Costefficient synthesis of realtime systems upon heterogeneous multiprocessor

Cost-efficient synthesis of real-time systems upon heterogeneous multiprocessor platforms Sanjoy Baruah The University of North Carolina at Chapel Hill Supported in part by the U. S. National Science Foundation

Multiprocessor real-time scheduling Multiprocessor systems are important 4 more computing capacity, at less cost 4 arise naturally in many situations Long-term goal: Extend real-time scheduling theory to multiprocessors In this work: schedule periodic tasks on heterogeneous multiprocessors Outline of talk: • background • problem description • results background – problem – results

Real-time process model Jobs: basic units of work 4 characterized by three parameters • arrival/ release time • execution requirement • deadline 4 are preemptable Recurring tasks 4 generate the jobs 4 are independent background – problem – results

The periodic (Liu & Layland) task model Task T = (e, p) 4 execution requirement 4 period 4 (utilization e/p) Jobs: 4 first job arrives at any time; consecutive arrivals at least p time units apart 4 each job has execution requirement e 4 each job’s deadline is p time units after arrival Example: T = (2, 5) (2) (2) (2) time 0 5 10 15 20 background – problem – results

Migration issues on multiprocessors Partitioned scheduling Each task may only execute on a specific processor Global scheduling Any task’s job may execute on any processor background – problem – results

Migration issues on multiprocessors Partitioned scheduling: 1. Determine a mapping of tasks to processors 2. Perform run-time scheduling The Earliest Deadline First (EDF) scheduling algorithm - provably optimal (utilization bound = 1. 0) on uniprocessors Partitioned with EDF 4 Assign tasks to the processors, such that no processor’s capacity is exceeded 4 Schedule each processor using EDF background – problem – results

Multiprocessor models identical multiprocessors: each processor has the same computing capacity uniform multiprocessors: different processors have different computing capacities heterogeneous multiprocessors: each (task, processor) pair may have a different computing capacity background – problem – results

Multiprocessor models Fraction of computing capacity P 1 P 2 P 3 background – problem – results

Multiprocessor models identical multiprocessors: each processor has the same computing capacity Task T 1 Task T 2 P 1 P 2 P 3 background – problem – results

Multiprocessor models uniform multiprocessors: different processors have different computing capacities Task T 1 Task T 2 y/2 y y/3 x x/2 P 1 speed = 1 x/3 P 2 speed = 2 P 3 speed = 3 background – problem – results

Multiprocessor models heterogeneous multiprocessors: each (task, processor) pair may have a different computing capacity Task T 1 Task T 2 y y 1. 5 y x x/2 P 1 x/3 P 2 P 3 background – problem – results

Why study heterogeneous multiprocessors? Natural generalization of earlier models Systems synthesized using specialized COTS processors y y 1. 5 y Number-crunching task: x x/2 Graphicsintensive task: CPU DSP chip x/3 Graphics co-processor background – problem – results

Problem statement Given 4 system specification, as a collection of periodic real-time tasks 4 a library of available processing units (and corresponding costs) Determine 4 a (multiprocessor) implementation, comprised of the available kinds of processing units, of minimum cost Periodic task system A COST-OPTIMAL Implementation of A SYSTEM SYNTHESIZER Available processors background – problem – results

Problem example System specification: as a utilization matrix + a cost vector Cost/ processor: 10 A= 2 4 P 1 P 2 P 3 T 1 0. 4 0. 8 T 2 0. 3 0. 25 0. 6 T 3 0. 4 0. 8 0. 5 T 4 0. 5 T 5 0. 35 0. 5 Periodic task system A COST-OPTIMAL T 2 needs 0. 6 of P 3’s capacity T 4 cannot execute on P 2 Implementation of A SYSTEM SYNTHESIZER Available processors background – problem – results

Problem example System specification: as a utilization matrix + a cost vector 10 A= 2 4 P 1 P 2 P 3 T 1 0. 4 0. 8 T 2 0. 3 0. 25 0. 6 T 3 0. 4 0. 8 0. 5 T 4 0. 5 T 5 0. 35 0. 5 A possible implementation: • uses P 1 procs only T 2 T 4 • cost = 10 + 10 = 30 T 1 T 3 T 5 P 1 P 1 background – problem – results

Problem example System specification: as a utilization matrix + a cost vector 10 A= 2 4 P 1 P 2 P 3 T 1 0. 4 0. 8 T 2 0. 3 0. 25 0. 6 T 3 0. 4 0. 8 0. 5 T 4 0. 5 T 5 0. 35 0. 5 A better implementation: T 1 uses one processor of each type • cost = 10 + 2 + 4 = 16 T 5 T 3 T 4 T 2 P 1 P 2 P 3 background – problem – results

Problem example System specification: as a utilization matrix + a cost vector 10 A= 2 4 P 1 P 2 P 3 T 1 0. 4 0. 8 T 2 0. 3 0. 25 0. 6 T 3 0. 4 0. 8 0. 5 T 4 0. 5 T 5 0. 35 0. 5 An even better implementation: T 1 uses one P 1 and two P 2’s cost = 10 + 2 = 14 T 5 T 3 T 4 T 2 P 1 P 2 background – problem – results

Results-I: intractability Given: An (n m) matrix representing a task system, and an m-vector of processor costs, determine a mapping of the n tasks onto processors to minimize the total processor cost. Result: The minimum cost heterogeneous multiprocessor synthesis problem is NP-hard in the strong sense Proof: Transform from bin-packing Consequence: Unlikely to be able to solve efficiently even for relatively small systems background – problem – results

Results-II: Approximation algorithms The minimum cost heterogeneous real-time system implementation problem is NP-hard in the strong sense OBJECTIVE: Obtain approximate solutions to this problem: • Obtain low-cost implementations… • …with cost a bounded amount greater than the minimum cost RESULTS: Polynomial time algorithms for obtaining system implementations of cost at most cost. OPT + c, • 2 cost. OPT + c, • for global scheduling algorithms for partitioned scheduling algorithms where c is a constant independent of the system being designed background – problem – results

Summary Fact: Low-cost implementations are important Fact: Heterogeneous multiprocessor implementations are common But, the heterogeneity is usually not exploited … because heterogeneous systems are not well understood NSF CCR-0309825: Real-time Scheduling on Heterogeneous Multiprocessors Results: Approximation algorithms for minimum-cost synthesis of periodic task systems upon heterogeneous multiprocessor platforms that are 1. asymptotically optimal, under the global scheduling paradigm 2. asymptotically 2 -approximate, under the partitioned scheduling paradigm