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Optical Interconnection Networks Design, Analysis, and Simulation Study of Optical Interconnection Networks M. S. Thesis Defense Presentation by Ch’ng Shi Baw Advisor: Prof. Mark A. Franklin 20 April 1999 Baw M.S. Thesis Presentation. Slide 1 Optical Interconnection Networks Presentation Organization • Introduction – Background information & related work • Thesis Contribution – Interconnection Network Simulator Framework – Improving the Gemini interconnect architecture • Conclusion – Summary and future work Baw M.S. Thesis Presentation. Slide 2 Optical Interconnection Networks Thesis Contributions • Interconnection Network Simulator (ICNS) framework – Design of the ICNS framework – Simulator Verification • Study of the Gemini network – Performance analysis – Improving Gemini’s throughput – Adding fair-scheduling capability to Gemini Baw M.S. Thesis Presentation. Slide 3 Optical Interconnection Networks Introduction • • • • Interconnection network in generic terms Motivation: why optics Overview of enabling technologies The Gemini interconnect architecture and related works • Simulation tool to aid design and study of interconnection networks Baw M.S. Thesis Presentation. Slide 4 Optical Interconnection Networks Interconnection Network • Terminals generate and/or consume data messages – e.g.: CPU, sensor banks, disks, other I/O devices • Links and switches transport data Baw M.S. Thesis Presentation. Slide 5 Optical Interconnection Networks Motivation • Want to solve large problems fast. • Target problems that are compute-, data-, and communications-intensive: – need multiple processors and high speed networks to connect processors. – want high bandwidth and low latency • Use optics to build interconnection networks Baw M.S. Thesis Presentation. Slide 6 Optical Interconnection Networks Motivation: Why Optics • Strengths of optics: – very high bandwidth (tens of Tb/s in one fiber) – low electro-magnetic interference – virtually no transmission line effects at high speed • Weaknesses of optics (current technology): – unsuitable to implement logical functions – optical components are generally costly Baw M.S. Thesis Presentation. Slide 7 Optical Interconnection Networks Optics: Technology Overview • Guided-wave optics • Free-space optics • “Smart Pixel Array” Arrays of VCSELs and detectors Baw M.S. Thesis Presentation. Slide 8 Optical Interconnection Networks Optics: Technology Overview • Free-space optics and “Smart Pixel Array” – Potential to provide physically clutter-free interconnect – Limited distance spanning capability – Insufficient reliability study Baw M.S. Thesis Presentation. Slide 9 Optical Interconnection Networks “Smart Pixel Array” ring architecture. [Chen98, Gourlay98, Lacroix98, Franklin] Baw M.S. Thesis Presentation. Slide 10 Optical Interconnection Networks Optics: Technology Overview • Guided-wave Optics – Fiber optics (mature, widely deployed) – Polymer wave guides • Recent developments: – polymer wave guides layout technology [Eldada96] – efficient fiber-to-polymer wave guide coupling [Barry97] – electro-optical switching elements [Sneh96, Lucent97] Baw M.S. Thesis Presentation. Slide 11 Optical Interconnection Networks Electro-optical Switching • The y-branch: – Refraction index of LiNbO3 changes in the presense of electric field. Baw M.S. Thesis Presentation. Slide 12 Optical Interconnection Networks Building on the y-branch • A 2x2 electro-optical switch – Issues: power loss and crosstalk. • Circuit-switched. No Buffering. Baw M.S. Thesis Presentation. Slide 13 Optical Interconnection Networks Reducing Crosstalk • Time-Dilation [Qiao96] – Reduce crosstalk using scheduling technique • Space-Dilation – Add hardware Baw M.S. Thesis Presentation. Slide 14 Optical Interconnection Networks – Space-dilation technique used by Lucent Technologies [Lucent97]. Next: Gemini Network Overview Baw M.S. Thesis Presentation. Slide 15 Optical Interconnection Networks The Gemini Network • Use two networks – one optically switched (Banyan topology to reduce power loss) – one electronically switched – as proposed, the two networks have identical topology [Chamberlain97] • Main idea: – off-load bulk data to high-bandwidth optical network – maintain low-latency in lightly-loaded electrical network to cater for control messages • Goals (not related to performance): – easily manufacturable (low cost) – forward compatibility