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Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations

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  • Ammar, Sherif I.

Abstract

In this paper, we carry out an analysis for a single server queue with impatient customers and multiple vacations where customers impatience is due to an absentee of servers upon arrival. Customers arrive at the system according to a Poisson process and exponential service times. Explicit expressions are obtained for the time dependent probabilities, mean and variance of the system size in terms of the modified Bessel functions, by employing the generating functions along with continued fractions and the properties of the confluent hypergeometric function. Finally, some numerical illustrations are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:97-105
    DOI: 10.1016/j.amc.2015.03.066
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    References listed on IDEAS

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    1. K. Kalidass & J. Gnanaraj & S. Gopinath & Ramanath Kasturi, 2014. "Transient analysis of an M/M/1 queue with a repairable server and multiple vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(2), pages 193-216.
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    Cited by:

    1. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    2. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    3. Xu Jia & Liu Liwei & Zhu Taozeng, 2018. "Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 69-84, February.
    4. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    5. R. Sudhesh & A. Azhagappan, 2018. "RETRACTED ARTICLE: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 787-806, November.
    6. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    7. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    8. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    9. 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.
    10. 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.
    11. A. Mohammed Shapique & R. Sudhesh & S. Dharmaraja, 2024. "Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-33, September.

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    2. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
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