Abstract
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.
Highlights
The queueing system is a part of our routine life where the customers must wait for the service facility
This paper deals with the study of a single server Markovian queueing model by considering the realistic feature of operational vacation
The situations of server breakdown and repair setup dealt in the model are studied successfully via Matrix geometric method
Summary
The queueing system is a part of our routine life where the customers must wait for the service facility. Upadhyaya and Kushwaha (2020) presented supplementary variable analysis of MX/G/1 retrial queue with impatient customers, unreliable server, modified vacation policy, delayed repair and Bernoulli feedback They used ANFIS computing approach to compare the numerical results obtained by explicit analytical formulae. 2. Model Description We consider a single server finite capacity Markovian M/M/1/N queueing system with operational vacation, impatient customer, server breakdown, and repair. Model Description We consider a single server finite capacity Markovian M/M/1/N queueing system with operational vacation, impatient customer, server breakdown, and repair This model is applicable in various fields like banking sector, telecommunication, power Supply Corporation, etc. A. Transition Rate Matrix A matrix analytic approach is employed for determining queue length distribution using the matrixgeometric method and probabilities at stationary state for bi-variate Markov Process.
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