Baw M.S. Thesis Presentation. Slide 16 Optical Interconnection Networks The Gemini Network Baw M.S. Thesis Presentation. Slide 17 Optical Interconnection Networks The Gemini Network – Layout polymer wave guides using wire-printing techniques [Eldada96] – Board level connection employs polymer-to-fiber coupling technique [Barry97] – Assume space-dilation (use Lucent switch [Lucent97]) Baw M.S. Thesis Presentation. Slide 18 Optical Interconnection Networks Related Work • Pan, Qiao, and Yang [Pan99] – Use 2x2 electro-optical switches – Banyan topology – Rely on time-dilation technique Baw M.S. Thesis Presentation. Slide 19 Optical Interconnection Networks Time-Dilation • Construct Contention-and-Conflict Free (CF) mappings – enforce switch element disjoint (SED) condition – schedule connections so that no two connections share a switch element • Assumes that a laser source can be completely turned off. Baw M.S. Thesis Presentation. Slide 20 Optical Interconnection Networks • Example A set of CF-mappings for a 4x4 network. • • • • • Challenge is to find an optimal set of mappings for a given (arbitrary) set of connections Need 8 mappings for a 16 connections in a 4x4 network Need about 50 for 1000 connections (32x32 network) Polynomial time algorithm by Qiao to construct optimal set of CF-mappings [Qiao96] Assume the existence of a centralized controller Next: The Need of a Simulation Tool Baw M.S. Thesis Presentation. Slide 21 Optical Interconnection Networks Simulation Tool • Simulation tools are generally helpful in the study of queueing systems • Need an extensible simulator – vast interconnection network design space – want the ability to easily extend simulator to simulate future optical network components • Tune network design to specific applications – want the ability to incorporate application models into simulation Next: Thesis Contribution Baw M.S. Thesis Presentation. Slide 22 Optical Interconnection Networks Thesis Contributions • Interconnection Network Simulator (ICNS) framework – Design of the ICNS framework – Simulator and Simulation Verification • Study of the Gemini network – Performance analysis – Improving Gemini’s throughput – Adding fair-scheduling capability to Gemini Baw M.S. Thesis Presentation. Slide 23 Optical Interconnection Networks Interconnection Network Simulator (ICNS) • Process-based discrete event simulation engine. • Object-oriented design. • Implementation environment: – Uses the MODSIM III language developed by CACI Products Company. – MODSIM III C++ executable. – Simulation engine and MODSIM III to C++ compiler by CACI. – C++ to executable compiler is gcc. – Developed in Solaris 2.5 environment. First Major Contribution of Thesis Baw M.S. Thesis Presentation. Slide 24 Optical Interconnection Networks ICNS Framework: Base Classes • MessageObj – models messages – provides uniform interface to NodeObj • NodeObj – abstract base class to be subclassed to model links, switches, terminals, etc. – provides uniform interface to MessageObj • NetworkObj – container of NodeObj’s – provide identifier-to-object-reference translation service Baw M.S. Thesis Presentation. Slide 25 Optical Interconnection Networks ICNS Class Hierarchy Baw M.S. Thesis Presentation. Slide 26 Optical Interconnection Networks Progression of a Simulation • Interactions between MessageObj and NodeObj drive simulation forward. • MessageObj’s operation: – Engaging a NodeObj: • • • • • Ask if NodeObj is busy If it is, ask to be queued and terminate Ask to be processed otherwise Wait for the processing to finish (elapse simulation time) Terminate Baw M.S. Thesis Presentation. Slide 27 Optical Interconnection Networks Progression of a Simulation • NodeObj’s operations: – When asked if it is busy: • answer yes or no – When asked to queue a MessageObj • action depends on queueing policy (subclass-specific) – When asked to process a MessageObj • action depends on which object is being simulated (subclass-specific) • tell MessageObj how long to wait Baw M.S. Thesis Presentation. Slide 28 Optical Interconnection Networks Description of Selected Objects • Message • Link • Terminal – Message Generator – Buffer – Central Processing Unit (CPU) • Switch Baw M.S. Thesis Presentation. Slide 29 Optical Interconnection Networks The Message Object Baw M.S. Thesis Presentation. Slide 30 Optical Interconnection Networks The Link Object • A Simple Link • A Multichannel Link Baw M.S. Thesis