Fuzziness is a new type of unavoidable circumstance. Ambiguity is depicted by the fuzzy set theory. Intuitionistic Fuzzy queuing model with flexible service policy is being investigated in this study. A parametric programming technique is designed to find the membership and non-membership functions of queue length and sojourn time in steady state, in which the arrival rate and service rate are being Intuitionistic pentagon fuzzy numbers. Based on  , -cuts and Zadeh’s extension principle, the intuitionistic fuzzy queues are evolved into family of crisp queues. The model’s potency is calculated for various possibilities of  -cuts and  - cuts.