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Time Petri nets (TPNs) have been widely used for the verification and validation of real-time systems during the software development process. Their quantitative analysis consists in applying enumerative techniques that suffer the well known state space explosion problem. To overcome this problem, several methods have been proposed in the literature, that either provide rules to obtain equivalent nets with a reduced state space or avoid the construction of the whole state space. In this paper, we propose a method that consists in computing performance bounds to predict the average operational behavior of TPNs by exploiting their structural properties and by applying operational laws. Performance bound computation was first proposed for timed (Timed PNs) and stochastic Petri nets (SPNs). We generalize the results obtained for Timed PNs and SPNs to make the technique applicable to TPNs and their extended stochastic versions: TPN with firing frequency intervals (TPNFs) and extended TPNs (XTPNs). Finally, we apply the proposed bounding techniques on the case study of a robot-control application taken from the literature.