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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 !