Presentation. Slide 31 Optical Interconnection Networks The Terminal Object • Processing Node Model • Processing Node Model Baw M.S. Thesis Presentation. Slide 32 Optical Interconnection Networks The Switch Object • The 2x2 Switch Model Baw M.S. Thesis Presentation. Slide 33 Optical Interconnection Networks An ICNS Application: sim • Separates topology from other network parameters – Topology descriptor file (text file) – Parameter descriptor file (text file) • ParamObj – parses parameter descriptor file – keeps track of all network parameters • BuildGNetwork Procedure – procedure parses topology descriptor file, instantiates and initializes objects accordingly Baw M.S. Thesis Presentation. Slide 34 Optical Interconnection Networks sim: User Interface • hand edit parameter file and topology file – or use Java-based GUI tools to generate files • to invoke the sim program, type sim param_file topology_file Baw M.S. Thesis Presentation. Slide 35 Optical Interconnection Networks Simulator Verification • Examine event trace (for small simulations) • Use visualization tool (for medium size simulations) – Visualization tool driven by event trace – Visualization developed by Wrighton [WUCCRC-99-02] • Simulate systems with known analytical results – Compare simulation results to analytical results Next: Visual Demonstration Baw M.S. Thesis Presentation. Slide 36 Optical Interconnection Networks Visualization Tool Demo... Baw M.S. Thesis Presentation. Slide 37 Optical Interconnection Networks M/M/1 and M/D/1 Simulations • Verification Example: – Simulate parallel M/M/1 and M/D/1 systems Baw M.S. Thesis Presentation. Slide 38 Optical Interconnection Networks M/M/1 and M/D/1 Simulations • Within 3% of analytical results for loads up to about 92% Baw M.S. Thesis Presentation. Slide 39 Optical Interconnection Networks Simulation Verification • Simulate for long enough time to get valid statistics • Wait out transient states to get valid steadystate statistics • Demonstrated that simulator produced valid results for a wide range of loads – within 3% of analytical results for loads up to 92% Next: The Gemini Network Baw M.S. Thesis Presentation. Slide 40 Optical Interconnection Networks The Gemini Network [Chamberlain97] • Architecture Overview – Network Model – Terminal Model – Switch Model • • • • Basic Protocol Performance Limits Simulation Results Improvements ... Baw M.S. Thesis Presentation. Slide 41 Optical Interconnection Networks Gemini Architecture Overview • Network Model – Banyan topology – Bufferless, optically circuit-switched network – Buffered, electronically packet-switched network Baw M.S. Thesis Presentation. Slide 42 Optical Interconnection Networks Gemini Architecture Overview • Terminal Model – CPU module models applications – One pair of optical output port – One pair of electrical output port Baw M.S. Thesis Presentation. Slide 43 Optical Interconnection Networks Gemini Architecture Overview • Switch Model – Electrical switch controls optical switch Baw M.S. Thesis Presentation. Slide 44 Optical Interconnection Networks Gemini Network Protocol • Original Protocol – Rely on Negative ACK – Fire-on-timeout mechanism – Issue: • How to set timeout parameter? Baw M.S. Thesis Presentation. Slide 45 Optical Interconnection Networks Evaluating Protocols... • Space Complexity – How much state information to keep (in switches) – Original protocol: O(1) per switch • Time Complexity – How many computational steps needed to (for a switch) process a control signal – Original protocol: O(1) • Performance measures – Throughput, latency, utilization, etc. Baw M.S. Thesis Presentation. Slide 46 Optical Interconnection Networks The setup-teardown Protocol • Similar to original protocol – But use positive ACK – Fire upon ACK • Signals – – – – setup(S,D,blocked) ackSetup(S,D) block(S,D) teardown(S,D) • Space Complexity O(1) per switch • Time Complexity O(1) Baw M.S. Thesis Presentation. Slide 47 Optical Interconnection Networks Switch Operation • Each switch keeps a list and a one bit optical switch state variable (= or x) • Processing a setup(S,D,blocked) signal: – – – – determine output port if setup already blocked, forward to output port. Determine requested state (= or x) if requested state conflict with current state and list is not empty • set blocked and forward to output port – else set state to requested state, add S to list, forward to output port • Processing a teardown(S,D) signal: – determine output port – if S in list, remove S from list – forward to output port Baw M.S. Thesis Presentation. Slide 48 Optical Interconnection Networks Switch Operation Complexity • Space Complexity O(1) – list size at most 2 • Time Complexity O(1) Next: Performance Analysis Baw M.S. Thesis Presentation. Slide 49 Optical Interconnection Networks Performance Limits numerator Send teardown Send setup … delay ... Receive ackSetup Send optical message denominator • Optical network utilization efficiency limited by o max lo / BWo lo / BWo (2(1 sig ) log 2 N 3)lsig / BWe • Define lo / lsig , BWo / BWe omax (2(1 sig ) log 2 N 3) Baw M.S. Thesis Presentation. Slide 50 Optical Interconnection Networks Performance Limits Next: Simulations Baw M.S. Thesis Presentation. Slide 51 Optical Interconnection Networks Performance Limits Next: Simulations Baw M.S. Thesis Presentation. Slide 52 Optical Interconnection Networks setup-teardown Simulations • Poisson arrival process • Fixed and Exponentially distributed message lengthes • Choose =16384, =12, sig=1.25 • Network sizes from 4x4 to 32x32 Baw M.S. Thesis Presentation. Slide 53 Optical Interconnection Networks setup-teardown Simulation Results Baw M.S. Thesis Presentation. Slide 54 Optical Interconnection Networks setup-teardown Simulation Results Baw M.S. Thesis Presentation. Slide 55 Optical Interconnection Networks setup-teardown Simulation Results Next: Blocking, the cause of low utilization Baw M.S. Thesis Presentation. Slide 56 Optical Interconnection Networks Problem: Blocking • Lose throughput due to blocking. Baw M.S. Thesis Presentation. Slide 57 Optical Interconnection Networks Solution: Virtual Output Queues • Terminals queue outgoing messages according to their destinations Second Major Contribution of Thesis Baw M.S. Thesis Presentation. Slide 58 Optical Interconnection Networks VOQ Protocol • Terminals allowed to send one setup request for each non-empty VOQ – Get around Head-of-Line blocking by exploring all possible optical paths in parallel • Switch processes setup, teardown signals as before – Add/delete source-destination pair to/from list instead – Have N2 source-destination pairs – but can bound list size to 2N • Space Complexity O(N) per switch • Time Complexity O(1) Baw M.S. Thesis Presentation. Slide 59 Optical Interconnection Networks VOQ Simulation Results Baw M.S. Thesis Presentation. Slide 60 Optical Interconnection Networks VOQ Simulation Results Baw M.S. Thesis Presentation. Slide 61 Optical Interconnection Networks VOQ Simulation Results Baw M.S. Thesis Presentation. Slide 62 Optical Interconnection Networks VOQ Simulation Results Baw M.S. Thesis Presentation. Slide 63 Optical Interconnection Networks VOQ Simulation Results • Load on the electrical network Network Size 4x4 8x8 16x16 32x32 Load < 0.6% < 1.2% < 2.4% < 4.6% • VOQ imposes minimal load on the electrical network – lightly loaded electrical network can maintain low latency for application control messages – variations of VOQ to further reduce electrical network load Baw M.S. Thesis Presentation. Slide 64 Optical Interconnection Networks VOQ Complexity • Even though there are N2 source-destination pairs, can implement list using bitmap and/or perfect hashing to make switch operations’ time complexities O(1). • Space complexity is – N2 bits per switch if list is implemented as a bitmap – 2N bits per switch if list is implemented using perfect hashing as well • Can exploit regularity of Banyan network to construct simple perfect hash functions Baw M.S. Thesis Presentation. Slide 65 Optical Interconnection Networks VOQ Implementation Complexity Baw M.S. Thesis Presentation. Slide 66 Optical Interconnection Networks VOQ Merits and Demerits • VOQ is good because: – VOQ significantly increases throughput – VOQ adds only minimal complexity to the system • But ... – VOQ may lead to starvation under very high load ... Prevent starvation using fair scheduling techniques. Next: Fair Scheduling in Gemini Baw M.S. Thesis Presentation. Slide 67 Optical Interconnection Networks Fair Scheduling in Gemini • Starvation – How and when it occurs – what is the tradeoff • Use fair scheduling to prevent starvation – concept of fairness in Gemini • fairness granularity • quantitative fairness measure • Gemini fair scheduler design – what are the desirable characteristics – the Distributed Deficit Round Robin (dDRR) fair scheduler • Fair scheduler evaluation