Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers

Kotb Abdel Hamid Kotb; Moamer Akhdar

doi:doi:10.11648/j.acm.20180702.12

| Peer-Reviewed

Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers

Kotb Abdel Hamid Kotb, Moamer Akhdar

Published in Applied and Computational Mathematics (Volume 7, Issue 2)

Received: 17 January 2018 Accepted: 31 January 2018 Published: 27 February 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The aim of this paper is to derive the analytical solution of the non-truncated single-channel Erlangian queue: M/E_k/1 at the steady-state with adding the concepts of balking, feedback strategy and retention of reneged customers. We obtain the probabilities that there are n customers in the system and the customers in the service occupces stage s, (s = 1, 2, …, k ), the probability of empty system and some measures of effecting of queuing system are obtained using the iterative method. Some important queueing models are derived as special cases of this system. Some numerical values are given showily the effect of correlation between the probabilities and the additional concepts.

Published in	Applied and Computational Mathematics (Volume 7, Issue 2)
DOI	10.11648/j.acm.20180702.12
Page(s)	40-49
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Balking, Non-Truncated, Feedback, Queueing System, Iterative Method, Retention of Reneged Customers

References

[1]	J. A. White, J. W. Schmidt and G. K. Bennett, Analysis of queueing system, Academic press, New York, (1975).
[2]	K. A. M Kotb, state-dependent queues, Ph.D. Thesis, faculty of science, Tanta university, 1994.
[3]	A. I. Shawky, The service Erlangian machine interference model: M/Er/1/k/N with balking and reneging, Journal applied mathematics & computing, 18 (2005), 431-439.
[4]	Madhu Jain and Praveen Kumar, M/E_k/1 queueing system with working vacation, queuing systems, 4 (2007), 455 - 470.
[5]	D. Groos and C. M. Harris, Fundamentals of queueing theory, New York, John wiley and sons, 4th edition, (2008).
[6]	S. S. Mishra and Dinesh Kumar Yadav, Cost and profit analysis of M / Ek / 1 queueing system with removable service station, Applied mathematical sciences, 2 (2008), 2777 - 2784.
[7]	M. S. El-Paoumy and M. M. Ismail, On a truncated Erlang queuing system with bulk arrivals, balking and reneging, Applied mathematical sciences, 3 (2009), 1103–1113.
[8]	Namh. A. Abid and Azmi. K. Al - Madi, On the queuing system M/Er/1/N, Baghdad science journal, 9 (2012), 367-371.
[9]	P. Jayachitra and A. James Albert, Optimal management policy for heterogeneous arrival M/E_k/1 queueing system with server breakdowns and multiple vacations, Advances in theoretical and applied mathematics, 1 (2014), 87-95.
[10]	P. Jayachitra and A. James Albert, Performance analysis of an n-policy M/Ek/1 queueing system with server start up, unreliable server and balking, International journal of mathematical archive, 6 (2015), 159–169.
[11]	P. Jayachitra and A. James Albert, Analysis of an n-policy M/E_k/1 queueing system with unreliable server, multiple vacations and balking, International journal of mathematics trends and technology, 21 (2015), 2231-5373.
[12]	K. A. M. Kotb and Moamer Akhdar, feedback of M/M/1 queue with catastrophe, repair and retention of reneged customers via transient behavior approach, Sylwan, 161 (2017), 357-371.
[13]	K. Jeganathan, M. Abdul Reiyas, S. Padmasekaran and K. Lakshmanan, An M/E_k /1/N queueing-inventory system with two service rates based on queue lengths, International Journal applied mathematics and computing, 1 (2017), 360-388.

Cite This Article

Plain Text BibTeX RIS

APA Style

Kotb Abdel Hamid Kotb, Moamer Akhdar. (2018). Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Applied and Computational Mathematics, 7(2), 40-49. https://doi.org/10.11648/j.acm.20180702.12

Copy | Download

ACS Style

Kotb Abdel Hamid Kotb; Moamer Akhdar. Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Appl. Comput. Math. 2018, 7(2), 40-49. doi: 10.11648/j.acm.20180702.12

Copy | Download

AMA Style

Kotb Abdel Hamid Kotb, Moamer Akhdar. Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Appl Comput Math. 2018;7(2):40-49. doi: 10.11648/j.acm.20180702.12

