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\documentclass{acmabs}

\begin{document}

\Journal{Journal of the ACM}

\refkey{ChangN95}

\title{Bounds on the Speedup and Efficiency of Partial Synchronization in
  Parallel Processing Systems}

\author{C.~S. Chang \and R. Nelson}

\Pages{204--231}

\Month{January}

\Year{1995}

\Volume{42}

\Number{1}

\maketitle

\begin{abstract}

In this paper, we derive bounds on the speedup and efficiency of applications
  that schedule tasks on a set of parallel processors. We assume that the
  application runs an algorithm that consists of $N$ iterations and before
  starting its $i + 1$st iteration, a processor must wait for data (i.e.,
  synchronize) evaluated in the $i$th iteration by a subset of the other
  processors of the system. Processing times and interconnections between
  iterations are modeled by random variables with possibly deterministic
  distributions. Scientific applications consisting of iterations of recursive
  equations are examples of applications that can be modeled within this
  formulation. We consider the efficiency of such applications and show that,
  although efficiency decreases with an increase in the number of processors,
  it has a nonzero limit when the number of processors increases to infinity.
  We obtain a lower bound for the efficiency by solving an equation that
  depends on the distribution of task service times and the expected number of
  tasks needed to be synchronized. We also show that the lower bound is
  approached if the topology of the processor graph is ``spread-out,'' a notion
  we define in the paper.

\end{abstract}

\begin{categories}

C.1.2[parallel processors]; C.4[performance attributes]; G.M[queuing theory]

\end{categories}

\begin{terms}

Measurement, Performance

\end{terms}

\begin{keywords}

Large deviations theory, synchronization

\end{keywords}

\end{document}
