Little's Law

In continuation with my earlier post “Decoding concepts of Performance Engineering” I will try to derive Little's law in this post for better understanding

Consider a steady state system which has only one user and sends the requests at consistant intervals and response time of the requests were observed to be 1 sec.

No of Customers in the System = 1
Response Time = 1 sec (Service Demand)
So Maximum Throughput = (1/Service Demand) = 1 Request/Sec (Based on Utilization Law)

It implies average number of customers required being in the system to achieve 1 request/ sec with an average response time is 1 sec is 1 user

Similarly assume if the response time of the system is 0.1 Sec

Response time = 0.1
Max Throughput = 1/Service Demand = 10 requests/Sec

So One single user can simulate max of 10 requests/sec with a average response time of 0.1 sec

Little's Law

Average Number of Customers = Response time * Throughput

Little’s Law states that average number of customers in a system is equal to product of throughput and response time.

Decoding concepts of Performance Engineering

In most of the situations we have a tendency of using the formula’s without understanding the concepts behind it, because of which we may not be able to apply the laws correctly where it is required. 

The following example will help in understanding the some of the performance rules

A system was subjected to 10 requests in a span of 2 min and got the responses for all requests during this period and Utilization of the system during the time frame was observed to be at 50%.

Request Arrival rate for that system is  10/2=5 requests/Min

Throughput = 10/2 = 5 Responses/Min

in the above example, system utilized 50% of its resources for serving 5 requests. For Each request, it consumed 50%/5 of system resources. This value is called service demand of that resource

From the above example the formula for service demand can be derived as below
Service Demand  =Utilization/Throughput. 
similarly Utilization = Throughput * Service Demand - This is also called utilization Law

The utilization of a resource is equal to the product of the throughput of that resource and the average service demand at that resource.