1. On Modeling the Lifetime Reliability of Homogeneous Manycore Systems Lin Huang and Qiang Xu CUhk REliable computing laboratory (CURE) The Chinese University of Hong Kong

2. Integrated Circuit (IC) Product Reliability IC errors can be broadly classified into two categories ●Soft errors Do not fundamentally damage the circuits ●Hard errors Permanent once manifest E.g., time dependent dielectric breakdown (TDDB) in the gate oxides, electromigration (EM) and stress migration (SM) in the interconnects, and thermal cycling (TC)

3. Manycore Systems State-of-the-art computing systems have started to employ multiple cores on a single die ●General-purpose processors, multi-digital signal processor systems ●Power-efficiency ●Short time-to-market Source: IntelSource: Nvidia

4. Problem Formulation To model the lifetime reliability of homogeneous manycore systems using a load-sharing nonrepairable k-out-of-n: G system with general failure distributions Key features ●k-out-of-n: G systems: to provide fault tolerance ●Load-sharing: each embedded core carries only part of the load assigned by the operating system ●Nonrepairable: embedded cores are integrated on a single silicon die ●General failure distribution: embedded cores age in operation

5. Queueing Model for Task Allocation Embedded cores execute tasks independently and one core can perform at most one task at a time Consider a manycore system composed of a set identical embedded cores ●The set of active cores, spare cores, and faulty cores

6. Queueing Model for Task Allocation A general-purpose parallel processing system with a central queue with a bulk arrival is modeled as queueing system The probability that a certain active core is occupied by tasks (also called utilization) is computed as Target system ●Gracefully degrading systems ●Standby redundant systems

7. Lifetime Reliability of Entire System – Gracefully Degrading System A functioning manycore system may contains good cores Let be the probability that the system has active cores at time The system reliability can therefore be expressed as Thus, the Mean Time to Failure (MTTF) of the system can be written as

8. Lifetime Reliability of Entire System – Gracefully Degrading System To determine ● ● Conditional probability ●For any Conditional probability The remaining is how to compute

9. Behavior of Single Processor Core States of cores ●Spare mode – cold standby ●Active mode Processing state Wait state – warm standby The same shape but different scale parameter ●E.g.,

10. Core Lifetime Reliability of A Single Core – Gracefully Degrading System Define accumulated time in a certain state at time as how long it spends in such a state up to time Calculation

11. Lifetime Reliability of A Single Core – Gracefully Degrading System Theorem 1 Suppose a manycore system with gracefully degrading scheme has experienced core failures, in the order of occurrence time at, respectively, for any core that has survived until time ●its accumulated time in the processing state up to time ●its accumulated time as warm standby up to time

12. Lifetime Reliability of A Single Core – Gracefully Degrading System Recall that the reliability functions in wait and processing states have the same shape but different scale parameter ●General reliability function, abbreviated as ●Reliability function in processing state, denoted as ●Reliability function in wait state, denoted as ●Relationships: and

13. Lifetime Reliability of A Single Core – Gracefully Degrading System A subdivision of the time : By the continuity of reliability function, we have wait processing wait Accumulated time in the processing state Accumulated time in the wait state

14. Lifetime Reliability of A Single Core – Gracefully Degrading System Theorem 2 Given a gracefully degrading manycore system that has experienced core failures which occur at respectively, the probability that a certain core survives at time provided that it has survived until time is given by where

15. Lifetime Reliability of Entire System – Standby Redundant System A standby redundant system is functioning if it contains at least good cores, among which are configured as active one, the remaining are spares To determine ● Again, the key point is to compute

16. Lifetime Reliability of A Single Core – Standby Redundant System Define a core’s birth time as the time point when it is configured as an active one Theorem 3 In a standby redundant manycore system, for any core with birth time that has survived until time ●its accumulated time in the processing state up to time ●its accumulated time as warm standby up to time

17. Lifetime Reliability of A Single Core – Standby Redundant System Theorem 4 In a manycore system with standby redundant scheme, the probability that a certain core with birth time survives at time is given by where

18. Experimental Setup Lifetime distributions ●Exponential ●Weibull ●Linear failure rate System parameters ● Consider a manycore system consisting of cores

19. Misleading Caused by Exponential Assumption Redundancy Scheme Sojourn Time (years) 0-Failure State 1-Failure State 2-Failure State 3-Failure State 4-Failure State 0—0.2188———— 1 Degrading0.21210.2188———0.4309 Standby0.2188 ———0.4376 2 Degrading0.20590.21210.2188——0.6368 Standby0.2188 ——0.6564 3 Degrading0.20000.20590.21210.2188—0.8368 Standby0.2188 —0.8752 4 Degrading0.19440.20000.20590.21210.21881.0312 Standby0.2188 1.0940 : Expected lifetime of the -core system

20. Lifetime Reliability for Non-Exponential Lifetime Distribution (a) Weibull Distribution(b) Linear Failure Rate Distribution

21. Detailed Results for Gracefully Degrading System Distributio n Sojourn Time (years) 0-Failure State 1-Failure State 2-Failure State 3-Failure State 4-Failure State Weibull 02.2039———— 12.21530.5573———2.7726 22.22600.56000.3055——3.0915 32.23590.56260.31420.1040—3.2167 42.24520.56490.29880.09550.08203.2864 Linear Failure Rate 01.8572———— 11.84631.1367———2.9830 21.83541.13250.8926——3.8605 31.82431.12820.87980.6941—4.5264 41.81331.12370.87620.70550.62695.1456

22. The Impact of Workload

23. Comparison Between Gracefully Degrading System and Standby Redundant System Distribution Redundancy Scheme Hot Standby Warm Standby Cold Standby Weibull 2 Degrading1.50391.82322.14972.29302.42652.6258 Standby1.53141.82272.11332.24882.34842.5309 4 Degrading1.50461.85212.23052.44322.57712.8376 Standby1.55771.85452.17152.31032.42662.6261 Linear Failure Rate 2 Degrading1.91152.31972.70702.86973.01053.2424 Standby1.96082.33142.73302.88513.00913.2146 4 Degrading2.13482.71223.36423.65293.93854.3590 Standby2.30082.78993.43073.60153.85884.1881

24. Conclusion State-of-the art CMOS technology enables the chip-level manycore processors The lifetime reliability of such large circuit is a major concern We propose a comprehensive analytical model to estimate the lifetime reliability of manycore systems Some experimental results are shown to demonstrate the effectiveness of the proposed model

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