Omega example
- 1. 1 Omega Network • The omega network is another example of a banyan multistage interconnection network that can be used as a switch fabric • The omega differs from the delta network in the pattern of interconnections between the stages • The omega MIN uses the “perfect shuffle”
- 2. 2 Perfect Shuffle • The interconnections between stages are defined by the logical “rotate left” of the bits used in the port ids • Example: 000 ---> 000 ---> 000 ---> 000 • Example: 001 ---> 010 ---> 100 ---> 001 • Example: 011 ---> 110 ---> 101 ---> 011 • Example: 111 ---> 111 ---> 111 ---> 111
- 3. 3 8 x 8 OMEGA NETWORK 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7
- 4. 4 Self Routing • Omega network has self-routing property • The path for a cell to take to reach its destination can be determined directly from its routing tag (i.e., destination port id) • Stage k of the MIN looks at bit k of the tag • If bit k is 0, then send cell out upper port • If bit k is 1, then send cell out lower port • Works for every possible input port (really!)
- 5. 5 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 4 Example of Self Routing Cell destined for output port 4 (= 100 )2
- 6. 6 Example of Self Routing Cell destined for output port 4 (= 100 )2 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 4
- 7. 7 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 )2 4
- 8. 8 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 )2 4
- 9. 9 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 )2 4
- 10. 10 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 )2 4
- 11. 11 1 2 3 4 6 7 5 0 0 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 )2 4
- 12. 12 Path Contention • The omega network has the problems as the delta network with output port contention and path contention • Again, the result in a bufferless switch fabric is cell loss (one cell wins, one loses) • Path contention and output port contention can seriously degrade the achievable throughput of the switch
- 30. 30 A Solution: Batcher Sorter • One solution to the contention problem is to sort the cells into monotonically increasing order based on desired destination port • Done using a bitonic sorter called a Batcher • Places the M cells into gap-free increasing sequence on the first M input ports • Eliminates duplicate destinations