Load Shedding Algorithm

1. Load Shedding Algorithm • Evaluation Step • When to shed load? • Load Shedding Road Map (LSRM) • Where to shed load? • How much load to shed?

2. L = c1 s1 c2 s2 cn sn … I O Load Evaluation • Load Coefficients (L) • the number of processor cycles required to push a single tuple through the network to the outputs • n operators • ci = cost • si = selectivity

3. L2 = 14 L3 = 5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O1 L1 = 22 1 c1 = 10 s1 = 0.5 I L4 = 10 4 c2 = 10 s2 = 0.9 L(I) = 22 O2 Load Evaluation Load Coefficient L1 = 10 + (0.5 * 10) + (0.5 * 0.8 * 5) + (0.5 * 10) = 22 L2 = 10 + (0.8 * 5) = 14

4. S = Load Evaluation • Stream Load (S) • load created by the current stream rates • m input streams • Li = load coefficient • ri = input rate

5. L2 = 14 L3 = 5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O1 L1 = 22 1 c1 = 10 s1 = 0.5 I L4 = 10 4 c2 = 10 s2 = 0.9 L(I) = 22 O2 r = 10 Load EvaluationStream Load S = 22 * 10 = 220

6. Load Evaluation • Queue Load (Q) • load due to any queues that may have built up since the last load evaluation step • MELT_RATE = how fast to shrink the queues (queue length reduction per unit time) • Li = load coefficient • qi = queue length Q = MELT_RATE * Li * qi

7. L2 = 14 L3 = 5 q = 100 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O1 L1 = 22 1 c1 = 10 s1 = 0.5 I L4 = 10 4 c2 = 10 s2 = 0.9 L(I) = 22 O2 r = 10 Load EvaluationQueue Load MELT_RATE = 0.1 Q = 0.1 * 5 * 100 = 50

8. L2 = 14 L3 = 5 q = 100 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O1 L1 = 22 1 c1 = 10 s1 = 0.5 I L4 = 10 4 c2 = 10 s2 = 0.9 L(I) = 22 O2 r = 10 Load EvaluationTotal Load • Total Load (T) = S + Q T = 220 + 50 = 270

9. T > H * C processing capacity headroom factor Load Evaluation • The system is overloaded when

10. Load Shedding Algorithm • Evaluation Step • When to drop? • Load Shedding Road Map (LSRM) • How much to drop? • Where to drop?

11. how many cycles will be saved <Cycle Savings Coefficients (CSC) Drop Insertion Plan (DIP) Percent Delivery Cursors (PDC)> set of drops that will be inserted where the system will be running when the DIP is adopted ENTRY 1 … … … ENTRY n CSC DIP PDC max savings … (0,0,0,…,0) cursor less load shedding more load shedding Load Shedding Road Map (LSRM)

12. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS take the least ratio take the least ratio how much to drop? how much to drop? insert Drop determine predicate create LSRM entry insert Filter create LSRM entry LSRM Construction

13. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS L1 = 17 L2 = 14 L3 = 5 1 c1 = 10 s1 = 0.5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O I A B C D Drop Locations Single Query

14. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS L1 = 17 L2 = 14 L3 = 5 1 c1 = 10 s1 = 0.5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O I A Drop Locations Single Query

15. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS L2 = 14 L3 = 5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 D E O1 B L1 = 22 1 c1 = 10 s1 = 0.5 A I L4 = 10 C 4 c2 = 10 s2 = 0.9 F O2 Drop Locations Shared Query

16. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS L2 = 14 L3 = 5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O1 B L1 = 22 1 c1 = 10 s1 = 0.5 A I L4 = 10 C 4 c2 = 10 s2 = 0.9 O2 Drop Locations Shared Query

17. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS utility 1 0.7 0 % tuples 100 50 0 Loss/Gain RatioLoss • Loss – utility loss as tuples are dropped – determined using loss-tolerance QoS graph Loss for first piece of graph = (1 – 0.7) / 50 = 0.006

18. set Drop Locations compute & sort Loss/Gain ratios Drop-Based LS Filter-Based LS Gain G(x) = Loss/Gain RatioGain • Gain – processor cycles gained • R = input rate into drop operator • L = load coefficient • x = drop percentage • D = cost of drop operator • STEP_SIZE = increments for x to find G(x)

19. Drop-Based LS take the least ratio how much to drop? insert Drop create LSRM entry Drop-Based Load Sheddinghow much to drop? • Take the least Loss/Gain ratio • Determine the drop percentage p

20. Drop-Based LS take the least ratio how much to drop? insert Drop create LSRM entry L1 = 17 L2 = 14 L3 = 5 1 c1 = 10 s1 = 0.5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O I A drop drop drop drop Drop-Based Load Sheddingwhere to drop? If there are other drops in the network, modify their drop percentages.

21. Drop-Based LS take the least ratio how much to drop? insert Drop create LSRM entry Drop-Based Load Sheddingmake LSRM entry • All drop operators with the modified percentages form the DIP • Compute CSC • Advance QoS cursors and store in PDC LSRM Entry <Cycle Savings Coefficients (CSC) Drop Insertion Plan (DIP) Percent Delivery Cursors (PDC)>

22. Filter-Based LS take the least ratio how much to drop? determine predicate insert Filter create LSRM entry Filter-Based Load Sheddinghow much to drop?predicate for filter • Start dropping from the interval with the lowest utility. • Keep a sorted list of intervals according to their utility and relative frequency. • Find out how much to drop and what intervals are needed to . • Determine the predicate for filter.

23. Filter-Based LS take the least ratio how much to drop? determine predicate insert Filter create LSRM entry L1 = 17 L2 = 14 L3 = 5 1 c1 = 10 s1 = 0.5 2 c2 = 10 s2 = 0.8 3 cn = 5 sn = 1.0 O I A filter filter filter filter Filter-Based Load Sheddingplace the filter If there are other filters in the network, modify their selectivities.