An analytical approach of Markov modulated Poisson input with feedback queue and repeated service under N-policy with setup time

ABSTRACT

In this paper, we analyze an $MMPP/\left(\begin{array}{c}{G}_1\\ G_2\end{array}\right)/1$ queue with general server setup time under $N$-policy based on the case that the arrival rates vary according to the server’s status and a customer can repeat the same type of service. After the completion of service, the customer can also repeat the service as a feedback if he/she is not satisfied with his/her service. The steady-state analysis of the system has been carried out using the supplementary variable technique. Further, the expected busy period has been also derived. Finally, numerical and graphical results are included to illustrate the impact of parameters on the behavior of the model.

KEYWORDS:

• Feedback queue
• N-policy
• repeated service
• setup time

Acknowledgements

The authors wish to thank the editor and anonymous referees for their valuable comments and suggestions which led to the paper in the current form.

Disclosure statement

No potential conflict of interest was reported by the authors.