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

Short Summery • Dynamic networks – Omega network • Static networks – Main topologies: star, ring, mesh, tree, hypercube – Hypercube properties • partitioning • Hamming distance • subcubes

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, log p 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

Metrics for Static Networks (2) • Bisection Width is the min number of links that need to be removed to partition the network in two equal halves – p 2 /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

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

Communication latency components • Startup time ( t s ): time required to prepare the message on the sender node • Per-hop time ( switch latency) ( t h ): time the header takes to traverse a link • Per-word transfer time ( t w ): if r is the link bandwidth in word/sec, the t w = 1/ r

Switching techniques • Store-and-forward – t comm = t s + l ( t h + mt w ) • Cut-through – t comm = t s + lt h + mt w • 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. t comm = t s + mt w1 + lt h + t w2 (r+s)+(m/r - 1) t w2 (r+s) Network is capable of communicating one word every t w2 seconds. t comm = t s + mt w + lt h t w = t w1 + t w2 (1 + s/r)

Improving Communication Time • Communicate in bulk • Minimize the volume of data • Minimize distance of data transfer t comm = t s + mt w + lt h