Sojourn-time Distribution for M/Ga/1 Queue with Batch Service of Fixed Size - Revisited

This paper presents an explicit and straightforward method for finding the sojourn-time distribution of a random customer in an M / G a / 1 queue with a fixed-size batch service. The exhibited process is much more straightforward than the approach discussed by Yu and Tang (Methodology and Computing...

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Bibliographic Details
Published in:Methodology and computing in applied probability Vol. 24; no. 4; pp. 2897 - 2912
Main Authors: Goswami, Veena, Chaudhry, Mohan, Banik, Abhijit Datta
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2022
Springer Nature B.V
Subjects:
Business and Management
Customer services
Distribution functions
Economics
Eigenvalues
Eigenvectors
Electrical Engineering
Life Sciences
Mathematics and Statistics
Probability
Probability density functions
Queues
Random variables
Statistics
Sojourn time
Distribution function
Partial fractions
Batch service
Roots
ISSN:1387-5841, 1573-7713
Online Access:Get full text
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Summary:This paper presents an explicit and straightforward method for finding the sojourn-time distribution of a random customer in an M / G a / 1 queue with a fixed-size batch service. The exhibited process is much more straightforward than the approach discussed by Yu and Tang (Methodology and Computing in Applied Probability 20(4):1503–1514,  2018 ). We obtain two closed-form expressions for probability density functions by using the inside and outside roots of the underlying characteristic equation. Applying partial fractions and residue theorem, we determine an explicit form of sojourn-time distribution and evaluate the distribution function for any specific time. In illustrative examples, we compare the results obtained by both methods and find that the results match excellently.
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09963-0