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Transient analysis of an M/G/1 retrial queue subject to disasters and server failures

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  • Wang, Jinting
  • Liu, Bin
  • Li, Jianghua

Abstract

An M/G/1 retrial queueing system with disasters and unreliable server is investigated in this paper. Primary customers arrive in the system according to a Poisson process, and they receive service immediately if the server is available upon their arrivals. Otherwise, they will enter a retrial orbit and try their luck after a random time interval. We assume the catastrophes occur following a Poisson stream, and if a catastrophe occurs, all customers in the system are deleted immediately and it also causes the server's breakdown. Besides, the server has an exponential lifetime in addition to the catastrophe process. Whenever the server breaks down, it is sent for repair immediately. It is assumed that the service time and two kinds of repair time of the server are all arbitrarily distributed. By applying the supplementary variables method, we obtain the Laplace transforms of the transient solutions and also the steady-state solutions for both queueing measures and reliability quantities of interest. Finally, numerical inversion of Laplace transforms is carried out for the blocking probability of the system, and the effects of several system parameters on the blocking probability are illustrated by numerical inversion results.

Suggested Citation

  • Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1118-1132
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    Cited by:

    1. Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    2. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    3. Raina Raj & Vidyottama Jain, 2024. "Resource optimization for MMAP[c]/PH[c]/S catastrophic queueing model with PH retrial times," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1192-1223, September.
    4. Shan Gao & Jinting Wang & Tien Van Do, 2016. "A repairable retrial queue under Bernoulli schedule and general retrial policy," Annals of Operations Research, Springer, vol. 247(1), pages 169-192, December.
    5. A. Azadeh & M. S. Naghavi lhoseiny & V. Salehi, 2018. "Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 68(3), pages 535-562, July.
    6. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.

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