Fuzzy waiting line models venture diversified footprints galvanizing on uncertain realm of the world. This study explains a fuzzy queuing model which signifiesthe arrival distribution????????asPoisson and the service time????????is arbitrarily distributed, FCFS discipline. The synchronization of this paper is to extract the membership functions of the execution proportions like the average and variance of queue length for two fuzzy queues based on Randomness principle and the efficacy of different parameters of the system performance measuresis fathomed by numerical exploration.