Interconnection Networks Contd. L.N. Bhuyan Partly from Berkeley Notes. More Static Networks: Linear Arrays and Rings. Linear Array Diameter? Average Distance? Bisection bandwidth? Route A -> B given by relative address R = B-A Torus?
Partly from Berkeley Notes
Ex: Intel Paragon (2D), SGI Origin (Hypercube), Cray T3E (3DMesh)
correct dimensions in order
N = 26 nodesS = (sn-1 sn-2… si …s2s1s0)D = (dn-1 dn-2… di… d2d1d0)E-cube routing For i=0 to n-1 Compare si and di Route along i dimension if they differ.Distance = Hamming distance between S and D = the no. of dimensions by which S and D differ.Diameter = Maximum distance = n = log2 N = Dimension of the hypercubeNo. of alternate parts = nFault tolerance = (n-1) = O(log2 N)
Routing in Hypercube
- Shared Bus: The bus arbiter connects a processor to a memory
- Crossbar: Consists of a lot of switching elements, which can be enabled to connect many inputs to many outputs simultaneously
- Multistage Network: Consists of several stages of switches that are enabled to get connections
- The nodes in static networks (like Mesh) also consist of dynamic crossbars
N**2 switches => Cost O(N**2)
Time taken by the arbiter = O(N**2)
Multiplexors are controlled from controller
A network consisting of multiple stages of crossbar switches has the following properties.
Omega Network and Self Routing
Conflict, less BW than Crossbar, but cost effective;
Q. Compare the efficiency of store-and-forward (packet switching) vs. wormhole routing for transmission of a 20 bytes packet between a source and destination, which are d-nodes apart. Each node takes 0.25 microsecond and link transfer rate is 20 MB/sec.
Answer: Time to transfer 20 bytes over a link = 20/20 MB/sec = 1 microsecond.
Packet switching: # nodes x (node delay + transfer time)= d x (.25 + 1) = 1.25 d microseconds
Wormhole: (# nodes x node delay) + transfer time
= 0.25 d + 1
Book: For d=7, packet switching takes 8.75 microseconds vs. 2.75 microseconds for wormhole routing