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Queueing and risk models with dependencies

Author

Listed:
  • O. J. Boxma

    (Eindhoven University of Technology)

  • M. R. H. Mandjes

    (University of Amsterdam)

Abstract

This paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous arrival; or the service time of a customer depends on her waiting time. In each case, we derive and solve a fixed-point equation for the Laplace–Stieltjes transform of a key performance measure of the model, like waiting time or ruin time.

Suggested Citation

  • O. J. Boxma & M. R. H. Mandjes, 2022. "Queueing and risk models with dependencies," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 69-86, October.
    • Handle: RePEc:spr:queues:v:102:y:2022:i:1:d:10.1007_s11134-022-09863-7
    DOI: 10.1007/s11134-022-09863-7
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    References listed on IDEAS

    as
    1. Peter Iseger & Paul Gruntjes & Michel Mandjes, 2013. "A Wiener–Hopf based approach to numerical computations in fluctuation theory for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 101-118, August.
    2. Boxma, O. J. & Perry, D., 2001. "A queueing model with dependence between service and interarrival times," European Journal of Operational Research, Elsevier, vol. 128(3), pages 611-624, February.
    3. Ivo Adan & Onno Boxma & Jacques Resing, 2022. "Functional equations with multiple recursive terms," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 7-23, October.
    4. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    5. Janssen, Jacques & Reinhard, Jean-Marie, 1985. "Probabilités de Ruine pour une Classe de Modèles de Risque Semi-Markoviens," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 123-133, November.
    6. M. Posner, 1973. "Single-Server Queues with Service Time Dependent on Waiting Time," Operations Research, INFORMS, vol. 21(2), pages 610-616, April.
    7. Naser M. Asghari & Peter Iseger & Michael Mandjes, 2014. "Numerical Techniques in Lévy Fluctuation Theory," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 31-52, March.
    8. Nasser Hadidi, 1985. "Further Results on Queues with Partial Correlation," Operations Research, INFORMS, vol. 33(1), pages 203-209, February.
    Full references (including those not matched with items on IDEAS)

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