Scheduling Algorithms for CIOQ Switches

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Scheduling Algorithms for CIOQ Switches

• Prashanth Pappu
• Applied Research Laboratory
• Washington University in St Louis

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Anatomy of a Router

• Transmission interfaces - terminate physical
  links, conversion and encoding functions for
  target physical layer.
• Port processors queue packets and perform all
  packet processing.
• Switching fabric single (crossbar) or multi
  stage.
• Control processor routing and network
  management protocols.

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Output Queuing

• Queuing is done only at output ports.
• Maximizes throughput.
• Contentions between packets - only at output
  ports.
• SpeedupN, impractical but ideal model.

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Combined Input Output Queuing (CIOQ)

• Use of VOQs, speedup typically lt2.
• The scheduling problem ideal OQ behavior.
• Focus of thesis Scheduling Algorithms for CIOQ
  switches.

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Crossbar Switches

• Bipartite graph matching problem.
• Stability results
• MSM stable for i.i.d, uniform admissible
  traffic.
• MWM stable for independent admissible traffic.
• Too complex, O(N5/2) and O(N3logN).
• Router with 10Gb/s links has lt 40 ns to make
  scheduling decision.
• Maximal size matching. (PIM iSLIP)
• Simple to implement but do not perform well under
  extreme traffic conditions.

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Crossbar Switches (contd.)

• Worst case results
• Critical cell first (CCF) and Lowest Output
  Occupancy First Algorithm (LOOFA) O(N) - work
  conserving with speedup of 2.
• Significant results but not practical.
• Traffic in IP networks unregulated and can
  cause sustained overloads (inadmissible traffic).
• Slow congestion control mechanisms.
• Rapid traffic shifts due to route changes.
• Route selection mechanisms not guided by session
  needs.
• Presence of malicious users etc.
• How do practical scheduling algorithms perform
  under these conditions?

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Multi-stage switches

• Scalable no scheduling algorithm.
• Use buffered switch elements, dynamic routing and
  modest speedup.
• Loss of performance in extreme traffic
  conditions.
• How do we regulate traffic in such multi-stage
  switches using buffered switch elements?

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Proposal Overview

• Stress resistant scheduling algorithms.
• Simple, practical algorithms for crossbar
  switches.
• Maintain throughput under uniform traffic and
  extreme traffic conditions (stress tests).
• Stress tests adversarial traffic patterns to
  simulate extreme conditions.
• Stress resistant scheduling algorithms for CIOQ
  switches, Prashanth Pappu and Jon Turner. In
  ICNP 2003.
• Distributed scheduling (DS)
• A novel, scalable (coarse-grained and
  distributed) mechanism for regulating traffic in
  multi-stage switches.
• Comprehensive study covering work conserving,
  backlog based, time-sliced and fair DS
  algorithms.
• Distributed queuing for scalable, high
  performance routers, Prashanth Pappu, Jyoti
  Parwatikar, Jon Turner and Ken Wong. In Infocom
  2003.

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Stress Tests

• How do we simulate extreme traffic conditions?
• Adversarial approach in overloading outputs.
• Stress (overload) various outputs with the
  objective of increasing misses.
• New metric, miss fraction 1 NA/ NI. (instead
  of delay)
• Tests can be varied by changing number of
  participating inputs and phases.

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Stress Test (Example)

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

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Stress Tests

• Parallel Iterative Matching (PIM) and iterative
  SLIP (iSLIP) iterative,
• simple to implement.
• Lowest Output Occupancy first Algorithm (LOOFA)
  provably good
• worst case performance but too complex to
  implement.

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Approximate Output Ordering

• ordering outputs is the key
• complete ordering can be too complex.
• persistent and slowly changing traffic condition
  approximate ordering can be good enough.
• Lowest Layer Selection
• 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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Stress Test
Miss fractions for LLS-R, LLS-S (using 16 layers)
and LOOFA.
Test B
Test A
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Approximate LOOFA (A-LOOFA)

• LOOFA can be used as the basis for a simpler
  algorithm.
• Matching in A-LOOFA is accomplished using a
  simple combinational circuit (O(N) complexity but
  constant factor gate delays)
• .13 um ASIC process, gate delays are 25-50 ps.
  Match can be completed in 3.2-6.4 ns for N32.
• Outputs (columns) are sorted using odd-even sort.
• Inputs (rows) are ordered using a permutation
  based on perfect shuffle (for fairness).

