Parallel Job Scheduling with Overhead: A Benchmark Study

1
Parallel Job Scheduling with Overhead A
Benchmark Study

• Richard Dutton
• Weizhen Mao
• Jie Chen
• William Waston

2
Motivation

• Parallel system with identical processors
• Malleable jobs that can be executed by any number
  of available processors
• Effect of the number of processors assigned to a
  job on the jobs execution time
• Ideally, the more the processors assigned, the
  shorter the execution time
• In reality, overhead (due to communication,
  synchronization and processor management)
  proportional to the number of processors

3
Linear Model

• Assume p is the length of a job and k is the
  number of processors assigned
• The execution time of the job is t p / k
• The linear model reflects the linear speedup in
  computation time but ignores the overhead
  slowdown
• Most often mentioned and used

4
Overhead Model

• The execution time t p / k (k - 1) c
• c is the constant overhead per slave processor,
  linked to the parallel system
• The overhead model combines the computation
  speedup and communication slowdown due to the use
  of multiple processors
• Sophisticated enough to reflect reality and
  simple enough for theoretical analysis

5
t p / k vs. t p / k (k - 1) c
6
Some Questions about the Overhead Model

• Is the overhead model truly better than the
  linear modle in reflecting the effect of multiple
  processors on execution times?
• When too many processors are used, does the
  execution time indeed increase (or at least
  decrease at a slower rate than in the linear
  model)?

7
Assessment Method

• Choose parallel benchmarks and a parallel system
• Run each benchmark on various of processors and
  record execution times
• For each benchmark, use LSF to fit the
  (k,t)-curve using the linear and overhead models
• Compare fitting results for both models

8
Parallel Benchmarks Selected

• Conjugate Gradient (CG)
• Fourier Transform (FT)
• Integer Sort (IS)
• Block Tridiagonal (BT)
• High Performance Linpack (xhpl)

9
Parallel System Used

• A cluster of 128 nodes at Jefferson Lab
• 1 node 2 quad-core AMD Opteron processors
  (1.9GHz) 4GB memory
• A total of 1024 processors to use
• 20GB bandwidth Infiniband DDR
• Fedora Core 7, Linux Kernel 2.6.22, gcc 4.1.2,
  and MVAPICH 0.9.9

10
Experiment Result CG
11
Experiment Result FT
12
Experiment Result IS
13
Experiment Result BT
14
Experiment Result xhpl
15
Experiment Result Relative error histogram
16
A Scheduling Problem

• n malleable jobs job j with length p_j
• m identical parallel processors
• t_j p_j / k_j (k_j - 1) c if k_j processors
  are used for job j
• Online scheduling job 1, , job n
• Minimize the makespan

17
Two Algorithms How to choose k_j

• SET (Shortest Execution Time first) Minimize
  t(k) p_j / k (k - 1) c
• ECT (Earliest Completion Time first) Minimize
  C_j s_j p_j / k (k - 1) c, where s_j is the
  start time of job j and C_j is the completion time

18
Analysis of SET and ECT

• SET is guaranteed to construct schedules of
  makespan that is no more than 4 times of the
  optimal makespan
• ECT is conjectured to construct schedules of
  makespan that is no more than 30/132.31 times of
  the optimal makespan

19
Conclusions

• Compared with the traditionally used linear
  model, the overhead model more accurately
  reflects the effect of multiple processors on
  execution time
• Theoretical analysis for scheduling problems
  defined under the overhead model is nontrivial
  but possible