Performance Analysis of Three Stage Tandem Queues

Sreekanth. K; Kamlesh Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V52P523

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 3 | Year 2017 | Article Id. IJMTT-V52P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P523

Performance Analysis of Three Stage Tandem Queues

Sreekanth. K, Kamlesh Kumar

Citation :

Sreekanth. K, Kamlesh Kumar, "Performance Analysis of Three Stage Tandem Queues," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 3, pp. 171-176, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P523

Abstract

This paper deals with the three stage tandem queues and performance analysis is rendered through analytic approach. After constructing the system governing equations and using the Burke's theorem, we determine the steady-state probabilities and various performance measures of the three stage tandem queueing system.

Keywords

Tandem Queue, Burkes Theorem and Performance Analysis.

References

[1] Azadeh, A., Mohammad Ebrahima, R., Eivazy, H. : Parameter optimization of tandem queue systems with finite intermediate buffers via fuzzy simulation, Performance Evaluation, 67(2010) 353-360.
[2] Baumann, H. and Sandmann, W. : Multi- server tandem queue with Markovian arrival process, phase-type service times, and finite buffers, European Journal of Operational Re- search, 256(2017) 187-195.
[3] Bouhchouch, A., Frein, Y., Dallery, Y. : Per- formance evaluation of closed tandem queueing networks with finite buffers, Performance Eval- uation, 26(1996) 115-132.
[4] Burke, P. J. : The output of a queueing system , Operations Research, 4(1956) 699-704.
[5] Chang, K, -H. and Chen, W, -F. : Admission control policies for two-stage tandem queues with no waiting spaces, Computers and Oper- ations Research, 30(2003) 589-601.
[6] Do, T. V. : Aclosed-form solution for a toll booth tandem queue with two heterogeneous servers and exponential service times, European Journal of Operational Research, 247(2015) 672- 675.
[7] He, Q, -M. and Chao, X. : A tollbooth tandem queue with heterogeneous servers, European Journal of Operational Research, 236(2014) 177- 189.
[8] Hunt, G. C. : Sequential arrays of waiting lines, Operations Research, 4(1956) 674-683.
[9] Kim, C., Dudin, A., Dudina, O., Dudin, S. : Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution, European Journal of Operational Research, 235(2014) 170-179.
[10] Kim, C. S., Park, S. H., Dudin, A., Kli- menok, V., Tsarenkov, G. : Investigaton of the BMAP=G=1 ! F=PH=1=M tandem queue with retrials and losses Appl. Math. Modell, 34(2010) 2926-2940.
[11] Li, Y., Cai, X., Tu, F., Shao, X. : Optimiza- tion of tandem queue systems with finite buffers, Computers and Operations Research, 31(2004) 963-984.
[12] Mohammad, H., Yarmand, Douglas, G., Down : Server allocation for zero buffer tandem queues, European Journal of Operational Re- search, 230(2013) 596-603.
[13] Song, X. and Mehmet Ali, M. : A perfor- mance analysis of discrete-time tandem queues with Markovian sources, Performance Evalua- tion, 66(2009) 524-543.
[14] Tsiotras, G. D. : Closed form expected queueing times of a tandem system with finite intermedi- ate buffer: A recursive approach, Appl. Math. Lett., 5(1992) 33-35.