  Quasi-periodic pulsations (QPPs) with various periods that originate in the
underlying magnetohydrodynamic processes of the flaring structures are detected
repeatedly in the solar flare emissions. We apply a 2D cellular automaton (CA)
avalanche model to simulate QPPs as a result of a repetitive load/unload
mechanism. We show that the frequent occurrence of magnetic reconnections in a
flaring loop could induce quasi-periodic patterns in the detected emissions. We
obtain that among 21070 simulated flares, 813 events endure over 50 seconds,
scaled with the temporal resolution of the Yohkoh Hard X-ray Telescope, and
about 70 percent of these rather long-lasting events exhibit QPPs. We also
illustrate that the applied CA model provides a wide range of periodicities for
QPPs. Furthermore, we observe the presence of multiple periods in nearly 50
percent of the cases applying the Lomb-Scargle periodogram. A lognormal
distribution is fitted to the unimodal distribution of the periods as a
manifestation of an underlying multiplicative mechanism that typifies the
effect of the system's independent varying parameters. The global maximum of
the periods' lognormal distribution is located at 29.29 seconds. We compare
statistics of the simulated QPPs with parameters of the host flares and discuss
the impacts of flare properties on QPPs' periods. Considering the intrinsic
characteristic of CA models, namely the repetitive load/unload mechanism, and
the obtained pieces of evidence, we suggest that CA models may generate QPPs.
We also examine the applicability of the autoregressive integrated moving
average models to describe the simulated and observational QPPs.
