International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

Sonali Thakur
Department of Mathematics & Statistics, Manipal University Jaipur, Rajasthan, 303007, India.

Anamika Jain
Department of Mathematics & Statistics, Manipal University Jaipur, Rajasthan, 303007, India.

Madhu Jain
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand-247667, India.


Received on October 08, 2020
Accepted on March 05, 2021


In this paper, we investigate the M/M/1/N single server finite capacity Markovian queueing model with operational vacation and impatient behavior of the customers. To recover the server broken down during a busy period, M-threshold recovery policy along with set-up is used. Using the inflow and outflow transition rates, the state probabilities equations for different system states are constructed. For computing the stationary queue length, matrix-geometric analytic is performed. The sensitivity analysis is carried for the validation of the system performance measures. To examine the scope of the adaptive neuro-fuzzy inference system (ANFIS), computational results are presented using matric-geometric and ANFIS approaches.

Keywords- M/M/1/N, Operational vacation, Impatient customers, Matrix-geometric method, ANFIS.


Thakur, S., Jain, A., & Jain, M. (2021). ANFIS and Cost Optimization for Markovian Queue with Operational Vacation. International Journal of Mathematical, Engineering and Management Sciences, 6(3), 894-910.

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


The authors would like to express their sincere thanks to the editor and anonymous reviewers for their constructive comments and valuable suggestions.


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