We study the dynamics of laminar time between successive bursts in anomalous particle flux measured at the HL-1M tokamak plasma edge. The results reveal that the flux fluctuations are self-similar in a narrow range of time scales and that their probability distribution function is not Gaussian. These properties are not consistent with those predicted by self-organized criticality (SOC) models as well as the running sand-pile SOC model developed by Hwa and Kardar.