M/M/1/WV Interdependent queueing model with controllable arrival rates, service rates with inspection, delayed repaired times and feedback

G. Rani; R. Radhika

doi:https://doi.org/10.14445/22315373/IJMTT-V66I1P523

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P523

M/M/1/WV Interdependent queueing model with controllable arrival rates, service rates with inspection, delayed repaired times and feedback

G. Rani, R. Radhika

Citation :

G. Rani, R. Radhika, "M/M/1/WV Interdependent queueing model with controllable arrival rates, service rates with inspection, delayed repaired times and feedback," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 188-199, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P523

Abstract

In this paper M/M/1/WV interdependent queueing model with controllable arrival rates, service rates with inspection delayed repair times and feedback is considered. For this markov model is developed to explore the performance analysis of a state interdependent working vacation queuing model with feedback. The server is subjected to breakdown randomly by providing services. When a breakdown occurs , the server is immediately sent to repair station where the repairmen takes a setup time before starting the repair. The failed server is inspected by the repairman and is there is minor problem the server is repaired and is sent back to the service station with probability q. if some major faults is diagnosed during inspection. The server requires second phase of the repair with probability p. The matrix geometric method is applied to obtained the system characteristics, queue size distributed and other performance indices for varying arrival rates when the arrival and services processes are interdependent. The analytical results are numerically illustrated and the effect of the nodal parameters on the system characteristics are studied and relevant conclusion is presented.

Keywords

Single server markovian queueing model, finite capacity working vacation, discouragement, delayed repair, controllable arrival rates, feedback.

References

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