Bernoulli Vacation Policy for a Bulk Retrial Queue with Fuzzy Parameters

In this paper, we investigate the fuzzy logic based system characteristics of M/G/1 retrial queuing system with Bernoulli vacation schedule. The service time and vacation time are assumed to be generally distributed. It is found in many practical situations that the queuing models with fuzzy parameters are much more realistic than the classical crisp parameters based queuing models. We have chosen group arrival rate, service rate and vacation rate to be fuzzy parameters. The objective of this study in this paper is to transform M/G/1 retrial fuzzy queue with Bernoulli vacation schedule to a family of conventional crisp queues by employing -cut approach based on Zadeh’s extension principle. We formulate a pair of parametric non-linear programs (PNLPs) to describe the family of crisp queues with a vacationing server. To illustrate the validity of the proposed approach, the numerical examples are facilitated for different service time and vacation time distributions.