The immigration department receives around 10000 immigration

The immigration department receives around 10,000 immigration applications each year. On average, the processing of an application begins 30 calendar days after it was received. Furthermore, the average processing time for each application is 5 calendar days. Using Little’s Law, estimate the average number of applications that are waiting or are being processed.

Solution

Little\'s Law can be written as

The long-term average number of customers in a stable system L is equal to the long-term average effective arrival rate, , multiplied by the (Palm)average time a customer spends in the system, W; or expressed algebraically: L = W.

Here the rate of application arrival is 10,000 per year. Thus, = 10,000

Also, average time spent on an application = 30 + 5 days = 35/365 years = 0.0959 years

Thus, L = W. = 10,000 * 0.0959 = 958.9 appllications

Answer: the average number of applications that are waiting or are being processed are 958.9 ; so approximately 959.