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.