Tech Report NWU-CS-99-03: Stochastic Scheduling

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Computer Science Department

Technical Report

NWU-CS-99-3

May 27, 1999

Stochastic Scheduling

Jennifer M. Schopf Francine Berman

Abstract

There is a current need for scheduling policies that can leverage the performance variabilityobserved when scheduling parallel computations on multi-user clusters. We develop one solution to

this problem called stochastic scheduling that utilizes a distribution of application executionperformance on the target resources to determine a performance-efficient schedule.

In this paper, we define a stochastic scheduling policy based on time-balancing for data parallel

applications whose execution behavior can be adequately represented as a normal distribution. We

demonstrate using a distributed SOR application that a stochastic scheduling policy can achievegood and predictable performance for the application as evaluated by several performance measures.


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< HighVariability

if Varibility(TP_i) > HighVariability

Figure 2. Algorithm to Compute Tuning Factor.


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Mean

5% Conservative

Mean - 2 SD

Mean - 1 SD Mean + 1 SD

Mean + 2 SD

30% Conservative 70% Conservative

50% Conservative 95% Conservative

Schedules resulting from distinct work allocations

Work allocation based on stochastic prediction

Figure 3. Diagram depicting the range of possible schedules given stochastic information.


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Table 1. First 10 execution times for experiments pictured in Figure 4.

Table 2. Summary statistics using Compare evaluation for SOR experiments.


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Table 3. Window metric for each scheduling policy out of 58 possible windows.

Table 4. Average mean and average standard deviation for entire set of runs for each scheduling policy.


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910002000.0 910004000.0 910006000.0

Timestamps

20

25

30

35

40

ExecutoinT

ime(sec)

Mean Scheduling Policy

VTF Scheduling Policy

95TF Scheduling Policy

Figure 4. Comparison of , , and policies, for the SOR benchmark on the Linux clusterwith 2 low variability machines, one medium and one high.

910142000.0 910144000.0 910146000.0

Timestamps

28

30

32

34

36

38

40

ExecutoinTime(sec)




Figure 5. Comparison of

,

, and

policies, for the SOR benchmark on the Linux cluster

for 4 low variability machines.


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910528000.0 910529000.0 910530000.0 910531000.0 910532000.0

Timestamps

0

5

10

15

20

25

30

35

ExecutoinT

ime(sec)




Figure 6. Comparison of , , and policies, for the SOR benchmark on the PCL clusterwhen 2 of the machines had a low variability in available CPU and two had high.

910531000.0 910533000.0 910535000.0

Timestamps

0

5

10

15

20

25

30

35

ExecutoinTime(s

ec)




Figure 7. Comparison of

,

, and

policies, for the SOR benchmark on the PCL cluster

when 1 of the machines had a low variability in available CPU and three had high.


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Documents

Tech Report NWU-CS-99-03: Stochastic Scheduling