4.2.2 State representation under time allocation

In case you are working with time allocation, information on the state consists of the marking together with a vector, which describes the current clock position.

In the following examples, these vectors are given for a place/transition net with six places $(0,\ldots,5)$ and five transitions $(1,\ldots,5)$.

Time option duration for transitions - firing duration

Clocks are assigned to the transitions, and indicate the remaining time before the transition finishes firing, i.e., delivers tokens to its post-places.

 PL: 0 1 2 3 4 5
 MA: 1 1 0 0 1 1
 TR: 1 2 3 4 5
 TC: 0 1 0 3 0

In this state, the clock of transition 2 indicates, that firing this transition will last another cycle. Similarly, the firing of transition 4 will last another three time units.

In some outputs, you also find the abbreviations P.nr and toks, or T.nr and time, for place numbers and token amounts, or transition numbers and clock positions, respectively.

Time option intervals for transitions - eft/lft

Clocks are assigned to the transitions, and indicate the time that has passed since each one has been enabled.

 PL: 0 1 2 3 4 5
 MA: 0 1 1 0 0 1
 TR: 1 2 3 4 5
 TC: - 2 - 1 -

In this state, the clocks of transitions 1, 3, and 5 are switched off, because there are not enough tokens available to fire any of these transitions. The clocks of transitions 2 and 4 display 2 and 1, respectively, i.e. these transitions are enabled as far as tokens are concerned, and have been so for two and one cycle(s), respectively. Whether or not they can fire, depends on whether their earliest firing time eft has already been reached.

In some outputs, you also find the abbreviations P.nr and toks, or T.nr and time, for place numbers and token amounts, or transition numbers and clock positions, respectively.

Time option intervals for arcs - permeability

Clocks are assigned to the places and indicate the time that the most recently arrived token has already waited on the place.

 PL: 0 1 2 3 4 5
 MA: 1 0 1 1 0 1
 PC: 0 0 5 6 0 0

In this state, the tokens on places 0 and 5 are ``fresh``, i.e. originated with this state, while the tokens on places 2 and 3 have already waited 5 and 6 cycles, respectively, to be permitted by an arc.

In some outputs, you also find the abbreviations P.nr and toks, or T.nr and time, for place numbers and token amounts, or transition numbers and clock positions, respectively.