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Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience

Author

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  • R. Sudhesh

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • P. Savitha

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • S. Dharmaraja

    (Indian Institute of Technology Delhi)

Abstract

A two-heterogeneous servers queue with system disaster, server failure and repair is considered. In addition, the customers become impatient when the system is down. The customers arrive according to a Poisson process and service time follows exponential distribution. Each customer requires exactly one server for its service and the customers select the servers on fastest server first basis. Explicit expressions are derived for the time-dependent system size probabilities in terms of the modified Bessel function, by employing the generating function along with continued fraction and the identity of the confluent hypergeometric function. Further, the steady-state probabilities of the number of customers in the system are deduced and finally some important performance measures are obtained.

Suggested Citation

  • R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0428-x
    DOI: 10.1007/s11750-016-0428-x
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    References listed on IDEAS

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    1. Ke, Jau-Chuan & Liu, Tzu-Hsin & Wu, Chia-Huang, 2015. "An optimum approach of profit analysis on the machine repair system with heterogeneous repairmen," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 40-51.
    2. R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    3. Mor Armony & Amy R. Ward, 2010. "Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems," Operations Research, INFORMS, vol. 58(3), pages 624-637, June.
    4. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    5. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
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    Cited by:

    1. Ahuja, Anjali & Jain, Anamika & Jain, Madhu, 2022. "Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 464-490.
    2. Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, 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.

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