5.2 Switching Fabric Topologies

Transcription

1 5. Switching abric Topologies enes abrics recursive construction rearrangeably non-blocking (probably the lowest cost such) proof under circuit switching with switches anyan abrics one half of a enes internal blocking for non-uniform traffic patterns los Networks generalization of enes rearrangeably or strictly non-blocking, depending on midle-stage width at Trees like folded, bidirectional los Others meshes, tori, hypercubes, etc. S-5 - opyright University of rete

2 0 enes Network: Recursive efinition (N/) x (N/) non-blocking 5 (N/) x (N/) non-blocking 6 7 NxN enes network: rearrangeably non-blocking

3 0 x non-blocking x non-blocking ircuit onnections: Start from an input, use one of the subnets S-5 - opyright University of rete

4 S-5 - opyright University of rete ontinue from the brother port of the output, then the brother of the input x non-blocking x non-blocking

5 S-5 - opyright University of rete 5 Keep threading output and input switches, till closing or no-connection 5 5 x non-blocking x non-blocking

6 S-5 - opyright University of rete 6 Start a new thread (a) from an unconnected input, till completing all conn. 5 5 (a) x non-blocking x non-blocking

7 () Thread termination on input side ( of ) 0 subnet Threads always start on the input side If a thread terminates on the input side:... 5 all touched output switches are completely connected concerning touched input switches: 6 () if thread closes, all are complete, 7 subnet S-5 - opyright University of rete 7

8 () Thread termination on input side ( of ) 0 subnet Threads always start on the input side If a thread terminates on the input side:... (a) (a) (b) all touched output switches are completely connected concerning touched input switches: 5 () if thread closes (), all are complete, 6 7 (b) subnet () if thread terminates on half-used input (b): all touched input switches are complete, except the first one, which is half-covered by this thread S-5 - opyright University of rete 8

9 () Thread termination on output side 0 subnet Threads always start on the input side If a thread terminates on the output side: all touched output switches are completely connected 5 6 the first touched input switch is half-covered 7 subnet S-5 - opyright University of rete 9

10 0 () ompleting half-covered input switches subnet (a) 5 6 (b) (b) 7 (a) subnet New threads always start from a half-covered input switch, if there is one all threads cover all out-sw s they touch, in-sw s are covered in sequence S-5 - opyright University of rete 0

11 enes abric: Rearrangeably Non-locking 0 0 subnet (a)? 5? 6 (b) (b) 7 (a) subnet S-5 - opyright University of rete

12 Recursive onstruction of 6x6 enes Network out of x Switches step- sub-network step- step- sub-network banyan reverse banyan S-5 - opyright University of rete

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14 Reminder of topics discussed in class, which need to be included in future-year slides anyan fabric is like a set of binary trees with shared nodes. st/src ddress: in a banyan, a single field suffices for both, if each stage replaces one consumed destination-address bit with one corresponding source-address bit. Number of states of a fabric made of switch elements, internal blocking, and cost-minimality of non-blocking fabrics: banyan has (½ N log N) switches, and its number of states is less than (N!), hence it cannot route all permutations has internal blocking enes has (N (log N - ½)) switches, its number of states is more than (N!), it can route all permutations, and it is internally non-blocking the minimum-cost non-blocking fabric made of switches must have at least (log (N!)) switches, hence it must have a cost in-between the cost of the banyan and the cost of the enes. los Networks: N parameter is like internal speedup at Trees enes/los: bidirectional vs. unidirectional links: bidirectional links needed to carry flow control (backpressure) info. S-5 - opyright University of rete

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