{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T06:27:53Z","timestamp":1761719273564,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:00:00Z","timestamp":1706054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:00:00Z","timestamp":1706054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005727","name":"Universidade de Coimbra","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005727","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Event Dyn Syst"],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Simulation models have been described using different perspectives, or worldviews. In the process interaction world view (PI), every entity is modeled by a sequence of actions describing its life cycle, offering a comprehensive model that groups the events involving each entity. In this paper we describe <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc>, a formalism for representing hybrid models using a set of communicating processes. This set is dynamic, enabling processes to be created and destroyed at runtime. Processes are encapsulated into <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc> base models and communicate through shared memory. <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc>, however, can guarantee modularity by enforcing that models can only communicate by input and output interfaces. <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc> extends current PI approaches by providing support for <jats:sc>HyFlow<\/jats:sc> concepts of sampling and dense (continuous) outputs, in addition to the more traditional event-based communication. Likewise <jats:sc>HyFlow<\/jats:sc>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc> is a modeling &amp; simulation formalism driven by expressiveness and performance analysis. We present <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc> semantics, and several applications to illustrate <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sc>HyFlow<\/jats:sc> ability to describe a diversity of systems.<\/jats:p>","DOI":"10.1007\/s10626-023-00390-y","type":"journal-article","created":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T14:18:03Z","timestamp":1706105883000},"page":"95-124","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["$$\\pi $$HyFlow: formalism, semantics, and applications"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3792-2354","authenticated-orcid":false,"given":"Fernando","family":"Barros","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,24]]},"reference":[{"key":"390_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.peva.2017.04.007","volume":"113","author":"X Allamigeon","year":"2017","unstructured":"Allamigeon X, Boeuf V, Gaubert S (2017) Stationary solutions of discrete and continuous Petri nets with priorities. Performance Eval 113:1\u201312","journal-title":"Performance Eval"},{"issue":"1","key":"390_CR2","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1080\/03081070290008011","volume":"31","author":"F Barros","year":"2002","unstructured":"Barros F (2002) Towards a theory of continuous flow models. Int J General Syst 31(1):29\u201339","journal-title":"Int J General Syst"},{"key":"390_CR3","unstructured":"Barros F (2017) Chattering avoidance in hybrid simulation models: a modular approach based on the HyFlow formalism. In: Symposium on theory of modeling and simulation"},{"key":"390_CR4","doi-asserted-by":"crossref","unstructured":"Bastian J, Clau\u00dfC, Wolf S, Schneider P (2011) Master for co-simulation using FMI. In: Proceedings of the 8th modelica conference","DOI":"10.3384\/ecp11063115"},{"key":"390_CR5","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/S0005-1098(98)00178-2","volume":"35","author":"A Bemporad","year":"1999","unstructured":"Bemporad A, Morari M (1999) Control of systems integrating logic, dynamics, and constraints. Automatica 35:407\u2013427","journal-title":"Automatica"},{"key":"390_CR6","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/3-540-44798-9_10","volume":"2144","author":"G Berry","year":"2001","unstructured":"Berry G, Sentovich E (2001) Multiclock Esterel. Correct hardware design and verification methods, LNCS 2144:110\u2013125","journal-title":"Correct hardware design and verification methods, LNCS"},{"issue":"2","key":"390_CR7","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1109\/32.761446","volume":"25","author":"G Ciardo","year":"1999","unstructured":"Ciardo G, Nicol D, Trivedi K (1999) Discrete-event simulation of Fluid Stochastic Petri Nets. IEEE Trans Softw Eng 25(2):207\u2013217","journal-title":"IEEE Trans Softw Eng"},{"issue":"2","key":"390_CR8","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1145\/137926.137927","volume":"2","author":"B Cota","year":"1992","unstructured":"Cota B, Sargent R (1992) A modification of the process interaction world view. ACM Trans Model Comput Simulat 2(2):109\u2013129","journal-title":"ACM Trans Model Comput Simulat"},{"issue":"9","key":"390_CR9","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1145\/365813.365819","volume":"9","author":"O-J Dahl","year":"1966","unstructured":"Dahl O-J, Myhrhaug B, Nygaard K (1966) SIMULA - An ALGOL-based simulation language. Commun ACM 9(9):671\u2013678","journal-title":"Commun ACM"},{"key":"390_CR10","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1023\/A:1008330914786","volume":"11","author":"R David","year":"2001","unstructured":"David R, Alla H (2001) On hybrid Petri nets. Discrete Event Dynamic Systems: Theory and Applications 11:9\u201340","journal-title":"Discrete Event Dynamic Systems: Theory and