# How to calculate average arrival rate from arrival rate in queuing theory

During the busy hours of the day 8.00am to 4.00pm data was collected from an ATM facility of a bank for a period of ten (10) working days.The table below shows a summary of frequencies for the inter arrival time for an M/M/1 queuing model.

X: 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11
Y:  94  89  94  23  15  10   4   5   2   0     2


At X=0-1 implies that 94 times, customers arrived at an inter arrival time between 0 to 1 minute. The arrival rate 1/lambda is equal to 3.0832,while the average arrival rate is given to be equal to 19.46 per hour. Pls explain how they got these values for the arrival rate and the average arrival rate respectively?