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
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
