International Business Machines Corporation. Research Division

Mark S. Squillante

Vinod G. J. Peris

Vijay K. Naik

Abstract: "We consider an important tradeoff in distributed parallel processing systems between the impact of program inefficiencies toward reducing the number of processors allocated to parallel applications with increasing system loads and the performance impact of memory requirements toward larger allocations. To study this tradeoff, we formulate stochastic models of parallel program behavior, a distributed parallel processing system and the total memory overhead incurred by a program as a function of its processor allocation. A mathematical analysis of the models is developed, which can include the effects of contention for shared resources caused by paging activity. We conduct a detailed analysis of actual large-scale scientific applications and use these results to parameterize our models. Our results show that memory overhead resulting from processor allocation decisions can have a significant effect on system performance in distributed parallel environments. Thus, our analysis strongly suggests that memory considerations must be incorporated in the resource allocation policies for parallel systems. We also demonstrate the importance of the transient miss ratio, which is introduced in this paper and analyzed for the first time."

Analysis of the Impact of Memory in Distributed Parallel Processing Systems

Guy Latouche

Vaidyanathan Ramaswami

Jay Sethuraman

Karl Sigman

David Yao

Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.

Matrix-Analytic Methods in Stochastic Models

Mark S. Squillante

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