1 Two-type Heterogeneous Multiprocessor Scheduling: Is there a Phase Transition? Gurulingesh Raravi, Björn Andersson and Konstantinos Bletsas CISTER-ISEP Research Centre Polytechnic Institute of Porto 30/06/20151

2 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 30/06/20152

3 Introduction Phase Transition – Transition of a system from one state to another upon changing some system parameters 30/06/20153

4 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 30/06/20154

5 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 scheduling 30/06/20155

6 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 30/06/20156

7 Some Insights Simulations and Observations: – Simulation setup 30/06/20157

8 Some Insights Simulations and Observations: – Simulation setup 30/06/20158 Generate a random problem instance at most 15 tasks and 4 processors (2 of each type)

9 Some Insights Simulations and Observations: – Simulation setup 30/06/20159 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

10 Some Insights Simulations and Observations: – Simulation setup 30/06/ 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

11 Some Insights Simulations and Observations: – Simulation setup 30/06/ 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 = N succ /N valid

12 Some Insights Simulations and Observations: – Simulation setup 30/06/ 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 = N succ /N valid Repeat till feasible task sets are found

13 Some Insights Simulations and Observations: – Observations Plotted for feasible task sets 30/06/201513

14 Some Insights Simulations and Observations: – Observations (for feasible task sets) – Observations: No sharp threshold Fluctuations/peaks in the range 0 ≤ Z ≤ 0.4 is probably due to imbalanced task generation 30/06/201514

15 The Question – Observations (for 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 30/06/201515

16 Few Questions – Observations (for 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 30/06/ Thank You !