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Unified killing mechanism in a single server queue with renewal input

Author

Listed:
  • Nitin Kumar

    (Indian Institute of Technology)

  • F. P. Barbhuiya

    (Indian Institute of Technology)

  • U. C. Gupta

    (Indian Institute of Technology)

Abstract

Queueing systems experienced in real-life situations are very often influenced by negative arrivals which are independent of service process and cause the elimination of jobs from the system. Such a scenario occurs in computer network and telecommunication systems where an attack by a malicious virus results in the removal of some or all data files from the system. Along this direction many authors have proposed various killing processes in the past. This paper unifies different killing mechanisms into the classical single server queue having infinite capacity, where arrival occurs as renewal process with exponential service time distribution. The system is assumed to be affected by negative customers as well as disasters. The model is investigated in steady-state in a very simple and elegant way by means of supplementary variable and difference equation technique. The distribution of system-content for the positive customers is derived in an explicit form at pre-arrival and random epochs. The influence of different parameters on the system performance are also examined.

Suggested Citation

  • Nitin Kumar & F. P. Barbhuiya & U. C. Gupta, 2020. "Unified killing mechanism in a single server queue with renewal input," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 246-259, March.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:1:d:10.1007_s12597-019-00408-w
    DOI: 10.1007/s12597-019-00408-w
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    References listed on IDEAS

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    1. F. P. Barbhuiya & U. C. Gupta, 2019. "Discrete-time queue with batch renewal input and random serving capacity rule: $$GI^X/ Geo^Y/1$$ G I X / G e o Y / 1," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 347-365, April.
    2. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    3. F. P. Barbhuiya & Nitin Kumar & U. C. Gupta, 2019. "Batch Renewal Arrival Process Subject to Geometric Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 69-83, March.
    4. P., Vijaya Laxmi & M.L., Soujanya, 2015. "Perishable inventory system with service interruptions, retrial demands and negative customers," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 102-110.
    5. P. Rajadurai & V. M. Chandrasekaran & M. C. Saravanarajan, 2016. "Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 197-223, March.
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