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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P507

A FM/M/1/∞ Stochastic Feedback Arrival Model With Performance Measures


S.Gayathri, G.Rani
Abstract

In this paper the FM/M/1/∞ Queueing model with feedback arrival rates and single service rate is considered. The steady state solution and system characteristics are derived for this model. The analytical results are numerically illustrated and the effect of the nodal parameters on the system characteristics are derived and relevant conclusions are presented.

Keywords
feedback arrival rates, single server with service rate, infinite capacity, system characteristics.
References

[1] Gross, Donald. Fundamentals of queueing theory, John Wiley and Sons., (2008).
[2] Kalyanaraman, R., and Renganathan, N. A single server instantaneous Bernoulli feedback queue with multiple vacation, Optimization. 37(1) (1996) 87-96.
[3] Kalyanaraman, R., and Sumathy, S. A Feedback queue with multiple servers and Batch service, International Review of Pure and Applied Mathematics. 5(1) (2009) 23-27.
[4] Lindley, D. V. The theory of queues with a single server, In Mathematical Proceedings of the Cambridge Philosophical Society. 48(2) (1952) 277-289.
[5] Medhi, J. Stochastic models in queueing theory, Elsevier. (2002).
[6] G.Rani and A.Srinivasan, M/M/c/k Interdependent Queueing Model with controllable arrival rates and feedback, IJAMAA. 7(2) (2012) 131-141
[7] Rani, G., and Srinivasan, A. M. M/1/K Interdependent Queueing Model With Controllable Arrival Rates and Feedback, In Proceedings Of The Heber International Conference On Application Of Mathematics And Statistics. (2012) 271-277.
[8] Rani, G., and Srinivasan, A. M/M/c/k Loss and delay Interdependent queueing model with controllable arrival rates, No Passing and Feedback, International Journal of Mathematical Sciences and Engineering Applications. 7(4) (2013) 403-419.
[9] Takacs, L. A single‐server queue with feedback, Bell system Technical journal. 42(2) (1963) 505-519.
[10] Thangaraj, V., and Santhakumaran, A. A queue with Markovian feedback, International journal of information and management sciences. 6(4) (1995) 35-45.
[11] Thangaraj, V., and Vanitha, S. On the analysis of M/M/1 feedback queue with catastrophes using continued fractions, International Journal of Pure and Applied Mathematics. 53(1) (2009) 131-151.

Citation :

S.Gayathri, G.Rani, "A FM/M/1/∞ Stochastic Feedback Arrival Model With Performance Measures," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 61-67, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P507

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