Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

Miaomiao Yu () and Yinghui Tang ()
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Miaomiao Yu: Sichuan University of Science and Engineering
Yinghui Tang: Sichuan Normal University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1503-1514

Abstract: Abstract This paper presents a simple algorithm for computing the cumulative distribution function of the sojourn time of a random customer in an M/GL/1 queue with bulk-service of exactly size L. Both theoretical and numerical aspects related to this problem were not discussed by Chaudhry and Templeton in their monograph (1983). Our analysis is based on the roots of the so-called characteristic equation of the Laplace-Stieltjes transform (LST) of the sojourn time distribution. Using the method of partial fractions and residue theorem, we obtain a closed-form expression of sojourn time distribution, from which we can calculate the value of the distribution function for any given time t ∈ [0, + ∞). Finally, to ensure the reliability of the analytical procedure, employing the work done by Gross and Harris (1985), an effective way to validate the correctness of our results along with some numerical examples are also provided.

Keywords: Bulk-service; Sojourn time; Cumulative distribution function; Roots; Residue theorem; 60K25; 68M20; 90B22 (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/s11009-018-9635-2

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