THE DEADLINEBASED SCHEDULING OF DIVISIBLE REALTIME WORKLOADS ON

THE DEADLINE-BASED SCHEDULING OF DIVISIBLE REAL-TIME WORKLOADS ON MULTIPROCESSOR PLATFORMS Suriayati Chuprat Supervisors: Professor Dr Shaharuddin Salleh Professor Dr Sanjoy K. Baruah INSPIRING CREATIVE AND INNOVATIVE MINDS

Presentation Contents • Introduction • Summary of Contributions • Anomalous Observations & Theoretical Explanations • Optimal Algorithm --MINPROCS • LP-Based Algorithm --MIN-ξ • Conclusions INSPIRING CREATIVE AND INNOVATIVE MINDS

Introduction • Formal models for representing real-time workloads – Uniprocessor environments – One particular restriction: each task may execute upon at most one processor at each instant in time. – Liu pointed out [8], “the simple fact that a [job] can use only one processor even when several processors are free at the same time adds a surprising amount of difficulty to the scheduling of multiple processors"

Real-time DLT • Divisible workload, – Arrival time, Ai ≥ 0 – Total data size of a job, i>0 – Relative deadline, Di>0, Ai+Di • DLT allows for the simultaneous execution of a job upon multiple processors

Real-time DLT • DLT Computing Cluster = (N, Cp, Cm) • N – Number of processing nodes • Cp – Time taken to process • Cm – Time taken to transmit P 0 P 1 P 2 P 3 … PN

Real-time DLT P 0 11 C Cmm 22 C 3 C m 3 Cm P 1 n Cm 1 C p p 1 C P 2 2 C pp P 3 3 C p p 3 C Pn r 1 n Cp r 2 r 3 rn Data transmission and execution time =C diagram p/(Cp+Cm) when processors have different ready times

Computing Min-N • “Given a divisible load of size and processor ready-times r 1, r 2 , …, what is the minimum number of processors needed to meet a job’s deadline? ” • Approach by Lin et al. in [9] – Abstraction of heterogeneous clusters – Approximation • Non-optimal

Computing Min-N • When allocating processors in order to meet a divisible job's deadline , a scheduling algorithm must know the minimum number required by the job • When all the processors are allocated simultaneously, recall that the completion time is given by: • The minimum number of processors needed is computed from this equation by setting this completion time to the job's deadline (A + D)

Computing Min-N • When the processors have different ready times, using the previous approach is more challenging • Lin et al. (9, 7) – Map processors to heterogeneous clusters of virtual processors with different speeds (Cpi ) – Derive a formula to determine Cpi as – Approximation ** there is a circularity of reasoning going on here

Algorithm--MINPROCS

Simulation Results – x

Simulation Results – x

Computing Completion Time • “Given a divisible load of size and n (identical) processors with ready-times r 1, …, rn upon which to execute it, what is the earliest time at which can complete execution? ” • Approach by Lin et al. in [9] – Abstraction to heterogeneous clusters – Compute the fractions of load to be assigned to each virtual processor – Compute the completion time • Non-optimal

Computing Completion Time i: fraction of load assigned to Pi ri: ready time of Pi si: time data transmission begin to Pi : Completion time Computing the completion time: LP formulation

Computing Completion Time

Conclusion • RT-DLT has the potential to provide a solid theoretical foundation to real-time distributed clusters • We have studied two scheduling problems in RT-DLT when applied to clusters with different available times: – How does one compute the minimum number of processors needed to meet a job's deadline? – Given a number of processors, how does one determine the earliest completion time for the job on this many processors? • For both problems, we provide exact solutions