Third Major Contribution of Thesis Baw M.S. Thesis Presentation. Slide 68 Optical Interconnection Networks Starvation • How and when it occurs • Problem: – Switch reinforced to stay in the same state – Need to induce switch to change state Baw M.S. Thesis Presentation. Slide 69 Optical Interconnection Networks Starvation: When does it occur? • 4x4 network, 16 flows (i.e., source-destination pairs) • Load is 0.8 • Plot cumulative number of bits sent versus flow number – snapshots taken at 500 and 20 message time intervals. Baw M.S. Thesis Presentation. Slide 70 Optical Interconnection Networks Starvation: When does it occur? • 4x4 network, 16 flows (i.e., source-destination pairs) • Load is 1.0 • Plot cumulative number of bits sent versus flow number – snapshots taken at 500 and 20 message time intervals. Baw M.S. Thesis Presentation. Slide 71 Optical Interconnection Networks Starvation: When does it occur? • 4x4 network, 16 flows (i.e., source-destination pairs) • Load is 1.2. Observe starvation on right plot. • Plot cumulative number of bits sent versus flow number – snapshots taken at 500 and 20 message time intervals. Baw M.S. Thesis Presentation. Slide 72 Optical Interconnection Networks Starvation • The tradeoff – Under variable message size assumption, inducing a switch to change state means stopping a connection from sending data – The more frequent we induce a change in switch states, the more throughput we lose – Fairness granularity directly related to how often we induce a change in switch state Tradeoff between fairness granularity and throughput Next: The Concept of Fairness Baw M.S. Thesis Presentation. Slide 73 Optical Interconnection Networks Concept of Fairness • Fairness granularity – no smaller than maximum message size – no smaller than scheduler’s resolution • e.g., scheduler may keep tab using 1KB chunk as basic unit, thus fairness granularity cannot be finer than 1KB. • Quantitative Fairness Measure – make sense to measure fairness for a time interval iif • all flows are actively contending throughout the interval • there is a bound on message size Baw M.S. Thesis Presentation. Slide 74 Optical Interconnection Networks Fairness Measure • FairnessMeasure (modified from [SV95]) F set of all flows . I time interval of interest ai amount of access received by flow i during I qi weight assigned to flow i FM ( I ) max i , jF ai / ak kF qi / qk kF a j / ak kF q j / qk kF Baw M.S. Thesis Presentation. Slide 75 Optical Interconnection Networks Fairness Measure • Ideally fair system – FM(I) = 0 for all I • Worst case – one flow monopolize access, all other flows starve – FM(I) = |F| • Worst case for Gemini – assume all connections actively contending for access – FM(I) = N for an NxN network Next: Scheduler Design Considerations Baw M.S. Thesis Presentation. Slide 76 Optical Interconnection Networks Gemini Fair Scheduler Design Considerations • Existing fair schedulers assume: – many-to-one contention: multiple flows contending for one link (RR,WFQ,WF2Q,DRR,SCFQ,VCFQ,etc.) – many-to-many contention, but in a non-blocking network (crossbar) [e.g., Prabhakar97, McKeown95] – slotted time [Lu97, Prabhakar97, McKeown97] – intermediate buffering available • Gemini violates all the above assumptions. Baw M.S. Thesis Presentation. Slide 77 Optical Interconnection Networks Gemini Fair Scheduler Design Considerations • Where to put the scheduler – centralized scheduler – distributed schedulers in terminals – distributed schedulers in switches • Scheduler complexity – Space Complexity (SC) • How much storage to keep track of flow states – Time Complexity (TC) • How many computational steps needed to make a scheduling decision. Baw M.S. Thesis Presentation. Slide 78 Optical Interconnection Networks Gemini Fair Scheduler Design Considerations • Desirable Characteristics – – – – distributed in switches leverage underlying VOQ protocol low space and time complexities tunable fairness granularity (scheduler resolution) • Modify DRR [SV95] to work in Gemini Distributed DRR (dDRR) Baw M.S. Thesis Presentation. Slide 79 Optical Interconnection Networks DRR Description • Scheduler resolution (fairness granularity) determined by quota (quanta) assigned to flows • Keeps track of flow’s unused quotas • dDRR uses similar ideas Baw M.S. Thesis Presentation. Slide 80 Optical Interconnection Networks Switch to DRR slide show... Baw M.S. Thesis Presentation. Slide 81 Optical Interconnection