Qualitative Behavior of the EQS Parallel Processor Allocation Policy

Several studies of multiprogrammed parallel systems have observed that dynamic equiallocation policies have high performance for a variety of speciic parallel workloads. However, only very incomplete information is available about which workload parameters are key determinants of policy performance and how the mean response times of equiallocation policies behave as a function of key workload parameters. This paper addresses these issues for an idealization of the Spatial EQuiallocation policy (EQS) and a workload model that characterizes the essential features of parallel applications with respect to scheduling discipline performance. Important features of the workload model include general distribution for available job parallelism, controlled correlation between available parallelism and total job processing requirement, general distribution of processing requirement per class of jobs in the correlation model, and general nondecreasing deterministic job execution rates (i.e., speedups) that represent synchronization and communication overheads as well as load imbalance for parallel programs. The performance of EQS is analyzed using sample path analysis to derive bounds and using highly eecient and extensively validated interpolation approximations to derive estimates for mean response time (R EQS). The bounds show that under exponential job processing requirements (demands) and any concave nondecreasing job execution rate function for all jobs R EQS is minimum when all jobs are fully parallel and is maximum when all jobs are fully sequential. The upper bound is also shown to hold under very general workload conditions. The approximation is used to obtain the demand and parallelism parameters that are key determinants of EQS performance and to study the behavior of R EQS as a function of changes in the workload. Mean response time is shown to decrease with stochastic increase in available parallelism, decrease in variability of parallelism, and increase in correlation. Under certain potentially realistic assumptions, the mean response time is also shown to be fairly insensitive to parallel program overheads.

[1]  Raj Vaswani,et al.  A dynamic processor allocation policy for multiprogrammed shared-memory multiprocessors , 1993, TOCS.

[2]  P. Moran,et al.  Reversibility and Stochastic Networks , 1980 .

[3]  Mary K. Vernon,et al.  Approximate Analysis of Parallel Processor Allocation Policies , 1993 .

[4]  Donald F. Towsley,et al.  Analysis of Fork-Join Program Response Times on Multiprocessors , 1990, IEEE Trans. Parallel Distributed Syst..

[5]  David D. Yao,et al.  Optimal Task Scheduling on Distributed Parallel Processors , 1994, Perform. Evaluation.

[6]  Shikharesh Majumdar,et al.  Scheduling in multiprogrammed parallel systems , 1988, SIGMETRICS '88.

[7]  Rajesh Kishin Mansharamani.  Efficient analysis of parallel processor scheduling policies , 1993 .

[8]  Tim Brecht,et al.  Processor-pool-based scheduling for large-scale NUMA multiprocessors , 1991, SIGMETRICS '91.

[9]  Satish K. Tripathi,et al.  An analysis of several processor partitioning policies for parallel computers , 1991 .

[10]  Anoop Gupta,et al.  Process control and scheduling issues for multiprogrammed shared-memory multiprocessors , 1989, SOSP '89.

[11]  V. K. Naik,et al.  Performance analysis of job scheduling policies in parallel supercomputing environments , 1993, Supercomputing '93.

[12]  Shikharesh Majumdar,et al.  Scheduling in multiprogrammed parallel systems , 1988, SIGMETRICS 1988.

[13]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[14]  L. Goddard,et al.  Operations Research (OR) , 2007 .

[15]  Asser N. Tantawi,et al.  Performance analysis of parallel processing systems , 1987, SIGMETRICS '87.

[16]  Armand M. Makowski,et al.  Distributed Parallelism Considered Harmful , 1992 .

[17]  Shikharesh Majumdar,et al.  Characterisation of Programs for Scheduling in Multiprogrammed Parallel Systems , 1991, Perform. Evaluation.

[18]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[19]  Mark S. Squillante,et al.  Scheduling of Large Scientific Applications on Distributed Memory Multiprocessor Systems , 1993, PPSC.

[20]  Satish K. Tripathi,et al.  Analysis of processor allocation in multiprogrammed parallel processing systems , 1992 .

[21]  Randolph D. Nelson,et al.  A performance evaluation of a general parallel processing model , 1990, SIGMETRICS '90.

[22]  G. Grimmett,et al.  Probability and random processes , 2002 .

[23]  Jean C. Walrand,et al.  An introduction to queueing networks , 1989, Prentice Hall International editions.

[24]  Mary K. Vernon,et al.  Response Time Bounds for Parallel Processor Allocation Policies , 1993 .

[25]  Donald F. Towsley,et al.  A performance evaluation of several priority policies for parallel processing systems , 1993, JACM.

[26]  Anoop Gupta,et al.  Making effective use of shared-memory multiprocessors: the process control approach , 1991 .