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Stress Resistant Scheduling Algorithms

• Done
• Delay vs. Miss fraction as a metric.
• Performance of LLS-R and LLS-S with varying
  number of layers.
• Performance of A-LOOFA under stress test.
• To do
• More stress tests.
• Detailed notes on implementation.

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Distributed Scheduling
ControlProcessor
Switch Fabric
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Sched.
Routing
Routing
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Routing
Routing
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Distributed Scheduling

• Paradigm shift from scheduling cells to
  regulating rates.
• Very scalable router with 1000 links (10 Gb/s
  each) needs T lt 100 us for 5 overhead.
• Simple to implement voq status in control
  cells.
• Constraints on allocated rates input and output
  constraints.
• Throughput and delay properties depend on rate
  allocation algorithm used.

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Questions

• Can we design work conserving algorithms which
  make scheduling decisions only every T cycles?
• Work conserving scheduling algorithms.
• Can we make these work conserving algorithms
  non-iterative?
• No, work conserving algorithms need multiple
  iterations.
• How do we design simple non-iterative algorithms
  that have good throughput even under extreme
  traffic patterns?
• Backlog based DS algorithms.
• How do we design simple algorithms that have both
  good throughput and delay properties?
  (Approximate OQ emulation)
• Time sliced DS algorithms.
• How do we use the DS mechanism to provide per
  flow guarantees?
• Fair DS algorithms.

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Work conserving scheduling algorithms.

• Can a scheduling algorithm that makes a
  scheduling decision every T cycles be work
  conserving?
• Maximal A scheduling algorithm is said to be
  maximal if for any cell c that is not transferred
  in the transfer phase, either S x T cells at cs
  input are transferred or S x T cells are
  transferred to cs output.
• VOQs are ordered based on output queue length.
  Ordering can be extended to cells in VOQs too.
• Ordered A scheduling algorithm is said to be
  ordered if for any cell c that is not
  transferred, no cell preceded by c at the same
  output gets transferred unless cs output gets S
  x T cells.
• Claim - A scheduling algorithm that is both
  ordered and maximal is work conserving (with a
  speedup of 2).

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Backlog based DS algorithms

• Work conserving scheduling algorithms require
  multiple iterations impractical.
• Practical rate allocation algorithms have to be
  non-iterative too
• DSCs periodically exchange B(i,j) and B(j)
• Non-iterative DS algorithms that use only these
  backlogs carried in control cells backlog based
  DS algorithms.
• Objective To maintain throughput under both
  admissible and inadmissible traffic conditions.
• We design algorithms based on two heuristics.

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Backlog based DS algorithms

• Output constraint backlog proportional
  allocation
• avoids switch congestion
• ensures fairness for uniform traffic
• Input constraint urgency proportional
  allocation
• priority for outputs with smaller queue lengths.

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Time-sliced DS algorithms

• Backlog based DS algorithms can badly mis-order
  cells when arrival rates change abruptly.
• Information carried in cells has no timing
  information
• Can be overcome by using queue length slices
  instead of total queue lengths in the rate
  calculation.
• In the worst case, creates an overhead of one
  word per packet.

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Time sliced DS algorithms
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Fair DS algorithms

• To support fair queuing input and output
  maintain per flow queues.
• Switch fabric bandwidth allocated among inputs in
  proportion to sum of weights of backlogged flows.
• Excess bandwidth reallocated by inputs among
  local backlogged flows.
• Can render output non-work conserving but
  reallocation mechanisms require multiple
  iterations.

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Distributed Scheduling

• Done
• DS mechanism implementation.
• Work conserving scheduling algorithms.
• Performance study of backlog based non-iterative
  DS algorithms.
• To do
• Performance study of time-sliced DS algorithms.
• Performance study of Fair DS algorithms.