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

Souvik Ghosh () and A. D. Banik ()
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Souvik Ghosh: Indian Institute of Technology Bhubaneswar
A. D. Banik: Indian Institute of Technology Bhubaneswar

Annals of Operations Research, 2018, vol. 261, issue 1, No 8, 185-206

Abstract: 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.

Keywords: Batch Markovian arrival process (BMAP); Markovian service process (MSP); Random order service (ROS); RG-factorization; Expected sojourn time (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-017-2534-z

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