LOAD BALANCING IN PACKET SWITCHING

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LOAD BALANCING IN PACKET SWITCHING Nick
Bambos Stanford University Joint work with
Aditya Dua, Stanford
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Load Balancing QoS Fairness
Switching in data centers Switching in storage
networks Video servers, multimedia
streaming Issues load balancing, QoS, fairness
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Background
Lots of research on maximum throughput
scheduling Much less on QoS Giles et al (1997),
Li et al (1999), Rai et al (2001), Keslassy et
al 2003), Focus on alternative problem
formulation
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Model for Constrained Service
When S is used in a time slot, Sq cells (1/0) are
removed from queue q Empty queues (download
content) in a load-balanced manner that is
QoS-aware and fair
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Input Queued Packet Switches
2x2 switch simplest model (not simplistic)
scales to NxN
Service vectors Sa and Sb
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Traffic Streams, Inter-Packet Deadlines, Rates
Slotted time packets/cells all available at
0 Regular Traffic Stream X (1,0,0,0,1,0,0,
0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1, )
Inter-Packet Deadlines constant T Rate
1/T
General Traffic Stream X (1,0,1,1,1,0,0,0,1
,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,1, )
Inter-Packet Deadlines variable
Inter-Packet Deadlines (IPD) soft when
exceeded QoS degrades
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The Basic Idea Single Stream 1
Traffic Stream X desirable (flow
control) (0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0
,0,1, ) Cumulative Traffic (0,0,0,1,1,2,2,2,2,3
,3,3,3,4,4,4,4,4,5,5,5,6, ) Service Stream
S provided (0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
1,1,1,0,1, ) Cumulative Service (0,1,2,2,2,2,2,
2,2,2,2,2,2,2,2,3,4,5,6,7,7,8, ) Deviation D
cumService cumTraffic (0,1,2,1,1,0,0,0,0,-1,-
1,-1,-1,-2,-2,-1,0,1,2,2,2, )
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The Basic Idea Single Stream 2
(0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1, )
desirable traffic stream (0,1,1,0,0,0,0,0,0
,0,0,0,0,0,0,1,1,1,1,1,0,1, ) provided
service stream Deviation D cumService
cumTraffic (0,1,2,1,1,0,0,0,0,-1,-1,-1,-1,-2,-2,-
1,0,1,2,2,2,
Deviation 0 (0,0,0,0,0,0, ) perfectly
matched service to traffic
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Controlled System Dynamics 2x2 Switch Ex
Evolution of Service-Traffic Deviation of 4
Entangled Streams
D(n1) D(n) Sa X(n1)
D11 D12 D21 D22
D(n1) D(n) Sb X(n1)
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Cost Structure 2x2 Switch Ex
CDxy
Per Slot
Service Leads
Service Lags
CD CD11 CD12 CD21 CD22
Cumulative
C CD(1) CD(2) CD(N)
Dxy
Control Problem Find service sequence S(1),
S(2), ,S(n),,S(N) to miimize cumulative cost
up to N perfectly aligned traffic-service
streams have 0 cost
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Service Control
CDxy
Control (DP Formulation) Service sequence
S(1), S(2), ,S(n),,S(N) minimizing
cumulative cost up to N
Service Leads
Service Lags
Dxy

• Summary of Controls
• Myopic policies are good (Prop) and easy for
  2x2 switches
• For NxN switches too many permutations
• check 2x2 neighbors (Giaccone et al 2003)
• convex relaxations

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Performance - 3x3 Switch

• 3x3 switch 6 service configurations
• Benchmark round-robin on 6 configurations
• 150,000 packets
• CD D
• IPDs 4/2 from MC
• Policies
• myopic / exhaustive
• myopic / neighbors 2x2
• myopic / convex relaxation

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Symmetric Load / IPDs
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Asymmetric Load / IPDs
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Conclusions

• Load balancing, QoS, and fairness can be captured
  into the same model
• The model operates on micro time-scales (IPD),
• as opposed to macro (rates)
• Versions of the formulation/solution must be
  tuned to particular situations

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Thank You!