced here is applicable to many interconnection networks and switching protocols (as an example we examine toroidal networks and hypercube networks in this paper). An important application is improving chip area and chip scalability for networks on chips processing divisible style loads.

[1]  Theron Lammie,et al.  A Linear Daisy Chain with Two Divisible Load Sources , 2005 .

[2]  Axel Jantsch,et al.  Designing 2D and 3D Network-on-Chip Architectures , 2013 .

[3]  Luca Benini,et al.  Networks on Chips : A New SoC Paradigm , 2022 .

[4]  Francis Y. L. Chin,et al.  Finding the Constrained Delaunay Triangulation and Constrained Voronoi Diagram of a Simple Polygon in Linear Time , 1999, SIAM J. Comput..

[5]  T.G. Robertazzi,et al.  Switching in sequential tree networks , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Bharadwaj Veeravalli,et al.  Scheduling Multisource Divisible Loads on Arbitrary Networks , 2010, IEEE Transactions on Parallel and Distributed Systems.

[7]  T.G. Robertazzi,et al.  Optimal divisible job load sharing for bus networks , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Debasish Ghose,et al.  Divisible Load Theory: A New Paradigm for Load Scheduling in Distributed Systems , 2004, Cluster Computing.

[9]  Maciej Drozdowski,et al.  THE PERFORMANCE LIMITS OF A TWO-DIMENSIONAL NETWORK OF LOAD-SHARING PROCESSORS , 2011 .

[10]  Jacek Blazewicz,et al.  Scheduling a Divisible Task in a Two-dimensional Toroidal Mesh , 1999, Discret. Appl. Math..

[11]  Wlodzimierz Glazek.  A Multistage Load Distribution Strategy for Three-Dimensional Meshes , 2004, Cluster Computing.

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

[13]  Henri Casanova,et al.  Parallel Algorithms , 2019, Design and Analysis of Algorithms.

[14]  Jacek Blazewicz,et al.  Scheduling Divisible Jobs on Hypercubes , 1995, Parallel Comput..

[15]  Christof Teuscher,et al.  Scalable Hybrid Wireless Network-on-Chip Architectures for Multicore Systems , 2011, IEEE Transactions on Computers.

[16]  Franziska Hoffmann,et al.  Spatial Tessellations Concepts And Applications Of Voronoi Diagrams , 2016 .

[17]  Thomas G. Robertazzi,et al.  Introduction to Computer Networking , 2017 .

[18]  Debasish Ghose,et al.  Scheduling Divisible Loads in Parallel and Distributed Systems , 1996 .

[19]  Dantong Yu,et al.  Data Intensive Grid Scheduling: Multiple Sources with Capacity Constraints , 2003 .

[20]  Xiaolin Li,et al.  Scheduling Divisible Workloads from Multiple Sources in Linear Daisy Chain Networks , 2007, PDPTA.

[21]  T.G. Robertazzi,et al.  Multi-Source Grid Scheduling for Divisible Loads , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[22]  Maciej Drozdowski,et al.  Scheduling divisible loads in a three-dimensional mesh of processors , 1999, Parallel Comput..

[23]  Thomas G. Robertazzi.  Processor equivalence for daisy chain load sharing processors , 1993 .

[24]  Henri Casanova,et al.  A realistic network/application model for scheduling divisible loads on large-scale platforms , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[25]  Ivan Stojmenovic,et al.  Voronoi diagram and convex hull based geocasting and routing in wireless networks , 2003, Proceedings of the Eighth IEEE Symposium on Computers and Communications. ISCC 2003.

[26]  José E. Moreira,et al.  Job Scheduling for the BlueGene/L System (Research Note) , 2002, Euro-Par.

[27]  Maciej Drozdowski,et al.  Scheduling for Parallel Processing , 2009, Computer Communications and Networks.

[28]  Miodrag Potkonjak,et al.  Exposure in wireless Ad-Hoc sensor networks , 2001, MobiCom '01.

[29]  Maciej Drozdowski,et al.  Performance limits of divisible load processing in systems with limited communication buffers , 2004, J. Parallel Distributed Comput..