Markovian queueing model under Bernoulli vacation and servers’ malfunctioning: Metaheuristic optimization technique

Abstract

Bernoulli vacation and effect of malfunctioning are analyzed for Markovian queueing single server model. Server is allowed to opt for the vacation with probability or can serve the upcoming failed unit with probability under the Bernoulli vacation. Meanwhile during busy state servers can face malfunctioning and to overcome this situation a quick repair is imposed to sustain the server in the working state. Performance measures are estimated by framing the Chapman-Kolmogorov equation and the further impact of the model on average expected queue length of units, servers’ reliability and servers’ availability factors are analyzed through R-K fourth order method. Moreover, the cost function is formulated, and the direct search method is used to study the cost variation for the designed model. To explore the economic benefits of the model, the minimum cost is optimized by the meta-heuristic soft computing optimization techniques SCA, TLBO, PSO and GSA. A comparative analysis examines the best approach among the described optimization techniques. Different techniques are used to get the best results and better allocation of resources to achieve efficient costs.