Copy | Download

@article{10.11648/j.acm.20180702.12,
  author = {Kotb Abdel Hamid Kotb and Moamer Akhdar},
  title = {Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {2},
  pages = {40-49},
  doi = {10.11648/j.acm.20180702.12},
  url = {https://doi.org/10.11648/j.acm.20180702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180702.12},
  abstract = {The aim of this paper is to derive the analytical solution of the non-truncated single-channel Erlangian queue: M/Ek/1 at the steady-state with adding the concepts of balking, feedback strategy and retention of reneged customers. We obtain the probabilities that there are n customers in the system and the customers in the service occupces stage s, (s = 1, 2, …, k ), the probability of empty system and some measures of effecting of queuing system are obtained using the iterative method. Some important queueing models are derived as special cases of this system. Some numerical values are given showily the effect of correlation between the probabilities and the additional concepts.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers
AU  - Kotb Abdel Hamid Kotb
AU  - Moamer Akhdar
Y1  - 2018/02/27
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180702.12
DO  - 10.11648/j.acm.20180702.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 40
EP  - 49
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180702.12
AB  - The aim of this paper is to derive the analytical solution of the non-truncated single-channel Erlangian queue: M/Ek/1 at the steady-state with adding the concepts of balking, feedback strategy and retention of reneged customers. We obtain the probabilities that there are n customers in the system and the customers in the service occupces stage s, (s = 1, 2, …, k ), the probability of empty system and some measures of effecting of queuing system are obtained using the iterative method. Some important queueing models are derived as special cases of this system. Some numerical values are given showily the effect of correlation between the probabilities and the additional concepts.
VL  - 7
IS  - 2
ER  -

Copy | Download

Author Information

Kotb Abdel Hamid Kotb

Department of Mathematics and Statistics, Faculty of Science, Tanta University, Tanta, Egypt
Moamer Akhdar

Department of Mathematics and Statistics, Faculty of Science, Tanta University, Tanta, Egypt

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Kotb Abdel Hamid Kotb, Moamer Akhdar. (2018). Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Applied and Computational Mathematics, 7(2), 40-49. https://doi.org/10.11648/j.acm.20180702.12

Copy | Download

ACS Style

Kotb Abdel Hamid Kotb; Moamer Akhdar. Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Appl. Comput. Math. 2018, 7(2), 40-49. doi: 10.11648/j.acm.20180702.12

Copy | Download

AMA Style

Kotb Abdel Hamid Kotb, Moamer Akhdar. Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers. Appl Comput Math. 2018;7(2):40-49. doi: 10.11648/j.acm.20180702.12

Copy | Download

@article{10.11648/j.acm.20180702.12,
  author = {Kotb Abdel Hamid Kotb and Moamer Akhdar},
  title = {Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {2},
  pages = {40-49},
  doi = {10.11648/j.acm.20180702.12},
  url = {https://doi.org/10.11648/j.acm.20180702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180702.12},
  abstract = {The aim of this paper is to derive the analytical solution of the non-truncated single-channel Erlangian queue: M/Ek/1 at the steady-state with adding the concepts of balking, feedback strategy and retention of reneged customers. We obtain the probabilities that there are n customers in the system and the customers in the service occupces stage s, (s = 1, 2, …, k ), the probability of empty system and some measures of effecting of queuing system are obtained using the iterative method. Some important queueing models are derived as special cases of this system. Some numerical values are given showily the effect of correlation between the probabilities and the additional concepts.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers
AU  - Kotb Abdel Hamid Kotb
AU  - Moamer Akhdar
Y1  - 2018/02/27
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180702.12
DO  - 10.11648/j.acm.20180702.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 40
EP  - 49
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180702.12
AB  - The aim of this paper is to derive the analytical solution of the non-truncated single-channel Erlangian queue: M/Ek/1 at the steady-state with adding the concepts of balking, feedback strategy and retention of reneged customers. We obtain the probabilities that there are n customers in the system and the customers in the service occupces stage s, (s = 1, 2, …, k ), the probability of empty system and some measures of effecting of queuing system are obtained using the iterative method. Some important queueing models are derived as special cases of this system. Some numerical values are given showily the effect of correlation between the probabilities and the additional concepts.
VL  - 7
IS  - 2
ER  -

Copy | Download