Petri nets are a graph-based modelling formalism which has been widely used for the formal specification and analysis of concurrent systems. A common analysis technique is that of state space exploration (or reachability analysis). Here, every possible reachable state of the system is generated and desirable properties are evaluated for each state. This approach has the great advantage of conceptual simplicity, but the great disadvantage of being susceptible to state space explosion, where the number of states is simply too large for exhaustive exploration. Many reduction techniques have been suggested to ameliorate the problem of state space explosion. In the case of timed systems, the state space is infinite, unless analysis is restricted to a bounded time period. In this paper, we present a Petri net formalism based on the notion of relative time (as opposed to the traditional approach of dealing with absolute time). The goal is to derive a finite state space for timed systems which have repeating patterns of behaviour, even though time continues to advance indefinitely.