Short Summery Dynamic networks Omega network Static networks - - PowerPoint PPT Presentation

• Dynamic networks

– Omega network

• Static networks

– Main topologies: star, ring, mesh, tree, hypercube – Hypercube properties

• partitioning
• Hamming distance
• subcubes

Short Summery

Metrics for Static Networks

• Diameter (D): the max distance between any two

processors

– 1 for completely connected network, p/2 for ring, 2(√p - 1) for 2D mesh, 2 √p/2 for 2D wraparound mesh, logp for a hypercube, 2log((p + 1)/2) for a tree

• Connectivity is a way of measuring the

multiplicity of paths between any two processors

– arc connectivity - the min number of links that need to be removed to break the network in two

• 1 for linear arrays, star and tree networks, 2 for rings and 2D

meshes, 4 for 2D wraparound meshes

• Bisection Width is the min number of links that

need to be removed to partition the network in two equal halves

– p2/4 for a complete connected network, 2 for rings, √p for 2D mesh, 2√p for 2D wraparound mesh, p/2 for a hypercube

• Bisection Bandwidth is the min bandwidth

between any two halves of the network with the same # of nodes

– equal to Bisection Width times the channel bandwidth

Metrics for Static Networks (2)

Evaluation: cost metrics

• Number of links

– cost is proportional to copper, drive logic, etc. – one way is in terms of the number of communication links or the number of wires required by the network.

Interconnect comparison

Routing in static networks

• The routing mechanism determines the path that a message takes

to get from source to destination

• The routing has important performance implications
• Example: dimensional-ordered routing

– called XY-routing in meshes, E-cube routing in hypercubes

Routing in static networks (2)

• General classifications for routing mechanisms

– minimal vs. nonminimal

• shortest path vs. any path that can avoid congestion points

– deterministic vs. adaptive

• predetermined route vs. scheme using current network state

information

• example of deterministic routing is dimensional-ordered

routing

• Switching techniques also affect performance

– Store-and-forward vs. cut-through routing

• buffering of entire message at the switch vs. early forwarding
• cut-through routing flow-control digits or flits

• Startup time (ts): time required to prepare the

message on the sender node

• Per-hop time (switch latency) (th): time the

header takes to traverse a link

• Per-word transfer time (tw): if r is the link

bandwidth in word/sec, the tw = 1/r

Communication latency components

Switching techniques

• Store-and-forward

– tcomm= ts + l(th + mtw)

• Cut-through

– tcomm = ts + lth + mtw

• Wormhole routing is the

most common version of cut-through routing

• A message is broken to

fixed size units – Flow Control digits (flits)

Deadlock in cut-through routing

Packet Routing

• The message is broken into packets, and packets

are assembled with their error, routing and sequencing fields. tcomm = ts + mtw1 + lth + tw2(r+s)+(m/r - 1) tw2(r+s)

Network is capable of communicating one word every tw2 seconds.

tcomm = ts + mtw + lth tw = tw1 + tw2(1 + s/r)

Improving Communication Time

• Communicate in bulk
• Minimize the volume of data
• Minimize distance of data transfer

tcomm = ts + mtw + lth