A limited source Queuing model having single server is considering here to discuss its various parameters. The number of arriving customers in this model is fixed. Since the arriving customers are already fixed and system is busy in serving the customers one by one, the arrival rate of next coming customer gets reduced. This reduces the further congestion. The service discipline in the model is general discipline. As the arriving customers in the system are limited, binomial distribution is used to deal with the arrival rate of customers and service rate of server. Uniform distribution is applied to the inter-arrival time and service time. By using the binomial distribution, formula is derived to find the expected waiting time of a customer in the queue. The derived formula and littles formula are then used together to study the various parameters of the Queuing model. Finally comparing the results calculated by the newly derived formulae and existing formulae.