article

Priority tandem queueing model with admission control

Authors:

Sergey DudinAuthors Info & Claims

Computers and Industrial Engineering, Volume 61, Issue 1

Pages 131 - 140

https://doi.org/10.1016/j.cie.2011.03.003

Published: 01 August 2011 Publication History

Abstract

A two-stage multi-server tandem queue with two types of processed customers is analyzed. The input is described by the Marked Markovian Arrival Process (MMAP). The first stage has an infinite number of servers while the second stage has a finite number of servers. The service time at the both stages has an exponential distribution. Priority customers are always admitted to the system. Non-priority customers are admitted to the system only if the number of busy servers at the second stage does not exceed some pre-assigned threshold. Queueing system's behavior is described in terms of the multi-dimensional asymptotically quasi-Toeplitz continuous time Markov chain. It allows to exploit a numerically stable algorithm for calculation of the stationary distribution of the queueing system. The loss probability at the both stages of the tandem is computed. An economic criterion of the system operation is optimized with respect to the threshold. The effect of control on the main performance measures of the system is numerically demonstrated.

References

[1]

Optimal control of a two-stage tandem queuing system with flexible servers. Probability in the Engineering and Informational Sciences. i16. 453-469.

[2]

Wireless mesh networks: A survey. Computer Networks. i47. 445-482.

[3]

Applied probability and queues. Springer, New York.

[4]

A review on queueing network models with finite capacity queues for software architectures performance prediction. Performance Evaluation. i51. 269-288.

[5]

A two-phase BMAP/G/1/N�PH/1/M-1 system with blocking. Automation and Remote Control. i65. 117-130.

[6]

The batch Markovian arrival process: A review and future work. In: Krishnamoorthy, A. (Ed.), Advances in probability theory and stochastic processes, Notable Publications, NJ. pp. 21-49.

[7]

Handbuch der Bedienungstheorie. Akademie Verlag, Berlin.

[8]

A tandem queue with blocking and Markovian arrival process. Queueing Systems. i41. 343-370.

[9]

On a tandem G-network with blocking. Advances in Applied Probability. i34. 626-661.

[10]

A matrix-geometric approximation for tandem queues with blocking and repeated attempts. Operations Research Letters. i30. 360-374.

[11]

Sojourn times in a two-stage queueing network with blocking. Naval Research Logistics. i51. 1068-1089.

[12]

Kronecker products and matrix calculus with applications. Ellis Horwood, Cichester.

[13]

A tandem queue with a moving server: An eigenvalue approach. SIAM Journal of Matrix Analysis and Applications. i24. 465-474.

[14]

Queues with marked customers. Advances in Applied Probability. i28. 567-587.

[15]

A two-stage tandem queue attended by a moving server with holding and switching costs. Queueing Systems. i26. 203-228.

[16]

ITU (1996). Network grade of service parameters and target values for circuit-switched public lnd mobile services, International Telecommunication Union (ITU) ITU-T Recommendation E.771, October 1996. <http://www.itu.int/rec/T-REC-E.771-199610-I/en>.

[17]

Denumerable Markov chains. Van Nostrand, New York.

[18]

Kim, C. S., Klimenok, V. I., Dudin, S. A. (2006). Tandem queueing system as a model of enhanced operation of telephone network. In: Proceedings of the international scientific conference problems of cybernetics and informatics (pp. 157-160). Baku, Azerbaijan.

[19]

The BMAP/G/1/N�PH/1/M system with losses. Performance Evaluation. i61. 17-40.

[20]

Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory. Queueing Systems. i54. 245-259.

[21]

The BMAP/G/1��/PH/1/M tandem queue with feedback and losses. Performance Evaluation. i64. 802-818.

[22]

A tandem queueing network with feedback admission control. Lecture Notes in Computer Science. i4465. 129-137.

[23]

A tandem queue with coupled processors: Computational issues. Queueing Systems. i51. 29-52.

[24]

New results on the single server queue with a batch Markovian arrival process. Communication in Statistics-Stochastic Models. i7. 1-46.

[25]

Matrix-geometric solutions in stochastic models. The Johns Hopkins University Press, USA.

[26]

A bibliography of papers on queueing networks with finite capacity queues. Performance Evaluation. i10. 255-260.

[27]

A tandem queue with coupled processors. Operations Research Letters. i31. 383-389.

Cited By

Silva DZhang BAyhan H(2018)Admission control strategies for tandem Markovian loss systemsQueueing Systems: Theory and Applications10.1007/s11134-017-9569-390:1-2(35-63)Online publication date: 1-Oct-2018
https://dl.acm.org/doi/10.1007/s11134-017-9569-3
Dudin SDudina O(2013)Help desk center operating model as a two-phase queueing systemProblems of Information Transmission10.1134/S003294601301006749:1(58-72)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1134/S0032946013010067
Dudin SKim CDudina O(2013)MMAP|M|N queueing system with impatient heterogeneous customers as a model of a contact centerComputers and Operations Research10.1016/j.cor.2013.01.02340:7(1790-1803)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.cor.2013.01.023
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Priority tandem queueing model with admission control
1. Computing methodologies
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    1. Model development and analysis

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cover image Computers and Industrial Engineering

Computers and Industrial Engineering Volume 61, Issue 1

August, 2011

240 pages

ISSN:0360-8352

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Copyright © Elsevier Ltd © 2011.

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Pergamon Press, Inc.

United States

Publication History

Published: 01 August 2011

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Cited By

Silva DZhang BAyhan H(2018)Admission control strategies for tandem Markovian loss systemsQueueing Systems: Theory and Applications10.1007/s11134-017-9569-390:1-2(35-63)Online publication date: 1-Oct-2018
https://dl.acm.org/doi/10.1007/s11134-017-9569-3
Dudin SDudina O(2013)Help desk center operating model as a two-phase queueing systemProblems of Information Transmission10.1134/S003294601301006749:1(58-72)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1134/S0032946013010067
Dudin SKim CDudina O(2013)MMAP|M|N queueing system with impatient heterogeneous customers as a model of a contact centerComputers and Operations Research10.1016/j.cor.2013.01.02340:7(1790-1803)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.cor.2013.01.023
Klimenok VKim CDudin A(2011)Tandem queueing system with different types of customersProceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications10.5555/2022315.2022326(99-112)Online publication date: 20-Jun-2011
https://dl.acm.org/doi/10.5555/2022315.2022326

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