1 Two-type Heterogeneous Multiprocessor Scheduling: Is there a Phase Transition? Gurulingesh Raravi, Björn Andersson and Konstantinos Bletsas CISTER-ISEP.

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Two-type Heterogeneous Multiprocessor Scheduling: Is there

a Phase Transition?

Gurulingesh Raravi, Björn Andersson and Konstantinos BletsasCISTER-ISEP Research Centre

Polytechnic Institute of Porto

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Introduction• System Model

– Computing Platform• Two-type Heterogeneous platform

– A platform with two unrelated processor types

– Task set• implicit-deadline sporadic tasks

– Assumptions• Independent Tasks• No Migrations• No job parallelism

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Introduction• Phase Transition

– Transition of a system from one state to another upon changing some system parameters

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Introduction• Phase Transition

– Transition of a system from one state to another upon changing some system parameters

• Phase Transition in Real-Time Scheduling– Transition of a system from “almost surely

schedulable” state to “almost surely not schedulable” state upon changing the task set characteristics

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Introduction• Phase Transition

– Transition of a system from one state to another upon changing some system parameters

• Phase Transition in Real-Time Scheduling– Transition of a system from “almost surely

schedulable” state to “almost surely not schedulable” state upon changing the task set characteristics

• Uni-processor Rate Monotonic Scheduling:– U*

RM: Utilization threshold» U(τ) ≤ U*

RM then τ is almost surely schedulable

» U(τ) > U*RM then τ is almost surely not schedulable

• Identical multiprocessor scheduling19/04/23 5

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The Problem• Does there exist a phase transition behavior for

the two-type heterogeneous multiprocessor scheduling problem?– Is there a threshold for a parameter (or combination

of parameters) which classifies the task set from “almost surely schedulable” state to “almost surely not schedulable” state

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Some Insights

• Simulations and Observations:– Simulation setup

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Some Insights

• Simulations and Observations:– Simulation setup

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Generate a random problem instance

at most 15 tasks and 4 processors (2 of each type)

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Some Insights

• Simulations and Observations:– Simulation setup

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Generate a random problem instance

Is there a feasible

assignment? Z<=1

at most 15 tasks and 4 processors (2 of each type)

Using ILP formulation

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Some Insights

• Simulations and Observations:– Simulation setup

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Generate a random problem instance

Is there a feasible

assignment? Z<=1

at most 15 tasks and 4 processors (2 of each type)

Using ILP formulation

NO

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Some Insights

• Simulations and Observations:– Simulation setup

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Generate a random problem instance

Is there a feasible

assignment? Z<=1

at most 15 tasks and 4 processors (2 of each type)

Using ILP formulation

NO

YES

Compute the “success ratio”

Using Exhaustive Enumeration:

ratio = Nsucc/Nvalid

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Some Insights

• Simulations and Observations:– Simulation setup

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Generate a random problem instance

Is there a feasible

assignment? Z<=1

at most 15 tasks and 4 processors (2 of each type)

Using ILP formulation

NO

YES

Compute the “success ratio”

Using Exhaustive Enumeration:

ratio = Nsucc/Nvalid

• Repeat till 10000 feasible task sets are found

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Some Insights

• Simulations and Observations:– Observations

• Plotted for 10000 feasible task sets

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Some Insights

• Simulations and Observations:– Observations (for 10000 feasible task sets)

– Observations:• No sharp threshold• Fluctuations/peaks in the range 0 ≤ Z ≤ 0.4 is probably

due to imbalanced task generation

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The Question– Observations (for 10000 feasible task sets)

• Questions:– Is there a phase transition?

• Yes: What parameters should we observe?• No: What is its implication?

– considering such a behavior has been observed for:» uni-processor (RM) and identical multiprocessor scheduling

• Any insights will be useful 19/04/23 15

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Few Questions– Observations (for 10000 feasible task sets)

• Questions:– Is there a phase transition?

• Yes: What parameters should we observe?• No: What is its implication?

– Since such a behavior has been observed for:– uni-processor and identical multiprocessor scheduling

• Any insights will be useful 19/04/23 16

Thank You !