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Vishwadeep Khatri


Little's Law


Little's Law - is a law/theorem given by John Little which states that the average number of customers in a stable system, N, is equal to their average arrival rate, λ, multiplied by their average time in the system, T

N = λ x T

In more simplistic terms, Little's Law can be also be stated as

Items in Process (WIP or N) = Throughput (λ) x Lead Time (T)

This law is part of the Queuing Theory in Operations Research and is particularly useful in studying the length and waiting time in queues.



An application oriented question on the topic along with responses can be seen below. The best answer was provided by Priyer on 2nd January 2018.




Q 59. Little’s law is one interesting concept which has multiple applications in the business world. Enumerate some of the powerful applications of Little’s Law highlighting how and why it is an unavoidable tool in certain specific situations.  


Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.


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Little's law describes that the average time a unit of work stays in the process is equal to the ratio of Work in Progress units of work to the rate at which the unit of work is delivered out of the system (in other words Throughput)

Flow Time = Work In Progress Inventory/ Throughput of work delivered.


Applications of Little's law is powerful in the below scenarios


1) To determine the number of counters to be made available during issuing of Boarding passes , so that the rate at which boarding passes issued are more, in order to reduce the Average Wait Time at each of the queues. By decreasing the Average wait time a passenger spends in a queue, the Airport can be relatively less crowded at the boarding pass issuing centre, security checks and gate areas, thus enabling to cater to the inflow of passengers arriving for different flights at different instances of time with an unpredictable inflow rate.


2) In an Application Support life cycle model, Little's law can be applied to influence reduction of Average Turn Around Time  per Ticket by either increasing the rate at which Tickets are solved per unit of time or reducing Backlog of Tickets (Inventory on Hand).  This when studied with other metrics like number of Application support resources used for increasing throughput can give us an insight on Productivity of the Application support Team. Increasing the number of people to reduce backlog is not a good practice, but reducing backlog with the same number of people is definitely a good sign.

The real life application is the enhanced Customer Experience to their queries/requests , lesser churn and increased engagement from the Application service provide


 3) The number of toll gates on a highway is another application of Little's law to prevent queuing at Toll gates and ensure smooth flow of traffic.


 Little's law is of prime significance to maintain balance between inflow and outflow rates and helps study whether we would desire to keep the Inventory within the process at different stages to an acceptable limit , minimum or maximum. Hence it is unavoidable in cases, where Wait time in the process can result in significant business loss, brand reputation and dissatisfaction.

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Little's law came from Prof John Little. It is actually started for check average customers, equation is =>

L= A X W,

L => number of customer

A => effective average rate[long term, departure rate is identical]

W => time spent by customers 



it is a very simple tool by which data can be measured in granular level which allows deep insight of the business. As it measures the capacity of a system(Not retail outlets) the equation gets changed to :-


Work In Progress = Throughput X Lead time =>WiP = T X L [For Kanban]


For cycle time, we have to understand cycle time as well as WIP and through put properly as cycle time works per unit. So for 'x' throughput if we have 'y' cycle time and 'z' work in progress then the equation will come as :


WiP(z) = T(x) X L(y)


It is important all level of employees/management -


Investors: can identify when and what could help the business or when a business is getting profit or the potential risk associated with the business.   


Entrepreneur: They can identify the issues which is blocking the growth as we can derive data even for example on "per second" level, say how many "search" google's search engine handles per second. Or can check a dynamic range of time if they needed. 


Employees: they can identify what and why or how a business soared for a certain time, which stimulated it etc. 



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While decreasing cycle or flow time can be instrumental in improving customer service, we must be careful not to ignore the throughput (flow rate) of the system. Both measures are directly related to average inventory as defined by Little’s Law


Little’s Law defines the relationship among the three variables of flow rate (throughput), inventory and flow time (cycle time).


 I = R x T

where: I = average inventory; R = average flow rate; T = average flow time.


In any system, when one of these variables changes value, a second variable (and possibly a third) also must change value. The issue of which variables change value depends on the structure of the system. The capacity of the system determines the average flow rate for the system. For a system operating at capacity, an increase in inventory will result in a proportional increase in average flow time, with average flow rate remaining relatively constant. Obviously this is an undesirable result because the revenue from the system, which is proportional to flow rate, remains constant 

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