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### Synchronization and Linearity: An Algebra for Discrete Event Systems

Charles Leake, Francois Baccelli, Guy Cohen, Geert Jan Olsder, Jean-Pierre Quadrat
1994 Journal of the Operational Research Society
and all L A T E X cross-references are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc..  ...  In the present release, alterations of the original text are mild and need no special mention: they concern typographic style (which may result in a different pagination with respect to the original paper  ...  However, this requires an algebraic foundation which appeals to isomorphisms, quotients of dioids by congruences and residuation theory.  ...

### Half a century after Carl Adam Petri's Ph.D. thesis: A perspective on the field

Manuel Silva
2013 Annual Reviews in Control
Later, many other new lines of activity, including logic control and performance evaluation, flourished in Europe. Today Petri nets are widespread all over the world.  ...  for Standardization) or IEC (International Electrotechnical Commission) standards for the use of Petri nets in engineering, this work cannot hope to be a complete survey or a tutorial in the more classical  ...  All of them started to work on Petri nets around 1973 -1975 , who started to work on stochastic Petri nets at the very beginning of the 1980s, and was initially inspired by contributions from UCLA.  ...

### Max-Plus-Linear Systems for Modeling and Control of Manufacturing Problems [chapter]

Xavier David-Henriet, Laurent Hardouin, Jörg Raisch
2017 Mathematics in Industry
Second, standard open-loop and closed-loop control structures for (max, +)-linear systems are recalled.  ...  First, we discuss the modeling of such systems by linear statespace models in the (max, +)-algebra (due to this property, such systems are often called (max, +)-linear systems).  ...  Dioid Theory Dioids (or idempotent semirings) are algebraic structures which play a major role in the modeling of (max, +)-linear systems. Definition 1 (Dioid).  ...

### Periodic trajectories in P-time event graphs and the non-positive circuit weight problem [article]

Davide Zorzenon, Jan Komenda, Joerg Raisch
2021 arXiv   pre-print
In graph theory, the Proportional-Inverse-Constant-Non-positive Circuit weight Problem (PIC-NCP) consists in finding all the values of a parameter such that a particular parametric weighted directed graph  ...  for the existence of a consistent d-periodic trajectory of the same period, for any value of d.  ...  In contrast, in P-TEGs the time evolution of the marking is non-deterministic, since transitions are not required to fire as soon as they are enabled.  ...

### Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks [article]

Davide Zorzenon, Jan Komenda, Jörg Raisch
2022 arXiv   pre-print
P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows.  ...  We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called  ...  This would imply that SLDIs can be used to represent and solve scheduling problems for systems modeled by safe P-time Petri nets (cf. Komenda et al. [2020] ).  ...

### Idempotent and tropical mathematics and problems of mathematical physics (Volume I) [article]

Grigory Litvinov, Victor Maslov, Sergei Sergeev
2007 arXiv   pre-print
a place of the Petri Net.  ...  This method can be applied to the crossing and we obtain a Petri net with negative weights which has only one arc leaving each place (that we call deterministic Petri net) see Figure 6 .  ...

### Concurrent Dynamic Algebra [article]

Hitoshi Furusawa, Georg Struth
2014 arXiv   pre-print
The modal operators of concurrent dynamic algebra are obtained from abstract axioms for domain and antidomain operators; the Kleene star is modelled as a least fixpoint.  ...  Algebraic variants of Peleg's axioms are shown to be valid in these algebras and their soundness is proved relative to the multirelational model.  ...  at Kyushu University for a pleasant short stay and financial support.  ...

### Concurrent Kleene Algebra of Partial Strings [article]

2014 arXiv   pre-print
In particular, it gives a foundation for the analysis of programs that concurrently access relaxed memory as shown in subsequent work.  ...  Concurrent Kleene Algebra (CKA) is a recently proposed algebraic structure by Hoare and collaborators that unifies the laws of concurrent programming.  ...  The fact that all these works use partial orders to describe the dependency between events means that there is a close connection to the unfolding of petri nets to occurrence nets, an active research area  ...

### An introduction to idempotency [chapter]

Jeremy Gunawardena, John M. Taylor, Michael Atiyah, Jeremy Gunawardena
Idempotency
More recently, intriguing new connections have emerged with automata theory, discrete event systems, nonexpansive mappings, nonlinear partial differential equations, optimisation theory and large deviations  ...  and these topics are discussed further in the subsequent sections of this paper.  ...  If there is a hierarchy of Petri net models then free choice nets are the obvious candidate for the next level of complexity beyond event graphs.  ...

### What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

Yves Lucet
2010 SIAM Review
morphology operators), partial differential equations (solving Hamilton-Jacobi equations, and using differential equations numerical schemes to compute the convex envelope), max-plus algebra (computing  ...  Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical  ...  Hiriart-Urruty for a careful reading of the manuscript which greatly improved the paper, Pr. W. Hare for pointing out several typos, and Pr. H. H.  ...

### What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

Yves Lucet
2009 SIAM Journal on Optimization
morphology operators), partial differential equations (solving Hamilton-Jacobi equations, and using differential equations numerical schemes to compute the convex envelope), max-plus algebra (computing  ...  Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical  ...  Hiriart-Urruty for a careful reading of the manuscript which greatly improved the paper, Pr. W. Hare for pointing out several typos, and Pr. H. H.  ...

### Discrete event systems with standard and partial synchronizations [article]

Xavier David-Henriet, Technische Universität Berlin, Technische Universität Berlin, Laurent Hardouin, Jörg Raisch
2015
Furthermore, transfer relation and model reference control are provided for the secondary system under a predefined behavior of the main system.  ...  Optimal feedforward control and model predictive control for (max,+)-linear systems are extended to (max,+)-systems with partial synchronization.  ...  Depending on the selected modeling approaches, di erent theories, such as supervisory control theory for nite-state automata [ ] or state-based control for Petri nets (e.g., [ ]), have been introduced  ...

### Selected papers from the 3rd international workshop on QoS in multiservice IP networks (QoS-IP 2005)

Giuseppe Bianchi, Marco Listanti, Michela Meo, Maurizio M. Munafò
2006 Computer Networks
The schemes are analyzed by applying the Markov decision process theory. A linear programming technique is used to derive the optimal routing policy. Packet level schemes are also considered.  ...  The authors propose a mechanism for bandwidth dimensioning based on a hybrid combination of analytical and simulation models.  ...  Acknowledgements This work was supported in part by an Emmy Noether grant of the German Research Foundation (DFG) and in part by the Centre for Quantifiable Quality of Service in Communication Systems  ...

### SLA Calculus

Sebastian Vastag, Technische Universität Dortmund, Technische Universität Dortmund
2015
For modeling Service-Oriented Architectures (SOAs) and validating worst-case performance guarantees a deterministic modeling method with efficient analysis is presented.  ...  SOAs are a system design paradigm that encapsulate software functions in service applications.  ...  Otherwise, approximative methods for non-product-form nets can be applied.  ...