The research paper explores a queuing model where arrival and service rates are represented using fuzzy numbers, specifically hexagonal fuzzy numbers, Arrival rates, indicating the customers arrive, follows a Poisson distribution, while service rates, showing quickly customers are served, follows an Erlang-K distributin. Fuzzy queues offer a more realistic depiction compared to discrete queues, as they can handle uncertainties in real-world sytems. The study evaluates queue performance using various metrices, interpreted with hexagonal fuzzy numbers, to capture the inherent uncertainity and imprecision. Overall, the research contributes to queuing theory by using fuzzy logic to address uncertanities in queuing sytems.