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

Load Evaluation

• Load Coefficients (L)– the number of processor cycles required to push

a single tuple through the network to the outputs

c1

s1

c2

s2

cn

sn

…I O

n

i

i

ij

j

j cs1

1

1

*)(L = • n operators

• ci = cost

• si = selectivity

3

Load Evaluation Load Coefficient

L1 = 10 + (0.5 * 10) + (0.5 * 0.8 * 5) + (0.5 * 10) = 22

L2 = 10 + (0.8 * 5) = 14

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10L(I) = 22

4

• Stream Load (S)– load created by the current stream rates

Load Evaluation

m

i

ii rL1

*S = • m input streams

• Li = load coefficient

• ri = input rate

5

Load EvaluationStream Load

S = 22 * 10 = 220

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10L(I) = 22r = 10

6

• 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)

Load Evaluation

Q = MELT_RATE * Li * qi

• Li = load coefficient

• qi = queue length

7

Load EvaluationQueue Load

MELT_RATE = 0.1

Q = 0.1 * 5 * 100 = 50

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10L(I) = 22r = 10

q = 100

8

Load EvaluationTotal Load

•Total Load (T) = S + Q

T = 220 + 50 = 270

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10L(I) = 22r = 10

q = 100

9

• The system is overloaded when

Load Evaluation

T > H * C

headroom factor processing capacity

10

Load Shedding Algorithm

• Evaluation Step– When to drop?

• Load Shedding Road Map (LSRM)– How much to drop?– Where to drop?

11

Load Shedding Road Map (LSRM)

<Cycle Savings Coefficients (CSC)

Drop Insertion Plan (DIP)

Percent Delivery Cursors (PDC)>set of drops that will be inserted

how many cycles will be saved

where the system will be running when the DIP is adopted

…

max savings

…

(0,0,0,…,0)

CSC

DIP

PDC

ENTRY n……ENTRY 1

cursor more load sheddingless load shedding

12

LSRM Constructionset Drop Locations

compute & sort Loss/Gain ratios

how much to drop?

take the least ratio

insert Drop

create LSRM entry

how much to drop?

take the least ratio

insert Filter

create LSRM entry

determine predicate

Drop-Based LS Filter-Based LS

13

Drop LocationsSingle Query

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I O

L1 = 17 L2 = 14 L3 = 5

A B C D

14

Drop LocationsSingle Query

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I O

L1 = 17 L2 = 14 L3 = 5

A

15

Drop LocationsShared Query

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10A

B

C

D E

F

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

16

Drop LocationsShared Query

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I

O1

4

c2 = 10

s2 = 0.9

O2

L1 = 22

L2 = 14 L3 = 5

L4 = 10A

B

C

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

17

Loss/Gain RatioLoss

• Loss – utility loss as tuples are dropped

– determined using loss-tolerance QoS graph

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

100 50 0% tuples0

0.7

1

utility

Loss for first piece of graph

= (1 – 0.7) / 50

= 0.006

18

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)

Gain G(x) =

otherwise 0

0 x if )*(* DLxR

set Drop Locations

compute & sort Loss/Gain ratios

Drop-Based LS Filter-Based LS

19

Drop-Based Load Sheddinghow much to drop?

• Take the least Loss/Gain ratio

• Determine the drop percentage p

how much to drop?

take the least ratio

insert Drop

create LSRM entry

Drop-Based LS

20

Drop-Based Load Sheddingwhere to drop?

how much to drop?

take the least ratio

insert Drop

create LSRM entry

Drop-Based LS

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I O

L1 = 17 L2 = 14 L3 = 5

A drop drop dropdrop

If there are other drops in the network, modify their drop percentages.

21

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)>

how much to drop?

take the least ratio

insert Drop

create LSRM entry

Drop-Based LS

22

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.

how much to drop?

take the least ratio

insert Filter

create LSRM entry

determine predicate

Filter-Based LS

23

Filter-Based Load Sheddingplace the filter

how much to drop?

take the least ratio

insert Filter

create LSRM entry

determine predicate

Filter-Based LS

1

c1 = 10

s1 = 0.5

2

c2 = 10

s2 = 0.8

3

cn = 5

sn = 1.0

I O

L1 = 17 L2 = 14 L3 = 5

A filter filter filterfilter

If there are other filters in the network, modify their selectivities.