Evaluating the Mean Completion Time of a Fork-Join Barrier Synchronization

In this paper we analyze the mean completion time of a fork-join barrier synchronization for a parallel program model proposed in previous literature. The task service times in the model are derived from the total job demand by ratios of uniform random variables. We first compute an analytic expression for the mean time to barrier completion, S(n), for jobs that have n tasks. This expression is an alternating series of combinatorial terms that is numerically unstable for large values of n if summed in straightforward manner. We next derive an alternate method of computing S(n) that consists of an infinite series of positive terms that sums to less than 1. We obtain error estimates for truncated sums of this series and using the error estimates compute S(n) to a desired level of accuracy. Finally, we compare estimates of the mean time to barrier completion with other common models of parallel program task execution times. The main emphasis of this paper is on the techniques used to de..

Qualitative Behavior of the EQS Parallel Processor Allocation Policy

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 efficient and extensively validated interpolation approximations to derive estimates for mean response time (REQS ). The bounds show that under exponential job processing requirements (demands) and any concave nondecreasing job execution rate function for all jobs REQS 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 REQS 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

Estimating Mean Completion Times of a Fork-Join Barrier Synchronization

. In simulation studies of parallel processors, it is useful to consider the following abstraction of a parallel program. A job is partitioned into n processes, whose running times are independent random variables X 1 ; : : : ; Xn . As a measure of performance we consider the normalized job completion time S = maxfX i g= P n i=1 X i . We consider a simple approximation to the expected value of S, valid asymptotically whenever the X i 's are bounded, and assess its accuracy as a function of n both theoretically and experimentally. The approximation is easy to compute and involves only the first two moments of X i . 1 Introduction In this paper we study a simple performance metric for parallel programs. We are interested in so-called fork-join programs, of the following type. A job splits into n processes that run independently, then wait for the last one to complete. As a measure of performance we consider the ratio S := maxfT i g D ; (1) where T i is the time taken by process i, an..

Comparison of Processor Allocation Policies for Parallel Systems

The increasing use of parallel systems has led to the development of a number of multiprogrammed processor allocation policies. This paper analyzes the following four policies that have previously been shown to have high performance under specific workloads: adaptive static partitioning (ASP), dynamic first-comefirst -serve (FCFS), preemptive smallest available parallelism first (PSAPF), and spatial equipartitioning (EQS). The results in this paper are derived for a general workload model that includes general distribution of available job parallelism, controlled correlation between cumulative processing demand and available parallelism, general demand distribution per class of jobs in the correlation model, and general deterministic job execution rates that represent synchronization and communication overheads as well as load imbalance for parallel programs. Under the assumption that jobs can dynamically and efficiently redistribute their work across the processors allocated to them p..