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A class of Petri nets (DSPN) in which transitions can fire after either a deterministic or a random, exponentially distributed, firing delay is defined, and a solution technique is presented to obtain the steady-state probability distribution over markings, introducing restrictions on the use of deterministic firing delays. An example of application of this modeling technique is presented to demonstrate the impact that the use of a mix of deterministic and exponentially distributed firing delays (instead of all exponentially distributed firing delays) can have on performance and reliability estimates.