The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line

Vedat Sağlam; Murat Sağır; Erdinç Yücesoy; Müjgan Zobu

doi:doi:10.11648/j.pamj.20150405.12

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The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line

Vedat Sağlam, Murat Sağır, Erdinç Yücesoy, Müjgan Zobu

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 5)

Received: 17 August 2015 Accepted: 27 August 2015 Published: 8 September 2015

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Abstract

A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 5)
DOI	10.11648/j.pamj.20150405.12
Page(s)	216-218
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), 2024. Published by Science Publishing Group

Keywords

Heterogeneous Queueing Systems, Loss Probability, Optimization, Simulation, Markov Chain, Kolmogorov Equation, Transition Rates

References

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[2]	J. R. Artalejo and G. Choudhury, “Steady State Analysis of an M/G/1 Queue with Repeated Attempts and Two-Phase Service”, Quality Technology&Quantative Management, Vol.1, No.2, pp. 189-199, 2004.
[3]	M. Zobu, V. Sağlam, M. Sağır, E. Yücesoy and T. Zaman, “The Simulation and Minimization of Loss Probability in the Tandem Queueing with two Heterogeneous Channel”, Mathematical problems in Engineering, Vol. 2013, Article ID 529010, 4 pages, 2013.
[4]	V. Sağlam and M. Zobu, “A two-stage Queueing Model with No waiting Line between Channels”, Mathematical Problems in Engineering, Vol. 2013, Article ID 679369, 5 pages, 2013.
[5]	A. V. S. Suhasini, K. Srinivasa Rao, P. R. S. Reddy, “On parallel and series non homogeneous bulk arrival queueing model”, OPSEARCH (Oct-Dec 2013), 50(4):521-547, 2013.
[6]	N. U. Prabhu and Yixin ZHU, “Markov-modulated Queueing Systems”, Queueing System, 5 (1989) 215-246, 1989.
[7]	Frederick S. Hillier, Kut C. So, “On the optimal design of tandem queueing systems with finite buffers”, Queueing Systems 21 (1995) 245-266, 1995.
[8]	V. V. Rykov, “Monotone Control of Queueing Systems with Heterogeneous Servers”, Queueing Systems, 37, 391-403, 2001.
[9]	V. Sağlam and H. Torun, “ On Optimization of Stochastic Service System with Two Heterogeneous Channels”, International Journal of Applied Mathematics, 17, 1, 8 / 2005
[10]	Gross, D., Harris, C. M., Thompson, M. J., Shortle, F. J., Fundementals of Queueing Theory, 4th ed., John Wiley & Sons, New York, 2008.
[11]	Stewart, W. J., Probability, Markov Chains, Queues and Simulation, Princeton University Press, United Kingdom, 2009.
[12]	V. Ramaswami, “Algorithms for the Multi-Server Queue”, Commun. Statist.-Stochastic Models, 1(3), 393-417, 1985.
[13]	W. K. Grassmann, “Transient Solutions in Markovian queueing systems”, Computers & Operations Research, Volume 4, Issue 1, pages 47-53, 1977.
[14]	E. Brockmeyer, H. L. Halstrom and A. Jensen, “The life and works of A. K. Erlann.” Danish Acad. Techn. Sci, No. 2, Koben havn (Denmark), 1948.
[15]	F. Alpaslan, “On the minimization probability of loss in queue two heterogeneous channels,” Pure and Applied Mathematika Sciences, vol. 43, no. 1-2, pp. 21–25, 1996.
[16]	V. Saglam and A. Shahbazov, “Minimizing loss probability in queuing systems with heterogeneous servers,” Iranian Journal of Science and Technology, vol. 31, no. 2, pp. 199–206, 2007.

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Vedat Sağlam, Murat Sağır, Erdinç Yücesoy, Müjgan Zobu. (2015). The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure and Applied Mathematics Journal, 4(5), 216-218. https://doi.org/10.11648/j.pamj.20150405.12

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ACS Style

Vedat Sağlam; Murat Sağır; Erdinç Yücesoy; Müjgan Zobu. The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure Appl. Math. J. 2015, 4(5), 216-218. doi: 10.11648/j.pamj.20150405.12

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AMA Style

Vedat Sağlam, Murat Sağır, Erdinç Yücesoy, Müjgan Zobu. The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure Appl Math J. 2015;4(5):216-218. doi: 10.11648/j.pamj.20150405.12

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@article{10.11648/j.pamj.20150405.12,
  author = {Vedat Sağlam and Murat Sağır and Erdinç Yücesoy and Müjgan Zobu},
  title = {The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {5},
  pages = {216-218},
  doi = {10.11648/j.pamj.20150405.12},
  url = {https://doi.org/10.11648/j.pamj.20150405.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150405.12},
  abstract = {A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k  (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.},
 year = {2015}
}

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TY  - JOUR
T1  - The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line
AU  - Vedat Sağlam
AU  - Murat Sağır
AU  - Erdinç Yücesoy
AU  - Müjgan Zobu
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DO  - 10.11648/j.pamj.20150405.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
SN  - 2326-9812
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AB  - A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k  (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.
VL  - 4
IS  - 5
ER  -

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Author Information

Vedat Sağlam
Murat Sağır
Erdinç Yücesoy
Müjgan Zobu

Department of Statistics, Amasya University, Amasya, Turkey

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Plain Text BibTeX RIS

APA Style

Vedat Sağlam, Murat Sağır, Erdinç Yücesoy, Müjgan Zobu. (2015). The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure and Applied Mathematics Journal, 4(5), 216-218. https://doi.org/10.11648/j.pamj.20150405.12

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ACS Style

Vedat Sağlam; Murat Sağır; Erdinç Yücesoy; Müjgan Zobu. The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure Appl. Math. J. 2015, 4(5), 216-218. doi: 10.11648/j.pamj.20150405.12

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AMA Style

Vedat Sağlam, Murat Sağır, Erdinç Yücesoy, Müjgan Zobu. The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line. Pure Appl Math J. 2015;4(5):216-218. doi: 10.11648/j.pamj.20150405.12

Copy | Download

@article{10.11648/j.pamj.20150405.12,
  author = {Vedat Sağlam and Murat Sağır and Erdinç Yücesoy and Müjgan Zobu},
  title = {The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {5},
  pages = {216-218},
  doi = {10.11648/j.pamj.20150405.12},
  url = {https://doi.org/10.11648/j.pamj.20150405.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150405.12},
  abstract = {A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k  (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line
AU  - Vedat Sağlam
AU  - Murat Sağır
AU  - Erdinç Yücesoy
AU  - Müjgan Zobu
Y1  - 2015/09/08
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150405.12
DO  - 10.11648/j.pamj.20150405.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 216
EP  - 218
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150405.12
AB  - A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k  (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.
VL  - 4
IS  - 5
ER  -

Copy | Download