Stress Resistant Scheduling Algorithms for

CIOQ Switches Prashanth PappuApplied Research Laboratory

Washington University in St Louis

“Stress Resistant Scheduling Algorithms for CIOQ switches”, Prashanth Pappu, Jon Turner. To appear in ICNP 2003.

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Anatomy of a Router

Switch Fabric

IPP

OP

P

LineCard

IPP

OP

P

LineCard

IPP

OP

P

LineCard

IPP

OP

P

LineCard

IPP

OP

P

LineCard

IPP

OP

P

LineCard

ControlProcessor

Port processor queue packets and make routing decisions

Line cards encode data for transmission on target physical layer.

Control processor – routing protocols and monitoring functions.

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Output Queuing

Queuing is done only at output ports. Maximizes throughput. Contentions between packets - only at output ports. Speedup=N, impractical but ideal model.

SwitchingFabric

OutputPorts

InputPorts

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Combined Input Output Queuing (CIOQ)

Use of VOQs. Crossbar configured by centralized scheduler. Bipartite graph matching problem.

SwitchingFabric

OutputPorts

InputPorts

……

CentralizedScheduler

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Stability results Maximum size matching (MSM) – stable for i.i.d,

uniform, admissible traffic. Maximum weight matching (MWM) – stable for

independent, admissible traffic. Too complex, O(N5/2) and O(N3logN). Switch with 10 Gb/s links has < 40 ns to make

scheduling decision. Maximal size matching algorithms – Parallel

Iterative Matching (PIM) and iterative SLIP (iSLIP).

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Parallel iterative Matching (PIM) Iterative matching algorithm

each unmatched input sends request to every output for which it has a queued cell.

unmatched outputs randomly pick a request and send grant.

if input receives multiple grants, it picks one randomly.

O(log N) convergence.

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iterative SLIP (iSLIP) Iterative matching algorithm

unmatched inputs send requests to unmatched outputs (for which they have cells)

unmatched outputs pick a request that appears next in a fixed round-robin order from an input pointer. (input pointer is updated only in first iteration)

if input gets multiple grants, it picks one that appears next in a fixed round robin order from an output pointer. (update of output pointer)

Desynchronization effect. Simple to implement but do not perform well under

extreme traffic conditions.

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Worst case results

Critical Cells First (CCF) can emulate output queuing with speedup =2.

Lowest occupancy output first algorithm is work conserving with speedup =2.

Can be augmented with timestamps to emulate output queuing. (speedup=3)

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LOOFA

Iterative matching algorithm unmatched inputs send requests to outputs with

lowest occupancy (for which they have queued cells)

outputs pick a request randomly and send grant to input

O(N) iterations to perform correctly. Work conserving with speedup of 2. Significant result but not practical.

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Traffic in IP networks Unregulated nature of IP networks can cause

sustained overloads. use of slow congestion control mechanisms limited route diversity makes congested links common use of route selection mechanisms not guided by session

bandwidth needs sudden route changes causing rapid traffic shifts malicious users

How do practical scheduling algorithms perform in these conditions?

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Solution

We use targeted stress tests to study performance of practical scheduling

algorithms under extreme conditions study performance of work conserving scheduling

algorithms under speedups < 2 design stress resistant scheduling algorithms

which maintain throughput under uniform traffic and stress tests and can still be implemented at high speeds.

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Miss fraction

Previous work use average queuing delay as a metric.

Not useful under inadmissible traffic conditions.

Miss fraction

miss fraction = 1 – NA/NI

Determines relative loss in throughput.

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Stress Testphase 1 phase 2 phase 3 phase 4

Adversary approach in overloading (stressing) various outputs.

Output with empty queues have cells queued at various inputs.

Inputs with cells for an empty output also have cells queued forother outputs.

Test can be varied by changing number of participating inputs orphases.

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Stress Test (Example)

PIM (speedup =1.5). Stress test with 3 participating inputs, 4 phases.

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PIM (under uniform traffic)

Average Queuing delays Miss fraction

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iSLIP (under uniform traffic)

Average Queuing delays Miss fraction

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Stress Tests

Test A(Worst case for PIM(4), speedup=2)

Test B(Worst case for LOOFA, speedup=2)

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Stress resistant algorithms Better performance of LOOFA suggests, ordering

outputs is the key. Complete ordering can make algorithms too

complex to implement. But traffic conditions are persistent and change

slowly, use approximate ordering schemes. Lowest Layer Selection (LLS) heuristic which achieves a

coarser ordering of outputs. Odd-even sorting which achieves approximate ordering but

converges to ideal ordering under persistent traffic conditions.

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Lowest Layer Selection achieves coarser ordering bigger layers for larger

queue lengths beyond a queue limit all

outputs are treated equal number of layers

independent of N. algorithms give priority to

outputs in lowest layer in accept phase.

priority encoder or N-way minimum finding circuit can be used on a grant vector.

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Lowest Layer Selection - Random (LLS-R) Iterative matching algorithm

each unmatched input sends request to every output for which it has a queued cell.

unmatched outputs randomly pick a request and send grant.

if input receives multiple grants, it picks one randomly from lowest layer.

O(log N) convergence still holds.

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Lowest Layer Selection –SLIP (LLS-S) Iterative matching algorithm

unmatched inputs send requests to unmatched outputs (for which they have cells)

unmatched outputs pick a request that appears next in a fixed round-robin order from an input pointer. (input pointer is updated only in first iteration)

if input gets multiple grants, it picks one that appears next in the lowest layer in a fixed round robin order from an output pointer. (update of output pointer)

Both LLS-R and LLS-S have the same performance as PIM and iSLIP under uniform traffic.

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Stress TestMiss fractions for LLS-R, LLS-S (using 16 layers) and LOOFA.

Test A Test B

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Stress TestMiss fractions for LLS-S and LLS-R (single iteration) with varying layers.

LLS-S (Test A) LLS-R (Test A)

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Approximate LOOFA (A-LOOFA)

LOOFA is complex but can be used as the basis for a practical algorithm (with similar performance)

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Approximate LOOFA (A-LOOFA)

)()( ,1,1,,1,1,, jijijijijijiji cvrcvrr

Matching in A-LOOFA is accomplished using a simple combinational circuit.

O(N) but constant factor is determined by gate delays (2N times delay in each block).

.13 um ASIC process, gate delays are 25-50 ps. Match can be completed in 3.2-6.4 ns.

)()( 1,,,11,,,1, jijijijijijiji rvcrvcc

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A-LOOFA Columns are ordered using odd-even sort.

for all even j < N, swap Bj and qj with Bj+1 and qj+1, if qj > qj+1.

Similarly, for all odd j < N-1

Rows are ordered using a permutation based on perfect shuffle (to ensure fairness). for all even i<N, generate a pseudo random bit xi.

if xi = 0, values in row i are moved to row i/2 and those in i+1 are moved to (N+i)/2.

else, values in row i are moved to row (N+i)/2 and values in row i+1 are moved to row i/2.

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A-LOOFA performance

Test A Test B