Requirements on the Execution of Kahn Process Networks

1

• Requirements on the Execution of Kahn Process
  Networks

Marc Geilen and Twan Basten
11 April 2003
/e
2
Overview

1. Introduction Kahn Process Networks
2. Implementing KPNs
3. Execution of KPNs
4. An Improved Scheduling Algorithm
5. Conclusions

3
1. Introduction Kahn Process Networks
4
Kahn Process Networks

• Arcs carry (possibly infinite) streams of tokens
  (audio samples, video frames, etc.)

• Nodes compute (continuous) functions on streams

5
Kahn Process Networks

• Good for multimedia and signal processing
  applicationsE.g., JPEG/MPEG decoding,
  image/video processing
• Explicit parallelism and communication
• No synchronization between processes required
• Programming paradigm for modern multi-processor
  architecturesMITs RAW, Philips SpaceCake

6
KPN Semantics

• Arcs connecting functions
• Set of equations

• Continuous functionsunique least solution
• Semantics of KPN least fixed-point
• Yields new continuous functionCompositionality

7
2. Implementing KPNs
8
Realizations of KPNs

• Functions sequential (determinate) programs,
  e.g. C or Java

• Blocking read operations

9
Realizations of KPNs

• Functions sequential (determinate) programs,
  e.g. C or Java

• Blocking read operations

• Arcs FIFO queuesStore tokens that are written
  but not yet read

10
Realizations of KPNs

• DeterminacyOutput is independent of scheduling
  order
• CompositionalityHierarchically, recursively,
• The Kahn Principle Operational model with fair
  execution and unbounded channels realizes the
  formal semantics

11
Implementation Requirements

• When is an implementation of a KPN good?

12
Implementation Requirements

• Boundedness

13
Implementation Requirements

• Completeness infinite execution vs. chain of
  strings

14
3. Execution of KPNs
15
Implementations of KPNs

• Often follow Thomas Parks 95 scheduling
  approachYAPI, Jade/Pagis, Ptolemy II among
  others
• Bounded FIFOs combine aspects of data- and demand
  driven execution

• FIFO bounds balance memory usage and context
  switching
• (Minimal) FIFO bounds are undecidableRun-time
  management

16
Implementations of KPNs

• Blocking on full FIFO artificial deadlocks
• Causal chains

17
Implementations of KPNs

• Execution thread per processPOSIX threads, Java
  threads,
• Artificial deadlock detection and resolution
  strategies
• Often global deadlock detectionLow priority
  thread

18
Implementations of KPNs

• Parks algorithm yields infinite computation, but
  possibly not complete
• Local deadlocks may remain undetected(fairness
  is violated)

• Deadlocks are cyclic causal chains

19
4. An Improved Scheduling Algorithm
20
Improved Scheduling Algorithm

• Deadlocks cannot be avoided by scheduling
• Artificial deadlock occurs (only) if FIFO bounds
  are too small
• (At least) one of the full FIFOs on a deadlock
  cycle must be too small

• Increase size of the smallest full FIFO

21
Improved Scheduling Algorithm

1. Schedule enabled processes (in a fair way)
2. Until deadlock occurs (cyclic causal chain)
3. Resolve deadlock by increasing the smallest full
   FIFO

22
Correctness

• Operational (LTS) semantics of KPNs (see
  paper)Equivalent to KPN semantics by the Kahn
  Principle
• Operational semantics of realizations of
  KPNsbounded channels
• Show that both implement the same function

23
Correctness

• The new scheduling algorithm realizes the the
  formal semantics of Kahn Process Networks
• Every bounded and effective KPN is executed in
  bounded memory by our scheduler and produces the
  complete output.

24
Correctness

• PrerequisitesBoundedness there exists a fair
  execution with finite FIFO bounds
• Effectiveness every token that is produced on
  some channels is eventually also consumed

• Both prerequisites are necessary

25
Local deadlock detection

• Deadlock detection becomes more involved
• Need not be done at every step of the execution
• May be possible to do this concurrently

26
Conclusions

• Studied implementation requirements for KPNs
  boundedness and completeness
• Widely used implementation of KPNs does not
  schedule all KPNs correctly
• We have presented an improved scheduling
  algorithm that resolves the problem for a large
  class of KPNs
• And proved its correctness (in the paper)

27
Future Work

• An implementation of the improved scheduling
  algorithm is being made for YAPI
• Efficiency of scheduling. Optimal bounds,
  efficient deadlock detection
• Hierarchical or distributed implementationsDistri
  buted deadlock detection