The “bound reaching problem” on the fluidization of timed Petri nets

Fraca, Estíbaliz; Juúlvez, Jorge; Silva, Manuel

doi:10.3182/20140514-3-fr-4046.00100

Cited by 3 publications

(6 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A first possibility is to modify the flow of the continuous transition. For example, an "ad hoc" continuous flow estimation is explained in [13] as an alternative to ISS. However, it has some disadvantages such as no time homothecy.…”

Section: Methodsmentioning

confidence: 99%

“…TCPN under ISS approximate reasonably well the behaviour of MPN when the population is relatively large, as pointed out in Section 2.3. However, the Bound Reaching Problem (BRP) identifies a particular but important situation in which the quality of the approximation may be significantly worse [13]. The differences between discrete and continuous behaviour are due to the fact that synchronizations (arc weights and therefore joins) are strongly relaxed when the net system is fluidified.…”

Section: The Bound Reaching Problem (Brp)mentioning

confidence: 99%

“…In this particular construction, we can abstract the structure given by p ′ 1 , t ′ 1 , p a , p b , t imm by a unique transition which compacts the desired behaviour, resulting in the denoted ρ-semantics, based on ISS (see [13] and Fig. 3(c) for more details).…”

Section: A New Semantics To Approach the Bound Reaching Problemmentioning

confidence: 99%

“…2(b) can be seen as a simplification of any net system with analogous structure. Hence, it will be possible to use the heuristic formula (13) in other transitions suffering from the BRP such that | • t| = 1.…”

Section: A New Semantics To Approach the Bound Reaching Problemmentioning

confidence: 99%

“…It is the case of PN systems in which the enabling bound of a transition is equal to 1, and hence the probability of firing that transition may be very low in the discrete case but not so "difficult" on the continuous approximation. This problem is denoted as the Bound Reaching Problem (BRP) [13]. The BRP is a challenging problem that may appear in many practical cases.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fluid approximation of Petri net models with relatively small populations

Fraca

Júlvez

Silva

2017

Discrete Event Dyn Syst

Self Cite

View full text Add to dashboard Cite

Fluidization is an appealing relaxation technique based on the removal of integrality constraints in order to ease the analysis of discrete Petri nets. The result of fluidifying discrete Petri nets are the so called Fluid or Continuous Petri nets. As with any relaxation technique, discrepancies among the behaviours of the discrete and the relaxed model may appear. Moreover, such discrepancies may have a comparatively bigger effect when the population of the system, the marking in Petri net terms, is "relatively" small. This paper proposes two complementary approaches to obtain a better fluid approximation of discrete Petri nets. The first one focuses on untimed systems and is based on the addition of places that are implicit in the untimed discrete system but not in the continuous. The idea is to cut undesired spurious solutions whose existence worsens the fluidization. The second one focuses on a particular situation that can severely affect the quality of fluidization in timed systems. Namely, such a situation arises when the enabling degree of a transition is equal to 1. This last approach aims to alleviate such a state of affairs, which is termed the bound reaching problem, on systems under infinite servers semantics.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: The Bound Reaching Problem (Brp)mentioning

confidence: 99%

Section: A New Semantics To Approach the Bound Reaching Problemmentioning

confidence: 99%

Section: A New Semantics To Approach the Bound Reaching Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations