Open Access   Article Go Back

Development and Analysis of Generalized Queuing Model

Sachin Kumar Agrawal1 , B.K. Singh2

Section:Research Paper, Product Type: Journal Paper
Volume-6 , Issue-11 , Page no. 15-32, Nov-2018

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v6i11.1532

Online published on Nov 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.

View this paper at   Google Scholar | DPI Digital Library

XML View
PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: Sachin Kumar Agrawal, B.K. Singh, “Development and Analysis of Generalized Queuing Model,” International Journal of Computer Sciences and Engineering, Vol.6, Issue.11, pp.15-32, 2018.

MLA Style Citation: Sachin Kumar Agrawal, B.K. Singh "Development and Analysis of Generalized Queuing Model." International Journal of Computer Sciences and Engineering 6.11 (2018): 15-32.

APA Style Citation: Sachin Kumar Agrawal, B.K. Singh, (2018). Development and Analysis of Generalized Queuing Model. International Journal of Computer Sciences and Engineering, 6(11), 15-32.

BibTex Style Citation:
@article{Agrawal_2018,
author = {Sachin Kumar Agrawal, B.K. Singh},
title = {Development and Analysis of Generalized Queuing Model},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {11 2018},
volume = {6},
Issue = {11},
month = {11},
year = {2018},
issn = {2347-2693},
pages = {15-32},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=3120},
doi = {https://doi.org/10.26438/ijcse/v6i11.1532}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i11.1532}
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=3120
TI - Development and Analysis of Generalized Queuing Model
T2 - International Journal of Computer Sciences and Engineering
AU - Sachin Kumar Agrawal, B.K. Singh
PY - 2018
DA - 2018/11/30
PB - IJCSE, Indore, INDIA
SP - 15-32
IS - 11
VL - 6
SN - 2347-2693
ER -

VIEWS PDF XML
1258 1069 downloads 334 downloads
  
  
           

Abstract

In the present work a generalized queuing model has been developed to investigate the various queuing characteristics in steady state. The model consists of two global servers having three servers each which are connected in tri-cum biserial way. The comprehensive governing equations has been given in mathematical formulation which has been used to find the various output parameters i.e., queue lengths, variances, joint probabilities, traffic intensities, average waiting time for customers. The present model is named a generalized queuing model because several models available in the literature can be developed as the special cases.

Key-Words / Index Term

Queue length, Average waiting time, Poisson Law, Moment generating function, Probability

References

[1] R.R.P. Jackson, “Queuing systems with phase-type service”, Operational Research Quarterly, 5, pp. 109-120, 1954.
[2] P.L. Maggu, “Phase type service queues with two servers in biseries”, Journal of Operational Research Society of Japan, Vol. 13, No.1, pp. 6-16, 1970.
[3] K.L. Arya, “System of two servers in biseries with a serial service channel and phase type service” Zeitschrift fur Operations Research, Vol. 16 B, pp. 115-122, 1972.
[4] M. Singh, “Steady state behaviour of serial queuing processes with impatient customers”, Math, Operations forsch. U. statist. Ser., Vol. 15, No.2, pp. 289-298, 1984.
[5] R. Hassin, M. Haviv, “To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems”, International Series in Operations Research & Management Science, Vol. 59, pp. 109-122, 2003.
[6] D. Gupta, T.P. Singh, R. Kumar, “Analysis of a network queue model comprised of biserial and parallel channel linked with a common server” Ultra Science, Vol. 19, No. 2 M, 407-418, 2007.
[7] T.P. Singh, V. Kumar, R. Kumar, “On transient behaviour of a queuing network with parallel biserial queues”, JMASS, Vol.1, No.2, pp.68-75, 2005.
[8] V. Kumar, T.P. Singh, R. Kumar, “Steady state behaviour of a queue model comprised of two subsystems with biserial linked with common channel”, Reflection des ERA., Vol.1, No.2, pp.135-152, 2007.
[9] M.S. El-Paoumy, “On Poisson Bulk Arrival Queue: M X /M / 2 / N with Balking, Reneging and Heterogeneous servers”, Applied Mathematical Sciences, Vol. 2, No. 24, 1169 – 1175, 2008.
[10] S.K. Agrawal, 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), Vol. 56, No. 1, pp. 81-90, 2008. doi: 10.14445/22315373/IJMTT-V56P510.
[11] S.K. 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 (IJSRMSS), Vol. 5, Issue 2, pp. 46-56, 2008. doi: 10.26438/ijsrmss/v5i2.4656.
[12] S.K. Agrawal, B.K. Singh, “An Investigation of Tri-Cum Biserial Queuing Model Connected with Three Servers”, International Journal of Emerging Technologies and Innovative Research (JETIR), Vol. 5, issue 9, pp. 493-509, 2018. Doi: 10.1729/Journal.18346.
[13] S.K. Agrawal and B.K. Singh, “Influence of Reneging and Jockeying on Various Queuing Characteristics of Tri-Cum Biserial Based Queue Model”, International Journal of Mechanical Engineering and Technology (IJMET), Vol. 9, Issue 10, pp. (1062)-(1073), 2018.