Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 221Lecture 25: Interconnection Networks• Topics: communication latency, centralized and decentralized switches, routing, deadlocks (Appendix E)• Review session, Wednesday Dec 1st, 10-12, LCR (MEB 3147)• Final exam reminders• Come early, 10:35 – 12:15• Same rules as first midterm, open books/notes/…, • Can use calculators and laptops (no search or internet)• 20% from first midterm material; remaining 80% from caches, multiprocs, TM• 20% new problems• Attempt every question2Topologies• Internet topologies are not very regular – they grew incrementally• Supercomputers have regular interconnect topologies and trade off cost for high bandwidth• Nodes can be connected with centralized switch: all nodes have input and output wires going to a centralized chip that internally handles all routing decentralized switch: each node is connected to a switch that routes data to one of a few neighbors3Centralized Crossbar SwitchP1P2P3P4P5P6P7P0Crossbarswitch4Centralized Crossbar SwitchP1P2P3P4P5P6P7P05Crossbar Properties• Assuming each node has one input and one output, a crossbar can provide maximum bandwidth: N messages can be sent as long as there are N unique sources and N unique destinations• Maximum overhead: WN2 internal switches, where W is data width and N is number of nodes• To reduce overhead, use smaller switches as building blocks – trade off overhead for lower effective bandwidth6Switch with Omega NetworkP1P2P3P4P5P6P7P0000001010011100101110111 1111101011000110100010007Omega Network Properties• The switch complexity is now O(N log N)• Contention increases: P0  P5 and P1  P7 cannot happen concurrently (this was possible in a crossbar)• To deal with contention, can increase the number of levels (redundant paths) – by mirroring the network, we can route from P0 to P5 via N intermediate nodes, while increasing complexity by a factor of 28Tree Network• Complexity is O(N)• Can yield low latencies when communicating with neighbors• Can build a fat tree by having multiple incoming and outgoing linksP0 P3P2P1 P4 P7P6P59Bisection Bandwidth• Split N nodes into two groups of N/2 nodes such that the bandwidth between these two groups is minimum: that is the bisection bandwidth• Why is it relevant: if traffic is completely random, the probability of a message going across the two halves is ½ – if all nodes send a message, the bisection bandwidth will have to be N/2• The concept of bisection bandwidth confirms that the tree network is not suited for random traffic patterns, but for localized traffic patterns10Distributed Switches: Ring• Each node is connected to a 3x3 switch that routes messages between the node and its two neighbors• Effectively a repeated bus: multiple messages in transit• Disadvantage: bisection bandwidth of 2 and N/2 hops on average11Distributed Switch Options• Performance can be increased by throwing more hardware at the problem: fully-connected switches: every switch is connected to every other switch: N2 wiring complexity, N2 /4 bisection bandwidth• Most commercial designs adopt a point between the two extremes (ring and fully-connected): Grid: each node connects with its N, E, W, S neighbors Torus: connections wrap around Hypercube: links between nodes whose binary names differ in a single bit12Topology ExamplesGridHypercubeTorusCriteria Bus Ring 2Dtorus 6-cube Fully connectedPerformanceBisection bandwidthCostPorts/switchTotal links13Topology ExamplesGridHypercubeTorusCriteria Bus Ring 2Dtorus 6-cube Fully connectedPerformanceBisection bandwidth1 2 16 32 1024CostPorts/switchTotal links 131285192725664208014k-ary d-cube• Consider a k-ary d-cube: a d-dimension array with k elements in each dimension, there are links between elements that differ in one dimension by 1 (mod k)• Number of nodes N = kdNumber of switches :Switch degree :Number of links :Pins per node :Avg. routing distance:Diameter :Bisection bandwidth :Switch complexity :Should we minimize or maximize dimension?15k-ary d-Cube• Consider a k-ary d-cube: a d-dimension array with k elements in each dimension, there are links between elements that differ in one dimension by 1 (mod k)• Number of nodes N = kdNumber of switches :Switch degree :Number of links :Pins per node :Avg. routing distance:Diameter :Bisection bandwidth :Switch complexity :N2d + 1Nd2wdd(k-1)/2d(k-1)2wkd-1Should we minimize or maximize dimension?(2d + 1)2(with no wraparound)16Routing• Deterministic routing: given the source and destination, there exists a unique route• Adaptive routing: a switch may alter the route in order to deal with unexpected events (faults, congestion) – more complexity in the router vs. potentially better performance• Example of deterministic routing: dimension order routing: send packet along first dimension until destination co-ord (in that dimension) is reached, then next dimension, etc.17Deadlock• Deadlock happens when there is a cycle of resource dependencies – a process holds on to a resource (A) and attempts to acquire another resource (B) – A is not relinquished until B is acquired18Deadlock ExamplePackets of message 1Packets of message 2Packets of message 3Packets of message 44-way switchOutput portsEach message is attempting to make a left turn – it must acquire anoutput port, while still holding on to a series of input and output portsInput ports19Deadlock-Free Proofs• Number edges and show that all routes will traverse edges in increasing (or decreasing) order – therefore, it will be impossible to have cyclic dependencies• Example: k-ary 2-d array with dimension routing: first route along x-dimension, then along y1 2 32 1 01 2 32 1 01 2 32 1 01 2 32 1 017181918171620Breaking Deadlock I• The earlier proof does not apply to tori because of wraparound edges• Partition resources across multiple virtual channels• If a wraparound edge must be used in a torus, travel on virtual channel 1, else travel on virtual channel 021Breaking Deadlock II• Consider the eight possible turns in a 2-d array (note that turns lead to cycles)• By preventing just two turns, cycles can be eliminated• Dimension-order routing disallows