Networks dDRR Switch Controller Structure • Each 2x2 electrical switch controller contains a partial dDRR scheduler. • The dDRR module selectively blocks setup requests • Blocking is resolved by the VOQ module Baw M.S. Thesis Presentation. Slide 82 Optical Interconnection Networks Differences Between DRR and dDRR’s Assumed Environments DRR • scheduler co-locates with queues, queue state information readily available • visits queues one by one in round robin order dDRR • queue state information needs to be explicitly conveyed to scheduler • receives (setup) requests in no particular order Next: Modify Signals to Pass Queue State Information Baw M.S. Thesis Presentation. Slide 83 Optical Interconnection Networks Passing Queue and Flow State Information to dDRR Schedulers VOQ • setup(S,D,blocked) • teardown(S,D) dDRR • setup(flowID,blocked,amount) • teardown(flowID,amount,more) terminal-S terminal-D Next: dDRR Data Structure Baw M.S. Thesis Presentation. Slide 84 Optical Interconnection Networks Switch to dDRR slide show... Baw M.S. Thesis Presentation. Slide 85 Optical Interconnection Networks dDRR Data Structure in a Switch qi dci spi nri morei q dc sp nr more qj dcj spj nrj morej qk dck spk nrk morek a dDRR entry for a flow q quantum is the amount by which a flow’s quota is replenished at each round dc deficit counter keeps track of a flow’s available quota (initialized to q) sp suspension flag indicates if a flow has exhausted its quota (initially set) nr new round flag indicates if a flow has contended in the current round (initially set) more more flag indicates if a flow’s queue is empty (initially unset) Next: dDRR Space Complexity Baw M.S. Thesis Presentation. Slide 86 Optical Interconnection Networks dDRR Complexity • Space Complexity O(N) per switch – – – – Each flow has one entry in each switch it passes through In an NxN network (N2 flows), each switch handles 2N flows Space Complexity is 2N entries per switch Can easily hash flow ID from N2 space to 2N space • given a flow ID, can directly hash into an entry in O(1) time. • Time Comlexity O(1) Next: dDRR operations (psuedo-code) Baw M.S. Thesis Presentation. Slide 87 Optical Interconnection Networks Processing a setup(i,amount) signal if sp i nri set blocked elsif dci amount if nri dci dci qi set blocked set sp i else unset sp i set morei unset nri pass setup(i, amount, blocked ) to VOQ module Next: Condition to set nri to be explained later Baw M.S. Thesis Presentation. Slide 88 Optical Interconnection Networks Processing a teardown(i,amount,more) signal if more dci dci amount else dci qi set sp i morei more pass teardown(i, amount, more) to VOQ module Note that the processing of setup and teardown signals is done in O(1) time. Next: Determining Round Boundary Baw M.S. Thesis Presentation. Slide 89 Optical Interconnection Networks Determine New Round Boundary • A round ends if all flows have – either exhausted their quota – or stopped contending (queues become empty) • Begin a new round if all flows suspension flags become set • Can check for New Round condition in O(1) time – test all suspension flags in parallel in hardware Baw M.S. Thesis Presentation. Slide 90 Optical Interconnection Networks The New Round Operation Upon NewRound do for each flow i set nri sp i morei • Note that all operations take O(1) time • dDRR complexity for an NxN network: – Space Complexity O(N) per switch – Time Complexity O(1) Next: dDRR Feature and Functionality Baw M.S. Thesis Presentation. Slide 91 Optical Interconnection Networks dDRR Feature and Functionality • Properties inherited from DRR: – Tunable Fairness Granularity • scheduler resolution determined by quanta assignment • assign larger quanta to get coarser grained fairness – can trade off fairness granularity with throughput – Weighted Fair Scheduling • assign different quanta to different flows to perform weighted fair scheduling • tradeoff not well understood Next: dDRR Simulation Results Baw M.S. Thesis Presentation. Slide 92 Optical Interconnection Networks Recall old results: • 4x4 network, 16 flows (i.e., source-destination pairs) • Load is 1.2. Observe starvation on right plot. • Plot cumulative number of bits sent versus flow number – snapshots taken at 500 and 20 message time intervals. Baw M.S. Thesis Presentation. Slide 93 Optical Interconnection Networks Same Simulation with dDRR: • 4x4 network, 16 flows, quantum is eight times average message size. • Load