A Queueing Networks-Based Model for Supply Systems

  • Massimo De Falco
  • Nicola Mastrandrea
  • Luigi RaritàEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 217)


In this paper, a stochastic approach, based on queueing networks, is analyzed in order to model a supply system, whose nodes are working stations. Unfinished goods and control electrical signals arrive, following Poisson processes, at the nodes. When the working processes at nodes end, according to fixed probabilities, goods can leave the network or move to other nodes as either parts to process or control signals. On the other hand, control signals are activated during a random exponentially distributed time and they act on unfinished parts: precisely, with assigned probabilities, control impulses can move goods between nodes, or destroy them. For the just described queueing network, the stationary state probabilities are found in product form. A numerical algorithm allows to study the steady state probabilities, the mean number of unfinished goods and the stability of the whole network.


Queueing networks Supply systems Product–form solution 


  1. 1.
    Artalejo, J.R.: G-networks: a versatile approach for work removal in queueing networks. Eur. J. Oper. Res. 126, 233–249 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bocharov, P.P., D’Apice, C., Pechinki,n A.V., Salerno, S.: Queueing Theory, Modern Probability and Statistics. VSP, The Netherlands (2004)Google Scholar
  3. 3.
    Cutolo, A., Piccoli, B., Rarità, L.: An Upwind-Euler scheme for an ODE-PDE model of supply chains. SIAM J. Comput. 33(4), 1669–1688 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    De Falco, M., Gaeta, M., Loia, V., Rarità, L., Tomasiello, S.: Differential quadrature-based numerical solutions of a fluid dynamic model for supply chains. Commun. Math. Sci. 14(5), 1467–1476 (2016)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Gelenbe, E.: Product form queueing networks with positive and negative customers. J. Appl. Probab. 28, 656–663 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Gelenbe, E.: G-networks with triggered customer movement. J. Appl. Prob. 30, 742–748 (1993)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Gelenbe, E., Pujolle, G.: Introduction to Queueing Networks, 2nd edn. Wiley, New York (1999)zbMATHGoogle Scholar
  8. 8.
    Jackson, J.R.: Networks of waiting lines. Oper. Res. 5, 518–521 (1957)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Pasquino, N., Rarità, L.: Automotive processes simulated by an ODE-PDE model. In: Proceedings of EMSS 2012, 24th European Modeling and Simulation Symposium, 19–21 Sept 2012, Vienna, Austria, pp. 352–361 (2012)Google Scholar
  10. 10.
    Tomasiello, S., Macías-Díaz, J.E.: Note on a picard-like method for caputo fuzzy fractional differential equations. Appl. Math. Inform. Sci. 11(1), 281–287 (2017)CrossRefGoogle Scholar
  11. 11.
    Yao, D.D., Buzacott, J.A.: The exponentialization approach to flexible manufacturing systems models with general processing times. Eur. J. Oper. Res. 24, 410–416 (1986)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Massimo De Falco
    • 1
  • Nicola Mastrandrea
    • 1
  • Luigi Rarità
    • 2
    Email author
  1. 1.Dipartimento di Scienze Aziendali - Management & Innovation SystemsUniversity of SalernoFisciano (SA)Italy
  2. 2.CO.RI.SA, COnsorzio RIcerca Sistemi Ad AgentiUniversity of SalernoFisciano (SA)Italy

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