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Modular Petri net modeling of healthcare systems

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Abstract

This paper presents a modular approach for modeling healthcare systems using Petri nets. It is shown that a healthcare system can be constructed by different modules whose inputs and outputs are connected according to their geographical location. Each module can be modeled in two phases: (1) obtain the sequences of treatments and cares received by a patient in the case of a particular disease/condition, and (2) add the resources necessary to perform the previous sequences. The global model is obtained by fusion the inputs and outputs of the modules and by adding information on the patients. The constructed modules together with the resources are Petri nets belonging to a new subclass called healthcare Petri nets that is proved to have equivalent behavior with \(S^4{\textit{PR}}\) nets, a well-known class of Resource Allocation Systems. This allows us to apply the structural results already existing in the literature for \(S^4{\textit{PR}}\) to the context of healthcare systems. In order to illustrate the results, a case study of a public healthcare area in Zaragoza is considered as a use case.

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Notes

  1. t is a fork transition if \(|{t}^\cdot |>1\), i.e., t has more than one output place.

  2. t is a join transition if \(|\,^\cdot {t}|>1\), i.e., t has more than one input place.

  3. An implicit place is a place that by its removal the behavior of the net is not changed.

References

  • Ajmone Marsan M, Conte G, Balbo G (1984) A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans Comput Syst 2(2):93–122. doi:10.1145/190.191

    Article  Google Scholar 

  • Augusto V, Xie X (2014) A modeling and simulation framework for health care systems. IEEE Trans Syst Man Cybern Syst 44(1):30–46

    Article  Google Scholar 

  • Bahi-Jaber N, Pontier D (2003) Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets. Math Biosci 185(1):1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Bernardi S, Albareda J, Colom J, Mahulea C (2004) A model-based approach for the specification and verification of clinical guidelines. In: M2H: Workshop on Models and Methods for Hospital Management and Planning held in conjunction with ETFA’2014

  • Boquet J (ed) (2005) Guía de Ayuda al Diagnóstico en Atención Primaria. Sociedad Española de Medicina de Familia y Comunitaria, Barcelona

    Google Scholar 

  • Brailsford S, Harper P, Patel B, Pitt M (2009) An analysis of the academic literature on simulation and modelling in health care. J Simul 3:130–140

    Article  Google Scholar 

  • Carey R, Lloyd R (1995) Measuring quality improvement in health care: a guide to statistical process control applications. ASQ Quality Press, New York

    Google Scholar 

  • Clavel D, Mahulea C, Albareda J, Silva M (2016) Operation planning of elective patients in an orthopedic surgery department. In: M2H’2016: second workshop on models and methods for Hospital Management and Planning held in conjunction with ETFA’2016: 21st IEEE international conference on emerging technologies and factory automation

  • Colom JM (2003) The resource allocation problem in flexible manufacturing systems. In: Aalst W, Best E (eds) Applications and theory of Petri nets. Lecture notes in computer science, vol 2679. Springer, Berlin, pp 23–35

    Google Scholar 

  • Davies R (1985) An assessment of models of a health system. J Oper Res Soc 36(8):679–687

    Article  Google Scholar 

  • Dotoli M, Fanti M, Mangini A, Ukovich W (2009) continuous Petri net model for the management and design of emergency cardiology departments. In: ADHS09: proceedings of the 3rd analysis and design of hybrid systems. Zaragoza, Spain

  • Fanti MP, Iacobellis G, Ukovich W (2010) Metamodelling approach to healthcare system management. In: Testi A, Ivaldi E, Carello G, Aringhieri R, Fraghelli V (eds) XXXVI ORHAS conference, operation research for patient—centered health care delivery, pp 110–121

  • Fanti MP, Mangini A, Dotoli M, Ukovich W (2012) A three level strategy for the design and performance evaluation of hospital departments. IEEE Trans Syst Man Cybern A Syst Hum 43(4):1–15

    Google Scholar 

  • Fanti MP, Mangini AM, Ukovich W, Lesage JJ, Viard K (2014) A Petri net model of an integrated system for the health care at home management. In: 2014 IEEE international conference on automation science and engineering (CASE), pp. 582–587

  • Forrester J (1960) The impact of feedback control concepts on the management sciences. Massachusetts institute of technology. School of industrial management. Foundation for Instrumentation Education and Research, New York

  • Gunal M (2012) A guide for building hospital simulation models. Health Syst 1(1):17–25

    Article  Google Scholar 

  • Homer J, Hirsch G (2006) System dynamics modeling for public health: background and opportunities. Am J Public Health 96(3):452–458

