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A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model

Sachin Kumar Agrawal1 , B.K. Singh2

  1. Department of Mathematics, IFTM University, Moradabad, India.
  2. Department of Mathematics, IFTM University, Moradabad, India.

Correspondence should be addressed to: sachin269mit@gmail.com .


Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.2 , pp.46-56, Apr-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.4656


Online published on Apr 30, 2018


Copyright © Sachin Kumar Agrawal, B.K. Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: Sachin Kumar Agrawal, B.K. Singh , “A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.46-56, 2018.

MLA Style Citation: Sachin Kumar Agrawal, B.K. Singh "A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.2 (2018): 46-56.

APA Style Citation: Sachin Kumar Agrawal, B.K. Singh , (2018). A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(2), 46-56.

BibTex Style Citation:
@article{Agrawal_2018,
author = {Sachin Kumar Agrawal, B.K. Singh },
title = {A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {4 2018},
volume = {5},
Issue = {2},
month = {4},
year = {2018},
issn = {2347-2693},
pages = {46-56},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=578},
doi = {https://doi.org/10.26438/ijcse/v5i2.4656}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i2.4656}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=578
TI - A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Sachin Kumar Agrawal, B.K. Singh
PY - 2018
DA - 2018/04/30
PB - IJCSE, Indore, INDIA
SP - 46-56
IS - 2
VL - 5
SN - 2347-2693
ER -

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Abstract :
In the present article, a queuing model having three servers connected in parallel in a tri-cum biserial way has been presented. Statistical tools, generating function technique and the law of calculus have been implemented to compute the various queuing characteristics such as Queue length, variance, average waiting time and probabilities. The arrival and service pattern is supposed to follow the Poisson law. Generic mathematical formulation of queuing model has been presented to ensure the implementation of the presented model in various problems occurred in real-time domain. The presented model is easy to understand and also deliver an important tool for the decision makers dealing with multi-tasking problems.

Key-Words / Index Term :
Queue length, variance, average waiting time, probabilities

References :
[1] I. Adan, J. Resing, “Queuing theory department of mathematics and computing science”, Eindhoren University of Technology Eindhoren, 1–123, 2002.
[2] P.L. Maggu, “Phase type service queues with two servers in biseries”, Journal of Operational Research Society of Japan, 13(1), 1-6, 1970.
[3] P.L. Maggu and G. Das, “Equivalent jobs for job block in job sequencing”, Opsearch, 14(4), 277-281, 1977.
[4] Singh, Man, “Steady state behaviour of serial queuing processes with impatient customers", Math, Operations forsch. U. statist. Ser. 15(2),289-298, 1984.
[5] D. Gupta, S. Sharma, and S. Sharma, “On linkage of a flowshop scheduling model including job block criteria with a parallel biserial queue network”, Computer Engineering and Intelligent System, 3(2), 17-28, 2012.
[6] R.R.P. Jackson, “Queuing systems with phase-type service”, Operational Research Quarterly, 5, 109-120, 1954.
[7] S.K. Agrawal, and B.K. Singh, “Computation of various queue characteristics using tri-cum biserial queuing model connected with a common server”, International Journal of Mathematics Trends and Technology (IJMTT) – Volume 56 Number 1, 81-90, 2018. doi: 10.14445/22315373/IJMTT-V56P510.

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