Timed Petri nets and max-plus automata are well known modelling frameworks for timed discrete-event systems. In this paper we present an iterative procedure that constructs a max-plus automaton from a timed Petri net while retaining the timed behaviour. Regarding the Petri net, we essentially impose three assumptions: (a) the Petri net must be bounded, i.e, the reachability graph must be finite; (b) we interpret the Petri net with single server semantics; and (c) the Petri net operates according to the race policy, i.e., the earliest possible transition will fire and thereby possibly consume tokens required by other competing transitions. Under these assumptions we show that the proposed procedure terminates with a finite deterministic max-plus automaton that realises the same timed behaviour as the Petri net. As a variation of the plain race policy, we also consider that a subsequently designed supervisor may temporarily disable distinguished transitions. Again, we present a terminating procedure that constructs a behaviour equivalent deterministic max-plus automaton. We demonstrate by example how the latter automaton can be utilised as an open-loop model in the context of supervisor control.

定时 Petri 网和最大加自动机是用于定时离散事件系统的众所周知的建模框架。在本文中，我们提出了一个迭代过程，该过程从定时 Petri 网构造一个最大加自动机，同时保留定时行为。关于 Petri 网，我们基本上强加了三个假设： (a) Petri 网必须是有界的，即可达图必须是有限的；(b) 我们用单服务器语义解释 Petri 网；(c) Petri 网根据竞争策略运行，即最早可能的转换将触发，从而可能消耗其他竞争转换所需的代币。在这些假设下，我们表明所提出的程序以一个有限确定性最大加自动机终止，该自动机实现了与 Petri 网相同的定时行为。作为普通竞赛策略的一种变体，我们还考虑到随后设计的监督器可能会暂时禁用可区分的转换。同样，我们提出了一个终止过程，它构建了一个行为等价的确定性最大加自动机。我们通过示例演示了后一种自动机如何在主管控制的上下文中用作开环模型。