A Pixelized Photon Detector (PPD) is a generic name for the semiconductor devices operated in the Geiger-mode, such as Silicon PhotoMultiplier and Multi-Pixel Photon Counter, which has high photon counting capability. While the internal mechanisms of the PPD have been intensively studied in recent years, the existing models do not include the avalanche process. We have simulated the multiplication and quenching of the avalanche process and have succeeded in reproducing the output waveform of the PPD. Furthermore our model predicts the existence of dead-time in the PPD which has never been numerically predicted. For searching the dead-time, we also have developed waveform analysis method using deconvolution which has the potential to distinguish neighboring pulses precisely. In this paper, we discuss our improved model and waveform analysis method.