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Computing conditional sojourn time of a randomly chosen tagged customer in a $$\textit{BMAP/MSP/}1$$ BMAP / MSP / 1 queue under random order service discipline

Author

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  • Souvik Ghosh

    (Indian Institute of Technology Bhubaneswar)

  • A. D. Banik

    (Indian Institute of Technology Bhubaneswar)

Abstract

This paper deals with the analysis of a single server queue with non-renewal batch arrival and non-renewal service, where the customers are selected randomly for service. The Laplace–Stieltjes transform of the waiting time distribution of a randomly chosen k-type ( $$k{\ge }1$$ k ≥ 1 ) customer, i.e., the customer who finds k ( $${\ge }1$$ ≥ 1 ) other customers in the system at his arrival epoch, is derived using matrix-analytic (RG-factorization) technique. The expression of the expected sojourn time of a k-type ( $$k\ge 0$$ k ≥ 0 ) customer is formulated. The detailed computational procedure along with the numerical results is presented in this paper. A comparison among the random order service (ROS), first-come first-serve, egalitarian processor sharing and generalized processor sharing discipline in terms of the expected sojourn time of a k-type ( $$k\ge 0$$ k ≥ 0 ) customer is presented in the numerical section. The present study indicates that the ROS discipline may be preferred over other scheduling policies for certain correlated arrival and/or service processes.

Suggested Citation

  • Souvik Ghosh & A. D. Banik, 2018. "Computing conditional sojourn time of a randomly chosen tagged customer in a $$\textit{BMAP/MSP/}1$$ BMAP / MSP / 1 queue under random order service discipline," Annals of Operations Research, Springer, vol. 261(1), pages 185-206, February.
    • Handle: RePEc:spr:annopr:v:261:y:2018:i:1:d:10.1007_s10479-017-2534-z
    DOI: 10.1007/s10479-017-2534-z
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    References listed on IDEAS

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    1. Caulkins, Jonathan P., 2010. "Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time?," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 19-24, March.
    2. L. Durr, 1971. "Priority Queues with Random Order of Service," Operations Research, INFORMS, vol. 19(2), pages 453-460, April.
    3. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2008. "A factorization property for BMAP/G/1 vacation queues under variable service speed," Annals of Operations Research, Springer, vol. 160(1), pages 19-29, April.
    4. M. L. Chaudhry & A. D. Banik & A. Pacheco, 2017. "A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞," Annals of Operations Research, Springer, vol. 252(1), pages 135-173, May.
    5. Grace M. Carter & Robert B. Cooper, 1972. "Queues with Service in Random Order," Operations Research, INFORMS, vol. 20(2), pages 389-405, April.
    6. W. Rogiest & K. Laevens & J. Walraevens & H. Bruneel, 2015. "Random-order-of-service for heterogeneous customers: waiting time analysis," Annals of Operations Research, Springer, vol. 226(1), pages 527-550, March.
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    Cited by:

    1. Sujit Kumar Samanta & Kousik Das, 2023. "Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    2. Abhijit Datta Banik & Souvik Ghosh & M. L. Chaudhry, 2020. "On the optimal control of loss probability and profit in a GI/C-BMSP/1/N queueing system," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 144-162, March.

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