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

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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 (\(k{\ge }1\)) customer, i.e., the customer who finds k (\({\ge }1\)) 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 (\(k\ge 0\)) 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 (\(k\ge 0\)) 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.

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Acknowledgements

Authors are thankful to the referee for his valuable comments and suggestions which has led to significant improvement of the paper. Authors are also grateful to Dr. Debasis Basu of Indian Institute of Technology Bhubaneswar for his valuable advice and encouragement.

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  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Permanent Campus Argul, Khurda, Odisha, 752050, India

    Souvik Ghosh & A. D. Banik

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  1. Souvik Ghosh
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  2. A. D. Banik
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Correspondence to A. D. Banik.

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Ghosh, S., Banik, A.D. Computing conditional sojourn time of a randomly chosen tagged customer in a \(\textit{BMAP/MSP/}1\) queue under random order service discipline. Ann Oper Res 261, 185–206 (2018). https://doi.org/10.1007/s10479-017-2534-z

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