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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P523

Steady State Analysis of M/M/1 Retrial Queueing Network with Catastrophes


S. Shanmugasundaram, S. Vanitha
Abstract

In this paper we analyze the M/M/1 retrial queueing network with catastrophes. Here we derive the steady state probabilities, the stationary probabilities of the giving network. The expectation number of customers in the nodes 1, 2 and 3 are derived. The particular cases are also derived. The numerical examples are given to test the correctness of the result.

Keywords
Average queue length, Catastrophes, Steady state probability, Steady state solution
References

[1] A. K. Erlang, The theory of probabilities and telephone conversations, NytJindsskriff Math. B 20 (1909) 33-39.
[2] B. Krishna Kumar, A. Krishnamoorthy, S. PavaiMadheswari, S. SadiqBasha, Transient analysis of a single server queue with catastrophes, failures and repairs, Queueing Systems. 56 (2007) 133-141.
[3] B. Krishna Kumar, D. Arivudainambi, Transient solution of an M/M/1queue with catastrophes, Computers and Mathematics with Applications. 40 (2000) 1233-1240.
[4] E. Gelenbe, Product form queueing networks with positive and negative customers, Journal of Applied Probability. 28(3) (1991) 656-663.
[5] G. I. Falin, A survey of retrial queues, Queueing system. 7 (1990) 127-167.
[6] J. R. Jackson, Job shop-like queueing systems, Management Science. 10 (1963)131-142.
[7] J. R. Jackson, Networks of waiting lines, Operation Research. 5(4) (1957) 518-521.
[8] J. W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls”, Philips Telecommunication Review. 18 (1957) 49-100.
[9] L. Kosten, On the influence of repeated calls in the theory of probabilities of blocking, De Ingenieur. (1947) 591-25.
[10] N. K. Jain, and R. Kumar, M/G/1 Queue with Catastrophes, Indian Journal of Mathematics and Mathematical Sciences. 1(1) (2005) 45-50.
[11] Rakesh kumar, Sumeet Kumar Sharma, A Multi- server Markovian Feedback Queue with Balking Reneging and Retention of Reneged customers, Advanced Modeling and Optimization. 16(2) (2014) 395-405.
[12] S. Shanmugasundaram, S. Chitra, “Time dependent solution of M/M/1 retrial queue and feedback on nonretrial customers with catastrophes”, Global Journal of Pure and Applied Mathematics. 11(1) (2015).
[13] S. Shanmugasundaram, S. Vanitha, A M/M/1 queueing network with classical retrial policy (2020).
[14] S. Sophia, Transient analysis of a single server queue with chain sequence rates subject to catastrophes, failures and repairs, International Journal of Pure and Applied Mathematics. 119(15) (2018) 1969-1988.
[15] V. G. Kulkarni, On queueing systems with retrials, J.Appl.Prob.20 (1983) 380-389.
[16] V. M. Chandrasekaran, M. C. Saravanarajan, Transient and Reliability analysis of M/M/1 feedback queue subject to catastrophes, server failures and repairs. 77(5) (2012) 605-625.
[17] V. Thangaraj, S. Vanitha , On the analysis of M/M/1 feedback queue with Catastrophes using continued fractions, International Journal of Pure and Applied Mathematics. 53(1) (2009) 133-151.
[18] X. Chao, A queuing network model with catastrophes and product form Solution, Operation Research Letters. 18 (1995) 75-79.

Citation :

S. Shanmugasundaram, S. Vanitha, "Steady State Analysis of M/M/1 Retrial Queueing Network with Catastrophes," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 170-181, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P523

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