  In competitive parallel computing, the identical copies of a code in a phase
of a sequential program are assigned to processor cores and the result of the
fastest core is adopted. In the literature, it is reported that a superlinear
speedup can be achieved if there is an enough fluctuation among the execution
times consumed by the cores. Competitive parallel computing is a promising
approach to use a huge amount of cores effectively. However, there is few
theoretical studies on speedups which can be achieved by competitive parallel
computing at present. In this paper, we present a behavioral model of
competitive parallel computing and provide a means to predict a speedup which
competitive parallel computing yields through theoretical analyses and
simulations. We also found a sufficient condition to provide a linear speedup
which competitive parallel computing yields. More specifically, it is
sufficient for the execution times which consumed by the cores to follow an
exponential distribution. In addition, we found that the different
distributions which have the identical coefficient of variation (CV) do not
always provide the identical speedup. While CV is a convenient measure to
predict a speedup, it is not enough to provide an exact prediction.