    Article  Google Scholar 

  • Jensen K, Kristensen LM (2009) Coloured Petri nets—modelling and validation of concurrent systems. Springer, Berlin

    Book  MATH  Google Scholar 

  • Jun JB, Jacobson SH, Swisher JR (1999) Application of discrete-event simulation in health care clinics: a survey. J Oper Res Soc 50:109–123

    Article  MATH  Google Scholar 

  • Lamiri M, Xie X, Dolgui A, Grimaud F (2008a) A stochastic model for operating room planning with elective and emergency demand for surgery. Eur J Oper Res 185(3):1026–1037

    Article  MathSciNet  MATH  Google Scholar 

  • Lamiri M, Xie X, Zhanga S (2008b) Column generation approach to operating theater planning with elective and emergency patientsy. IIE Trans 40(9):838–852

    Article  Google Scholar 

  • Laskowski M, Bryan C, Demianyk J, Shamir N, Friesen MM, McLeod R (2011) Agent-based modeling of the spread of influenza-like illness in an emergency department: a simulation study. IEEE Trans Inf Technol Biomed 15(6):877–889

    Article  Google Scholar 

  • Lehaney B, Hlupic V (1995) Simulation modelling for resource allocation and planning in the health sector. J R Soc Health 115(6):382

    Article  Google Scholar 

  • Macal M, North M (2010) Tutorial on agent-based modelling and simulation. J Simul 4(3):151–162

    Article  Google Scholar 

  • Mahulea C, Garcia-Soriano JM, Colom JM (2012) Modular Petri net modeling of the Spanish health system. In: ETFA’2012: 17th IEEE conference on emerging technologies and factory automation. Krakow, Poland

  • Mahulea  C, Mahulea L, Garcia-Soriano JM, Colom JM (2014) Petri nets with resources for modeling primary healthcare systems. In: ICSTCC’2014: 18th international conference on system theory, control and computing. Sinaia, Romania

  • Mans R, Schonenberg M, Song M, Aalst W, Bakker P (2009) Application of process mining in healthcare—a case study in a Dutch hospital. Biomed Eng Syst Technol 25:425–438

    Article  Google Scholar 

  • Murata T (1989) Petri nets: properties, analysis and applications. Proc IEEE 77(4):541–580

    Article  Google Scholar 

  • Sibbel R, Urban C (2001) Agent-based modeling and simulation for hospital management. Springer, Dordrecht

    Book  Google Scholar 

  • Silva M (1993) Practice of Petri nets in manufacturing. In: Dicesare F, Harhalakis G, Proth JM, Silva M, Vernadat F (eds) Introducing Petri nets. Springer, Netherlands, pp 1–62

    Google Scholar 

  • Sobolev BG, Sanchez V, Vasilakis C (2011) Systematic review of the use of computer simulation modeling of patient flow in surgical care. J Public Health Med 35(1):1–16

    Google Scholar 

  • Tricas F, García-Valles F, Colom J, Ezpeleta J (2005) A Petri net structure-based deadlock prevention solution for sequential resource allocation systems. In: International conference on robotics and automation. Barcelona, Spain

  • Whittaker SJ, Rudie K, McLellan J (2015) An augmented Petri net model for health-care protocols. IEEE Trans Autom Control 60(9):2362–2377

    Google Scholar 

  • Zimmermann A (2012) Modeling and evaluation of stochastic Petri nets with TimeNET 4.1. In: VALUETOOLS2012: 6th international conference on performance evaluation methodologies and tools, pp 54–63. IEEE

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Authors and Affiliations

  1. Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain

    Cristian Mahulea & José Manuel Colom

  2. Servicio Aragonés de la Salud, Zaragoza, Spain

    Liliana Mahulea & Juan Manuel García Soriano

Authors
  1. Cristian Mahulea
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  2. Liliana Mahulea
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  3. Juan Manuel García Soriano
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  4. José Manuel Colom
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Corresponding author

Correspondence to Cristian Mahulea.

Additional information

This work has been partially supported by CICYT-FEDER Projects TIN2013-40809-R and DPI2014-57252-R. This work has been also co-financed by the Industry and Innovation Department of the Aragonese Goverment and European Social Funds (COSMOS and GISED Research Groups, refs. T93 and T27). It extends our previous results in Mahulea et al. (2012) and Mahulea et al. (2014).

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Mahulea, C., Mahulea, L., García Soriano, J.M. et al. Modular Petri net modeling of healthcare systems. Flex Serv Manuf J 30, 329–357 (2018). https://doi.org/10.1007/s10696-017-9283-9

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  • DOI: https://doi.org/10.1007/s10696-017-9283-9

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