Robust resource allocations through performance modeling with stochastic process algebra

Parallel and distributed computing has led to a proliferation in solving computationally intensive mathematical, science, or engineering problems. However, such computational environments are often prone to unpredictable variations due to problem, algorithm, and system characteristics. Therefore, a robustness study of resource allocations and application scheduling is required to guarantee a desired level of performance. Given an initial workload, a mapping of applications to resources is considered to be robust if it optimizes the execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research work, a stochastic process algebra, performance evaluation process algebra, is used for obtaining performance of various resource allocations via a numerical analysis of performance modeling of the parallel execution of applications on parallel computing resources. Further, a robustness analysis of various allocations is performed for finding a robust mapping from a set of initial mapping schemes. The numerical results obtained from this performance modeling of resource allocations have been validated by the simulation results of earlier research, which are available from the existing literature, thus underscoring the significance of using stochastic process algebra models in providing a cost‐effective and low overhead analysis of robustness. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Stephen Gilmore,et al.  Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler , 2003, 11th IEEE/ACM International Symposium on Modeling, Analysis and Simulation of Computer Telecommunications Systems, 2003. MASCOTS 2003..

[2]  Ray Jain,et al.  The art of computer systems performance analysis - techniques for experimental design, measurement, simulation, and modeling , 1991, Wiley professional computing.

[3]  Ladislau Bölöni,et al.  Robust scheduling of metaprograms , 2002 .

[4]  Robert H. Storer,et al.  Robustness Measures and Robust Scheduling for Job Shops , 1994 .

[5]  Anthony A. Maciejewski,et al.  Dynamic resource allocation heuristics that manage tradeoff between makespan and robustness , 2007, The Journal of Supercomputing.

[6]  R. L. Daniels,et al.  β-Robust scheduling for single-machine systems with uncertain processing times , 1997 .

[7]  Lee C. Potter,et al.  Statistical prediction of task execution times through analytic benchmarking for scheduling in a heterogeneous environment , 1999, Proceedings. Eighth Heterogeneous Computing Workshop (HCW'99).

[8]  Viktor K. Prasanna,et al.  MIP formulation for robust resource allocation in dynamic real-time systems , 2005, J. Syst. Softw..

[9]  Howard Jay Siegel,et al.  Representing Task and Machine Heterogeneities for Heterogeneous Computing Systems , 2000 .

[10]  Stephen Gilmore,et al.  Evaluating the Performance of Skeleton-Based High Level Parallel Programs , 2004, International Conference on Computational Science.

[11]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[12]  Stephen Gilmore,et al.  Scheduling Skeleton-Based Grid Applications Using PEPA and NWS , 2005, Comput. J..

[13]  Oscar H. Ibarra,et al.  Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors , 1977, JACM.

[14]  Ioana Banicescu,et al.  Towards the Robustness of Dynamic Loop Scheduling on Large-Scale Heterogeneous Distributed Systems , 2009, 2009 Eighth International Symposium on Parallel and Distributed Computing.

[15]  RICHARD L. DANIELS,et al.  β-Robust scheduling for single-machine systems with uncertain processing times , 1997 .

[16]  Ioana Banicescu,et al.  Towards Robust Resource Allocations via Performance Modeling with Stochastic Process Algebra , 2015, 2015 IEEE 18th International Conference on Computational Science and Engineering.

[17]  Anthony A. Maciejewski,et al.  Robust Resource Allocation in Heterogeneous Parallel and Distributed Computing Systems , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[18]  Angel R. Martinez,et al.  MATLAB Statistics Toolbox , 2001 .

[19]  Anthony A. Maciejewski,et al.  Static heuristics for robust resource allocation of continuously executing applications , 2008, J. Parallel Distributed Comput..

[20]  Victor L. Wallace,et al.  Markovian models and numerical analysis of computer system behavior , 1899, AFIPS '66 (Spring).

[21]  Rudolf Eigenmann,et al.  Robust resource allocation in dynamic distributed heterogeneous computing systems , 2003 .

[22]  John Shalf,et al.  The International Exascale Software Project roadmap , 2011, Int. J. High Perform. Comput. Appl..

[23]  Mikkel T. Jensen,et al.  Improving robustness and flexibility of tardiness and total flow-time job shops using robustness measures , 2001, Appl. Soft Comput..

[24]  Edward G. Coffman,et al.  Computer and job-shop scheduling theory , 1976 .

[25]  R. Needham,et al.  Tuning Systems : From Composition to Performance , 2004 .

[26]  Ioana Banicescu,et al.  Investigating the robustness of adaptive Dynamic Loop Scheduling on heterogeneous computing systems , 2010, 2010 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum (IPDPSW).

[27]  Arif Ghafoor,et al.  A distributed heterogeneous supercomputing management system , 1993, Computer.

[28]  David Fernández-Baca,et al.  Allocating Modules to Processors in a Distributed System , 1989, IEEE Trans. Software Eng..

[29]  Viktor K. Prasanna,et al.  Iterative integer programming formulation for robust resource allocation in dynamic real-time systems , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[30]  Stephen Gilmore,et al.  The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling , 1994, Computer Performance Evaluation.