is 1.2. Starvation eradicated. • Plot cumulative number of bits sent versus flow number – snapshots taken at 500 and 20 message time intervals. Baw M.S. Thesis Presentation. Slide 94 Optical Interconnection Networks More dDRR Simulation Results • • • • Pre-saturated queues, snapshots taken at 20 message time intervals No scheduler case: FairnessMeasure = 4.00, Throughput = 1.00 Left plot quantum = 4 MAX. FairnessMeasure = .33, Throughput = .86 Right plot quantum = MAX. FairnessMeasure = .11, Throughput = .71 Baw M.S. Thesis Presentation. Slide 95 Optical Interconnection Networks Fairness Granularity vs. Throughput Tradeoff • Pre-saturated queues, variable-size messages • Plots of normalized throughput vs. quantum size (normalized to MAX) Next: Weighted Fair Scheduling Baw M.S. Thesis Presentation. Slide 96 Optical Interconnection Networks Fairness Granularity vs. Throughput Tradeoff • • • • Pre-saturated queues. Plots of normalized throughput vs. quantum size. Left: fixed-size messages. Quantum size normalized to message size. Right: variable-size messages. Quantum size normalized to MAX. Next: Weighted Fair Scheduling Baw M.S. Thesis Presentation. Slide 97 Optical Interconnection Networks dDRR Weighted Fair Scheduling • Assign q to all flows, except 2q to flow 4 and 3q to flow 13. • Results: – flow 4 sent 1.9984 times the average traffic sent by others (except flow 13) – flow 13 sent 3.0029 times the average traffic sent by others (except flow 4) • Throughput is 81% of the case where all flows are assigned q Next: Prioritized Scheduling Baw M.S. Thesis Presentation. Slide 98 Optical Interconnection Networks Prioritized Fair Scheduling in Gemini qi dci spi nri morei qj dcj spj nrj morej qk dck spk nrk morek class 1 qi dci spi nri morei qj dcj spj nrj morej qk dck spk nrk morek class 2 qi dci spi nri morei qj dcj spj nrj morej qk dck spk nrk morek class 3 qi dci spi nri morei qj dcj spj nrj morej qk dck spk nrk morek class K Next: Conclusion Baw M.S. Thesis Presentation. Slide 99 Optical Interconnection Networks Conclusion • Summary of Thesis Contributions – Extensible interconnection network simulator framework – VOQ improves Gemini throughput • O(1) time complexity • O(N) per switch space complexity – dDRR scheduler adds fair scheduling capability to Gemini • O(1) time complexity • O(N) per switch space complexity • Tunable fairness granularity Next: Future Work Baw M.S. Thesis Presentation. Slide 100 Optical Interconnection Networks Conclusion • Future Work – Better understanding of the throughput vs. fairness granularity tradeoff • better understanding of many-to-many fair scheduling in general. – Gemini network interface design • need high speed network interface to take advantage of high bandwidth optical network – Gemini is only half optical • need to study the electrical half as well Next Slide: Many-to-Many Fiar Scheduling Baw M.S. Thesis Presentation. Slide 101 Optical Interconnection Networks Many-to-Many Weighted Fair Scheduling (Future Work) • Fundamental tradeoff: – Example 1: 4-flow, 4-parallel system, assign weights 1:1:1:2 • lose 3/8 throughput – Example 2: 4-flow, 4-parallel system, assign weights 1:1:1:3 • lose 1/2 throughput – Gemini (N2 flow, N-parallel system) • Nature of “fairness” and throughput tradeoff not yet understood. Baw M.S. Thesis Presentation. Slide 102 Optical Interconnection Networks Many-to-Many Weighted Fair Scheduling (Future Work) No reason to do fair scheduling here since resources are not under contention. • Fundamental tradeoff: – Example 1: 4-flow, 4-parallel system, assign weights 1:1:1:2 • lose 3/8 throughput – Example 2: 4-flow, 4-parallel system, assign weights 1:1:1:3 • lose 1/2 throughput – Gemini (N2 flow, N-parallel system) • Nature of “fairness” and throughput tradeoff not yet understood. Baw M.S. Thesis Presentation. Slide 103 Optical Interconnection Networks Conclusion • Future Work – Other optical technologies • “Smart Pixel Array” and free-space optics • Extend ICNS framework to include – Predicate interconnection network study on target applications • demonstrate that applications indeed benefit from using an optical network Baw M.S. Thesis Presentation. Slide 104 Optical Interconnection Networks Acknowledgement • Advisors: – Dr. Mark A. Franklin, Dr. Roger D. Chamberlain • Committee Members: – Dr. Jonathan S. Turner, Dr. George Varghese • NSF and DARPA for financial support Baw M.S. Thesis Presentation. Slide 105
