Individuals, populations and fluid approximations: A Petri net based perspective

EUROSIM 2019 Abstract Volume

“…Fluid relaxations of PN models lead to particular classes of hybrid systems. When fluidization is total and the nets are considered under infinite server semantics, the relaxed models constitute a subclass of piecewise affine systems, more precisely with a polytopic partition in the state domain and continuity in their derivatives (the applicability of the fluidization of PN models depends on the particular properties under study and on the structure of the system under consideration [Silva, 2016]). Because I frequently hear about simulation with some reluctance, you can simply interpret this keynote as a praise for simulation, assuming it is made taking "enough care" (epistemological matters regarding computer-based simulations is a topic that deserve a number of works, from quite different perspectives; among other examples, [Tolk et al, 2013] and [Greca et al, 2014]).…”

A Timed Colored Petri Net Simulation-Based Self-Adaptive Collaboration Method for Production-Logistics Systems

“…The transition aims at modeling the check of the worker t 2 The transition aims at modeling the check of the material t 3 The transition aims at modeling requesting the worker t 4 The transition aims at modeling requesting the material t 5 The transition aims at modeling the machine processing and publishing a logistics task t 6 The transition aims at modeling the quality detection t 7 The transition aims at modeling the selection of the AGV t 8 The transition aims at modeling the temporary storage t 9 The transition aims at modeling the selected AGV going to the start point t 10 The transition aims at modeling the reprocessing or the scarp t 11 The transition aims at modeling the rejection of the AGV t 12 The transition aims at modeling picking pallet and loading t 13 The transition aims at modeling the selected AGV going to the destination t 14 The transition aims at modeling the unloading Table 2. Places in Figure 3.…”

“…A token in this place represents a production task p 2 A token in this place represents a worker p 3 A token in this place represents a material p 4 A token in this place represents the attendance of the worker p 5 A token in this place represents enough materials p 6 A token in this place represents the absence of the worker p 7 A token in this place represents insufficient materials p 8 A token in this place represents the sataus information of a machine p 9 A token in this place represents the sataus information of an AGV p 10 A token in this place represents the finish of the machine processing p 11 A token in this place represents the request to the logistics task p 12 A token in this place represents the detection result p 13 A token in this place represents the qualified WIP p 14 A token in this place represents the nearest and available AGV p 15 A token in this place represents the unqualified WIP p 16 A token in this place represents the remote or unavailable AGV p 17 A token in this place represents an out-buffer p 18 A token in this place represents the selected logistics task p 19 A token in this place represents the correct start point p 20 A token in this place represents the transport time p 21 A token in this place represents the transport to the destination p 22 A token in this place represents the correct destination p 23 A token in this place represents the end and next cycle Figure 3 shows the TCPN model of the self-adaptive collaboration method. This model refers to the basic cycle of production-logistics systems, which consists of twenty-three places and fourteen transitions.…”

Fluid approximation of Petri net models with relatively small populations

“…The fluidization of a transition consists of relaxing its firing amount (and thus the marking of its neighbour places) to the non-negative real quantities. If all transitions are fluidized, the result is a fluid or continuous PN (CPN) [10,21,20]. By fluidization, more efficient analysis techniques can be developed at the price of losing some fidelity.…”

“…Synchronizations in PN can be expressed with two complementary constructions: (1) rendez-vous (or joins); and (2) weights in arcs going from places to transitions. At this point it should be pointed out that if the marking is "very large", the effect of those weights on arcs is not "seen" [20] (intuitively speaking, if the marking of the place at the origin of the k-weighted arc is 1000k -i.e, relatively very big-the enabling is 1000, so the continuous approximation is valid). However, if the marking is not "very large", the relative errors may be higher (intuitively speaking, rounding the number 1.5 to 1 lead to a relative error three orders of magnitude bigger than rounding 1000.5 to 1000).…”