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MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Author

Listed:
  • Divya Velayudhan Nair

    (Department of Mathematics, NSS College, Cherthala 688556, India)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, India)

  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku AZ 1148, Azerbaijan)

  • Sevinj Aliyeva

    (Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan)

Abstract

In this paper, we consider two single server queueing systems to which customers of two distinct priorities ( P 1 and P 2 ) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P 1 customer to feedback is θ on completion of his service. The feedback ( P 1 ) customers, as well as P 2 customers, join the low priority queue. Low priority ( P 2 ) customers are taken for service from the head of the line whenever the P 1 queue is found to be empty at the service completion epoch. We assume a finite waiting space for P 1 customers and infinite waiting space for P 2 customers. Two models are discussed in this paper. In model I, we assume that the service of P 2 customers is according to a non-preemptive service discipline and in model II, the P 2 customers service follow a preemptive policy. No feedback is permitted to customers in the P 2 line. In the steady state these two models are compared through numerical experiments which reveal their respective performance characteristics.

Suggested Citation

  • Divya Velayudhan Nair & Achyutha Krishnamoorthy & Agassi Melikov & Sevinj Aliyeva, 2021. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1797-:d:604014
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    References listed on IDEAS

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    5. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.
    6. N. K. Jaiswal, 1961. "Preemptive Resume Priority Queue," Operations Research, INFORMS, vol. 9(5), pages 732-742, October.
    7. V. Jailaxmi & R. Arumuganathan & A. Rathinasamy, 2017. "Performance analysis of an M x /G/1 feedback retrial queue with non-persistent customers and multiple vacations with N-policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 29(2), pages 149-169.
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    Cited by:

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