Question

Assuming input rate is fixed, if the capacity rate of the bottleneck is doubled in a process, the output rate (ie throughput rate) will be doubled. Explain with clear justification

Answer 1

To understand this logic, let's first study about Little's Law. This law tells us about the relationship existing between the flow inventory capacity, the flow rate and the flowtime of the. To understand deeply taking with an example, Little's Law states that the throughput rate or the or the average number of customers in any stable system (output) L would be equal to the average effective arrival rate of the customer (Input) λ, multiplied by the average time a customer spends (Capacity), W.

Expressing algebraically, This law would appear like this: L = λ W

L represents the output result or  average number of customers result from the system.

λ refers to the input provided or the customers’ arrival rate

W represents the average amount of time spent or the capacity of the business.

Thus, while calculating L, the average number of people at a business would make the formula look like this: λ W = L

Question: Imagine 10 customers are arriving at your cafe and have the capacity to stick around for like half an hour which 0.5 hour. Thus, calculating the average number of person at any given point of them you would have:

Input rate x Capacity rate = Output rate

10 x 0.5 = 5

5 is your average no. of people at any given point.

Assuming what question said, if the input rate is fixed (10 customers are arriving at your cafe), capacity rate is doubled (staying for 1 hour in your cafe) the output rate will double as

Input rate x Capacity rate = Output rate

10 x 1 = 10 customers now would remain at any point of time.

Which shows the output doubled if no change in input is seen but double is seen for the capacity rate!