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Weighted Differential Scheduler
Hans Eberle, Wladek Olesinski
Oracle Labs
Outline
•  Motivation
•  Digital Differential Analyzer
•  Weighted Differential Scheduler (WDS)
•  Simulation Results
•  Summary
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Motivation
•  Problem statement
•  Schedule use of a shared resource among several requesters
•  Weights determine requesters’ share of the resource
•  Access to the shared resource in fixed-size time intervals
•  Goal
•  Requester’s intervals are spaced apart at equal distances
•  Reduce forwarding latency and minimize buffer memory
capacity
•  Applications
•  Packet forwarding in network switches
•  Process scheduling etc.
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Jitter
… 0
w0 = 2
0 0 0
… 1
w1 = 3
1 1 1
1
… 0
w0 = 2
0 0 0
0
… 1
w1 = 3
1 1 1
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1
WRR
Scheduler
WDS
Scheduler
… 1
1
1
0
0
… 1
0
1
1
0
4
Related Work
Smoothed Round Robin (SRR)
Low-Jitter Scheduler (LJS)
JSRR/JLJS
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Digital Differential Analyzer
•  Used in computer graphics for rasterizing lines, e.g.
for interpolating the raster coordinates of the line
given a start and end point
•  Example: Bresenham line drawing algorithm
•  Avoids drift, i.e. accumulation of rounding errors
•  Can be implemented with integer additions and
subtractions
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Bresenham Line Drawing Algorithm
(x1,y1)
err
y
(x0,y0)
x
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func%on DrawLine ((x0,y0),(x1,y1)) x ⇐ x0 y ⇐ y0 err ⇐ 0 deltaerr ⇐ (y1 – y0)/(x1 – x0) while x < x1 do plot(x,y) x ⇐ x + 1 err ⇐ err + deltaerr while err ≥ 0.5 do y ⇐ y + 1 err ⇐ err – 1 end while end while 7
Scheduling Algorithm for Two Flows
WDS
err ⇐ 0 deltaerr ⇐ w1/w0 loop
serve f0 err ⇐ err + deltaerr
while err ≥ 0.5 do
serve f1 err ⇐ err – 1 end while end loop
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Bresenham err ⇐ 0 deltaerr ⇐ (y1 – y0)/(x1 – x0) while x < x1 do plot(x,y); x ⇐ x + 1 err ⇐ err + deltaerr while err ≥ 0.5 do y ⇐ y + 1 err ⇐ err – 1 end while end while 8
Using Integer Arithmetic Only
err1 ⇐ 0 deltaerr1 ⇐ w1/w0 | *2w0
loop
serve f0 err1 ⇐ err1 + deltaerr1 while err1 ≥ 0.5 do | *2w0
serve f1 err1 ⇐ err1 – 1 | *2w0
end while end loop
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err1 ⇐ 0 deltaerr1 ⇐ 2*w1 loop serve f0 err1 ⇐ err1 + deltaerr1 while err1 ≥ w0 do serve f1 err1 ⇐ err1 – 2*w0 end while end loop 9
Scheduling > 2 Flows – Iterative Method
•  Iteratively merge two flows at the time
f0
f1
f2
f3
S1
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S2
S3
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Scheduling > 2 Flows – Non-Iterative Method
err1 ⇐ 0; err2 ⇐ 0 deltaerr1 ⇐ w1/w0; deltaerr2 ⇐ w2/w0 loop serve f0 err1 ⇐ err1 + deltaerr1; err2 ⇐ err2 + deltaerr2 while err1 ≥ 0.5 or err2 ≥ 0.5 do if err1 ≥ 0.5 then serve f1; err1 ⇐ err1 – 1 end if if err2 ≥ 0.5 then serve f2; err2 ⇐ err2 – 1 end if end while end loop © 2012 Oracle Corporation
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Jitter Calculation
Jitter = stdev(Interdeparture Delays)
… 0
0
0
0
w0 = 2
w1 = 3
0
… 1
… 1
1
1
1
0
1
1
0
f0
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1
0
0
1
1
0
Scheduler
1
1
f1
0
1
3
2
2
2
1
J0 = 0.5
J1 = 0.47
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Results: Jitter for 2 Flows
1.8
Algorithms:
JLJS/JWDS
J
1.7 SRR/JWDS
WDS is better than SRR
WDS is better than SRR
jitter ratio
1.6
•  WDS = Weighted
Differential Scheduler
•  LJS = Low Jitter
Scheduler
•  SRR = Smooth Round
Robin Scheduler
1.5
1.4
1.3
1.2
WDS is better than LJS
WDS is better than LJS
1.1
1
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20
30
40 50 60 70
wmax = w0+w1
80
90 100
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Results: Jitter for 3 Flows
1.8
•  Alg. 4: Increment error
1.6
jitter ratio
1.4
1.2
1
JWDS,alg4/JWDS,iterative
JWDS,alg5/JWDS,iterative
JWDS,alg7/JWDS,iterative
JWDS,alg8/JWDS,iterative
0.8
0.6
2
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6
8
10 12
wmax
14
16
18
20
only when packet from f0
is forwarded
•  Alg. 5: Increment error
when packet from f0 or f1
is forwarded
•  Alg. 7: Treat flows
symmetrically
•  Alg. 8: Serve flow with
biggest error first
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Summary
•  Packet scheduling can be described as a Digital
Differential Analyzer
•  WDS has lower jitter than any other known weighted
scheduler
•  WDS requires integer additions/subtractions only
•  Future work: better understand and improve noniterative WDS versions
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[email protected]
[email protected]
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