Performance Analysis of Applications with Stochastic Task Execution Times

1
Performance Analysis of Applications with
Stochastic Task Execution Times

• Sorin Manolache, Petru Eles, Zebo Peng
• University of Linköping, Sweden
• sorma, petel, zebpe_at_ida.liu.se

2
Overview

• Toolset consisting of three tools
• Computation model set of annotated task graphs
• Main performance indicator expected deadline
  miss ratio per task or task graph

3
Computation Model
E

• Deadlines

B

• Late task policy

F

• Scheduling policy

D
4
Internals

1. Concurrently constructs and analyses the GSMP
   underlying the system. Method of supplementary
   variables tricks for memory reduction.
2. Constructs the GSMP. Approximates the GSMP with a
   much larger CTMC. Exploits the regular structure
   of the CTMC for on-the-fly generation of its
   infinitesimal generator.
3. Recursively computes the finishing time
   distribution, ignoring some dependencies among
   some of the random variables modelling the system.

5
Limitations

• We assume non-preemptive execution in all three
  methods
• First method is efficient only in the case of
  monoprocessor applications
• Third method is limited to fixed-priority
  scheduling

6
Scalability

• Third method is polynomial O(N?LCM/h?ETPDF/h)
• First two methods build the GSMP underlying the
  application ?
• Analysis visits each state that described the
  behaviour of the system ?
• Theoretically exponential, but practically

7
Practically
First method (for monoprocessors)

• 20 independent tasks
• 200 dependent tasks

8
Practically
Second method (for multiprocessors)

• 60 dependent tasks on 2 processors
• 18 dependent tasks on 6 processors

9
Accuracy

• First method gives exact results
• Second method relies on approximating generalised
  distributions with Coxian distributions ?
  problems with non-smooth distributions
• Third method gives approximate results. Its
  accuracy is experimentally investigated

10
Case Study

• Tasks A and B have exponentially distributed
  execution times, average rate 1/7 and 1/2
  respectively
• Task C, D, and E execute for 4, 5, and 6 time
  units respectively
• Interprocessor communication takes 0.5 time units
• Tasks on the orange processor in descending order
  of priorities E, C, D.

A
B
E
C
D
11
Case Study (contd)
12
Conclusions

• Three performance analysis approaches for
  applications with stochastic task execution times

Multiproc. Accuracy Exponential Design space exploration
Exact approach No Exact Theoretically yes, practically not a problem No
ETPDF approx. Yes Good for smooth distributions Yes, in the number of processors No
Equation-based Yes Coarser than ETPDF approx. No. Linear in the number of tasks. Yes