Applications"},{"key":"390_CR11","doi-asserted-by":"crossref","unstructured":"Fabiani F, Grammatico S (2018) A mixed-logical-dynamical model for automated driving on highways. In: IEEE Conference on decision and control, pp 1011\u20131016","DOI":"10.1109\/CDC.2018.8619852"},{"key":"390_CR12","unstructured":"Fritzson P (2003) Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley"},{"key":"390_CR13","volume-title":"Modeling Reactive Systems with Statecharts","author":"D Harel","year":"1998","unstructured":"Harel D, Politi M (1998) Modeling Reactive Systems with Statecharts. McGraw-Hill"},{"key":"390_CR14","unstructured":"Henriksen J (1981) GPSS - finding the apropriate world-view. In: Winter simulation conference, pp 505\u2013516"},{"key":"390_CR15","doi-asserted-by":"crossref","unstructured":"Henzinger T (1996) The theory of hybrid automata. In: 11th Annual IEEE symposium on logic in computer science, pp 278\u2013292","DOI":"10.1109\/LICS.1996.561342"},{"key":"390_CR16","volume-title":"Communicating Sequential Processes","author":"C Hoare","year":"1985","unstructured":"Hoare C (1985) Communicating Sequential Processes. Prentice-Hall"},{"key":"390_CR17","doi-asserted-by":"crossref","unstructured":"J\u00falvez J, Oliver S (2019) Flexible Nets: a modeling formalism for dynamic systems with uncertain parameters. Discrete Event Dynamic Syst 29:367\u2013392","DOI":"10.1007\/s10626-019-00287-9"},{"key":"390_CR18","first-page":"392","volume":"3414","author":"E Lee","year":"2005","unstructured":"Lee E, Zheng H (2005) Operational semantics of hybrid systems. Hybrid systems computation and control, of LNCS 3414:392\u2013406","journal-title":"Hybrid systems computation and control, of LNCS"},{"key":"390_CR19","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1006\/inco.1994.1083","volume":"114","author":"X Nicollin","year":"1994","unstructured":"Nicollin X, Sifakis J (1994) An overview and synthesis on timed process algebras. Inf Comput 114:131\u2013178","journal-title":"Inf Comput"},{"key":"390_CR20","doi-asserted-by":"crossref","unstructured":"Nielson C, Larsen P, Fitzgerald J, Woodcock J, Peleska J (2015) Systems of systems engineering: basic concepts, model-based techniques, and research directions. ACM Comput Surv 48(2):1\u201341","DOI":"10.1145\/2794381"},{"key":"390_CR21","volume-title":"Petri Net Theory and the Modeling of Systems","author":"J Peterson","year":"1981","unstructured":"Peterson J (1981) Petri Net Theory and the Modeling of Systems. Prentice-Hall"},{"issue":"3","key":"390_CR22","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1080\/03081079108935175","volume":"19","author":"H Praehofer","year":"1991","unstructured":"Praehofer H (1991) Systems theoretic formalisms for combined discrete-continuous system simulation. Int J General Syst 19(3):219\u2013240","journal-title":"Int J General Syst"},{"key":"390_CR23","unstructured":"Russel E (1999) Building Simulation Models with Simscript II.5. CACI, La Jolla"},{"issue":"11","key":"390_CR24","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1145\/182.358460","volume":"26","author":"L Schruben","year":"1983","unstructured":"Schruben L (1983) Simulation modeling with event graphs. Commun ACM 26(11):957\u2013963","journal-title":"Commun ACM"},{"issue":"1","key":"390_CR25","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1063\/1.442716","volume":"76","author":"W Swope","year":"1982","unstructured":"Swope W, Andersen H, Berens P, Wilson K (1982) A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J Chemical Phys 76(1):637\u2013649","journal-title":"J Chemical Phys"},{"issue":"4","key":"390_CR26","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1145\/1113830.1113834","volume":"4","author":"S Tripakis","year":"2005","unstructured":"Tripakis S, Sofronis C, Caspi P, Curic A (2005) Translating discrete-time Simulink to Lustre. ACM Trans Embedded Comput Syst 4(4):779\u2013818","journal-title":"ACM Trans Embedded Comput Syst"},{"key":"390_CR27","doi-asserted-by":"crossref","unstructured":"Valmari A (1998) The state explosion problem. Lectures on petri nets I: basic models, Springer 1491:429\u2013528","DOI":"10.1007\/3-540-65306-6_21"},{"key":"390_CR28","doi-asserted-by":"crossref","unstructured":"Yaakoubi H, Hagg\u00e8ge J (2022) Modeling of three-tank hybrid system using Mixed Logical Dynamical formalism. In: 5th International conference on advanced systems and emergent technologies, pp 55\u201360","DOI":"10.1109\/IC_ASET53395.2022.9765937"},{"key":"390_CR29","volume-title":"Theory of Modelling and Simulation","author":"B Zeigler","year":"1976","unstructured":"Zeigler B (1976) Theory of Modelling and Simulation. Wiley"}],"container-title":["Discrete Event Dynamic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-023-00390-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10626-023-00390-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-023-00390-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,18]],"date-time":"2024-02-18T23:07:36Z","timestamp":1708297656000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10626-023-00390-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,24]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["390"],"URL":"https:\/\/doi.org\/10.1007\/s10626-023-00390-y","relation":{},"ISSN":["0924-6703","1573-7594"],"issn-type":[{"type":"print","value":"0924-6703"},{"type":"electronic","value":"1573-7594"}],"subject":[],"published":{"date-parts":[[2024,1,24]]},"assertion":[{"value":"21 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declares that he has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}