Chapter

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Chapter 5.2 Static Process Scheduling

• Anjum Reyaz-Ahmed

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Outline

• Part I Static Process Scheduling
• Precedence process model
• Communication system model
• Part II Current Literary Review
• "Optimizing Static Job Scheduling in a Network of
  Heterogeneous Computers," ICPP 2000
• Design Optimization of Time- and Cost-
  Constrained Fault-Tolerant Distribution Embedded
  Systems, DATE 2005
• White Box Performance Analysis Considering
  Static Non-Preemptive Software Scheduling, DATE
  2009
• Part III Future Research Initiatives

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Static Process Scheduling

• Given a set of partially ordered tasks, define a
  mapping of processes to processors before the
  execution of the processes.
• Cost model CPU cost and communication cost, both
  should be specified in prior.
• Minimize the overall finish time (makespan) on a
  non-preemptive multiprocessor system (of
  identical processors)
• Except for some very restricted cases,
  scheduling to optimize the makespan are
  NP-Complete
• Heuristic solution are usually proposed

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Precedence Process Model

• This model is used to describe scheduling for
  program which consists of several sub-tasks.
  The schedulable unit is sub-tasks.
• Program is represented by a DAG.
• Precedence constraints among tasks in a program
  are explicitly specified.
• critical path the longest execution path in the
  DAG, often used to compare the performance of a
  heuristic algorithm.

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Precedence Process and Communication System Models
Communication overhead for A(P1) and E(P3) 4
2 8
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contd..

• Scheduling goal minimize the makespan time.
• Algorithms
• List Scheduling (LS) Communication overhead is
  not considered. Using a simple greedy heuristic
  No processor remains idle if there are some tasks
  available that it could process.
• Extended List Scheduling (ELS) the actual
  scheduling results of LS with communication
  consideration.
• Earliest Task First scheduling (ETF) the
  earliest schedulable task (with communication
  delay considered) is scheduled first.

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Makespan Calculation for LS, ELS, and ETF
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Communication Process Model

• There are no precedence constrains among
  processes
• modeled by a undirected graph G, node represent
  processes and weight on the edge is the amount of
  communication messages between two connected
  processes.
• Process execution cost might be specified some
  times to handle more general cases.
• Scheduling goal maximize the resource
  utilization.

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contd

• the problem is to find an optimal assignment of
  m process to P processors with respect to the
  target function
• P a set of processors. ej(pi) computation cost
  of execution process pi in processor Pj.
• ci,j(pi,pj) communication overhead between
  processes pi and pj.
• Assume a uniform communicating speed between
  processors.

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• This is referred as Module Allocation problem. It
  is NP-complete except for a few cases
• For P2, Stone suggested an polynomial time
  solution using Ford-Fulkersons maximum flow
  algorithm.
• For some special graph topologies such as trees,
  Bokharis algorithm can be used.
• Known results The mapping problem for an
  arbitrary number of processors is NP-complete.

Problem optimal polynomial time algorithm suboptimal
2 processor Yes
2 proc. with varying load Yes
tree-structured graph Yes
series parallel graph Yes
3 and more processor systems yes
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Stones two-processor model to achieve minimum
total execution and communication cost

• Example
• Partition the graph by drawing a line cutting
  through some edges
• Result in two disjoint graphs, one for each
  process
• Set of removed edges ? cut set
• Cost of cut set ? sum of weights of the edges
• Total inter-process communication cost between
  processors
• Of course, the cost of cut sets is 0 if all
  processes are assigned to the same node
• Computation constraints (no more k, distribute
  evenly)
• Example
• Maximum flow and minimum cut in a commodity-flow
  network
• Find the maximum flow from source to destination

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Maximum Flow Algorithm in Solving the Scheduling
Problem
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Minimum-Cost Cut
Only the cuts that separate A and Bare feasible
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Generalized solution for more than two processor

1. Stone uses a repetitive approach based on
   two-processor algorithm to solve n-processor
   problems.
2. Treat (n-1) processors as one super processor
3. The processors in the super-processor is further
   broken down based on the results from previous
   step.

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Other Heuristics

• Other heuristic separate the optimization of
  computation and communication.
• Assume communication delay is more significant
  cost
• merge processes with higher interprocess
  interaction into cluster of processes
• clusters of processes are then assigned to the
  processor that minimizes the computation cost
• With reduced problem size, the optimal is
  relatively easier to solve (exhaust search)
• A simple heuristic merge processes if
  communication costs is higher than a threshold C
• Also can put constrains on the total computation
  for the cluster, to prevent over clustering.

