In any real system, every event takes some amount of time, no matter how small. Therefore, conducting analyses related to evaluating the level of any system's performance very often refers to investigations of given systems' timing parameters. In practice, the timing analysis can be typically performed with the use of such techniques as timed automata, timed state charts, and Petri nets with time extensions. The main types of Petri nets models that allow the analysis of temporal aspects include time Petri nets (TPNs), timed Petri nets, stochastic timed Petri nets or coloured timed Petri nets. In general, based on the Petri nets approach implementation, the time parameters use are connected with three typical situations: 1) time parameters express the delay between the time when the transition is ready to fire and its firing, or 2) time parameters express the duration of firing the transition, or 3) time parameters are connected with tokens (appropriate age of tokens). In the presented paper, the authors introduce an alternative time Petri net model with dynamic time intervals. In the proposed approach a dynamic firing time interval is assigned to tokens. Following this, In the Introduction section, the authors present a short literature review of the investigated research area. Later, in section 2, the classical time Petri nets are presented. Section 3 introduces the new time Petri nets with time tokens. The proposed approach is presented based on the case example of transportation system performance. The paper ends with conclusions and a definition of future research directions.