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Analysis of a Discrete-Time Queueing Model with Disasters

Author

Listed:
  • Mustafa Demircioglu

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

  • Herwig Bruneel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

  • Sabine Wittevrongel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

Abstract

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

Suggested Citation

  • Mustafa Demircioglu & Herwig Bruneel & Sabine Wittevrongel, 2021. "Analysis of a Discrete-Time Queueing Model with Disasters," Mathematics, MDPI, vol. 9(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3283-:d:704694
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    Cited by:

    1. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.

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