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Cluster of Processes

• For C 9, We get three clusters (2,4), (1,6 )and
  (3,5)
• Clusters (2,4) and (1,6) must be mapped to
  processors A and B.
• Cluster (3,5) can be assigned to A 0r B But
  assigned to A due to lower communication cost
• Total Cost 41 ( Computation cost 17 on A and
  14 on B Communication cost 10)

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Part II Current Literary Review
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Optimizing Static Job Scheduling in a Network of
Heterogeneous Computers-----Xueyan Tang Samuel
T. Chanson-----IEEE 2000

• Summary
• Static job scheduling schemes in a network of
  computers with different speeds.
• Optimization techniques are proposed for workload
  allocation and job dispatching.
• The proposed job dispatching algorithm is an
  extension of the traditional round-robin scheme

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Optimization for Workload Allocation

• a fraction ai of all the jobs are sent to
  computer ci
• where

Tang Chanson 2000
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Simple Weighted Workload Allocation

• Amount of workload for each computer proportional
  to its processing speed
• All computers are equally utilized .
• Does not provide best performance

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Dynamic Least-Load Scheduling

• Beneficial to allocate a disproportional higher
  fraction of the workload to the more powerful
  computers.
• Assign new job to the machine with least
  normalized load
• it is known that jobs moved from a slow machine
  to a fast machine, decreases slow machines
  utilization decreases a lot whereas utilization
  of fast machine does not increase that much

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Optimizing Technique for Job Dispatching

• Random Based Job Dispatching
• Newly arrived job is scheduled to run on
  randomly selected computer
• Round-Robin Based Job Dispatching
• The objective here is to smooth inter-arrival
  intervals of consecutive jobs .
• For example suppose there are 4 computers c1, c2,
  c3 and c4 with workload fractions 1/8, 1/8, 1/4
  and ½ respectively.
• Dispatching scheme -? c4, c3, c4, c2, c4, c3, c4,
  c1, c4, c3, c4, c2, c4, c3, c4, c1,

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Summary

• The key idea of optimizing the workload
  allocation scheme it to send a disproportionately
  high fraction of workload to the most powerful
  computers.
• An analytical model is developed to derive the
  optimized allocation strategy mathematically
• For job dispatching an algorithm that extends
  round-robin to a general case is presented

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Design Optimization of Time- and Cost-Constrained
Fault-Tolerent Distributed Embedded Systems---- V
Izosimov, P Pop, P Eles Z Peng-------DATE, IEEE
2005

• Synopsis
• Re-execution and Replication are used for
  tolerating transient faults
• Processes are statically schedules and
  communication are performed using the time
  triggered protocol

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System Architecture

• Each node has a CPU and communication controller
  running independently
• Time Triggered Communication Protocol

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Fault-Tolerance Mechanisms

• Re-execution
• Active Replication

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Summary

• Addresses optimization of distributed embedded
  systems for fault tolerance
• Two fault-tolerance mechanism
• Re-execution time redundancy
• Active replication space redundancy

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White Box Performance Analysis Considering Static
Non-Preemptive Software Scheduling --- A Viehl, M
Pressler, Oliver Bringmann---- DATE IEEE 2009

• Synopsis
• A novel approach for the integration of
  cooperative and static non-preemptive scheduling
  in formal white box analysis presented

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Future Research Initialtive

• Use AI techniques for Static Scheduling
• Genetic Algorithm
• Simulated Annealing

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References

1. Randy Chow Theodore Johnson . Distributed
   Operating Systems Algorithms. pp 156-163
   Addison-Wesley 1997
2. Xueyan Tang Samuel T. Chanson. Optimizing
   Static Job Scheduling in a Network of
   Heterogeneous Computers. pp 373- 382, icpp,
   IEEE 2000
3. Viacheslav Izosimov, Paul Pop, Petru Else Zebo
   Peng. Design Optimization of Time- and
   C0st-Constrained Fault Tolerant Distribution
   Embedded Systems. Design Automation and Test in
   Europe (DATE), IEEE, 2005
4. Alxander Viehl, Michael Pressler and Oliver
   Bringmann. White Box Performance Analysis
   Considering Static Non-Preemptive Software
   Scheduling. Design Automation and Test in Europe
   (DATE), IEEE, 2009

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• Thank you!!