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Computer Architecture II 1 Computer architecture II Network topologies

# Computer Architecture II 1 Computer architecture II Network topologies

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• Slide 1
• Computer Architecture II 1 Computer architecture II Network topologies
• Slide 2
• Computer Architecture II 2 Plan for today Scalable interconnection networks Basic concepts, definitions Topologies Switching Routing Performance
• Slide 3
• Computer Architecture II 3 Outline Basic concepts, definitions Topologies Switching Routing Performance
• Slide 4
• Computer Architecture II 4 Formalism Graph G=(V,E) V : switches and nodes E: communication channels (edges) e V V Route: (v 0,..., v k ) path of length k between nodes 0 und k, where (v i,v i+1 ) E Routing distance Diameter: the maximal route length between two nodes Average distance Degree: number of input (output) channels of a node Bisection width: minimal number of parallel connections that saturates the network
• Slide 5
• Computer Architecture II 5 What characterizes a network? Bandwidth (offered bandwidth) b = wf where width w (in bytes) and signaling rate f = 1/t (in Hz) Latency Time a message travels between two nodes Throughput (delivered bandwidth) How much from the offered bandwidth is effectively used
• Slide 6
• Computer Architecture II 6 What characterizes a network? Topology physical interconnection structure of the network graph Routing Algorithm restricts the set of paths that messages may follow many algorithms with different properties Switching Strategy how data in a message traverses a route circuit switching vs. packet switching Flow Control Mechanism when a message or portions of it traverse a route what happens when traffic is encountered?
• Slide 7
• Computer Architecture II 7 Goals Latency as small as possible High Throughput As many concurrent transfers as possible Bisection width gives the potential number of parallel connection Cost as low as possible
• Slide 8
• Computer Architecture II 8 Bus (e.g. Ethernet) Degree = 1 diameter = 1 No routing necessary bisection width = 1 CSMA/CD-protocol limited bus length 12345 Simplest and cheapest dynamic network
• Slide 9
• Computer Architecture II 9 Complete graph degree= n-1 too expensive for big nets diameter = 1 bisection width= n/2 n/2 12345 Static Network Connection between each Pair of nodes When cutting the network into two halves, each node has connection to n/2 other nodes. There are n/2 such Nodes.
• Slide 10
• Computer Architecture II 10 Ring degree= 2 diameter = n/2 slow for big networks bisection width = 2 12345 Static network A node i linked with nodes i+1 and i-1 modulo n. Examples: FDDI, SCI, FiberChannel Arbitrated Loop, KSR1
• Slide 11
• Computer Architecture II 11 For d dimensions degree= d diameter = d ( d n 1) bisection width = ( d n) d1 d-dimensional grid 1,1 1,21,3 2,12,22,3 3,1 3,23,3 Cray T3D und T3E. Static network
• Slide 12
• Computer Architecture II 12 Crossbar fast and expensive (n 2 switches) Most: Processor x memory degree= 1 diameter = 2 bisection width = n/2 Ex: 4x4, 8x8, 16x16 1 1 2 3 Dynamic network 23 switch
• Slide 13
• Computer Architecture II 13 0011 Hypercube (1) Hamming-Distance = number of bits in which the binary representation of two numbers differ Two nodes are connected if the Hamming distance is 1 Routing from x to y by decreasing the Hemming distance 0000 0001 0010 0000 0001 0011 0010 0100 0101 0111 0110 Static network
• Slide 14
• Computer Architecture II 14 Hypercube (2) degree= k diameter = k bisection width = n/2 Two (k-1)-hypercubes are linked through n/2 edges to form a k-hypercube 0000 0001 0011 0010 0000 0001 0011 0010 0100 0101 0111 0110 Intel iPSC/860, SGI Origin 2000 k dimensions, n= 2 k nodes
• Slide 15
• Computer Architecture II 15 Building block: 2x2 Shuffle Perfect Shuffle Target = cyclic left shift Omega-Network (1) 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
• Slide 16
• Computer Architecture II 16 Omega-Network (2) Log 2 n levels of of 2x2 Shuffle building block dynamic network Level i looks at bit i If 0 goes up If 1 goes down See example for 100 sending to 110 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
• Slide 17
• Computer Architecture II 17 Omega-Network (3) n nodes, (n/2) log 2 n building blocks degree= 2 for nodes, 4 for building blocks diameter = log 2 n bisection width = n/2 for a random permutation, n/2 messages are expected to cross the network in parallel Extremes If all the nodes want to send to 0, only one message in parallel If each sends a message to himself n messages in parallel
• Slide 18

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