This thesis focuses on the microscopic features of cellular models, which can be considered as simple models of traffic or pedestrian flow. First part of the thesis focuses on the one-dimensional model TASEP driven by various updates. The main contribution consists in analytical derivation of distance-gap and time-headway distribution for TASEP model with continuous-time, forward-, backward-, and random-sequen\-tial update. Further, the stationary-state solution of the TASEP with generalized update is presented for the periodic boundaries. The phase diagram of the generalized update is investigated by means of computer simulations. Second part focuses on the pedestrian flow in a single room with one exit and one entrance with controlled inflow $\alpha$ [pedestrians/second]. Conclusions from the experimental study of this systems are used to improve the floor field model on the microscopic basis by introducing adaptive time span and principle of bonds. The influence of these modifications on the phase transition and travel-time distribution is discussed.