Problem of queue management has been a great barrier to the financial institutions. Another way of measuring efficiency in banking industries is how fast the service of saving and withdraw is been rendered. Imagine customers that spend the whole day in the banking hall for one service or the other, due to poor service delivery and long stay on the queue will not hesitate to change his bank. Data was collected by direct observation in two banks, one old generation bank and one new generation bank, queue model and other statistical tools were used to analyze the data. Result of the analysis shows that Guaranty Trust Bank is more efficient than First Bank in that the later has a prolonged service time attributed to the preference of it by a pool of customers for many reasons.