Relationship between Metrics

Things to note : Queuing Theory basics

1. The utilization of a service center is dependent on the Arrival rate.
2. The Service Demand remains constant irrespective of the load (for Load Independent devices).
3. Throughput increases with the Utilization.
4. Queues will be formed even when the utilization is less than 100% & its also possible that there can be no queues during 100% utilization too. Hence there is no relationship between the Utilization & Queue length.
5.The response time does not depend on the Utilization. It depends on the Queue length, hence the arrival pattern.
6. The maximum CPU utilization that can be achieved can be calculated using the formula Queue length / Queue Length + 1.
(i.e) For a four CPU m/c maximum utilization that can be achieved = 4/5 = 80%

Importance of Little's Law

Little's law is quite simple and intuitively appealing.

The law states that the average number of customers in a system (over some time interval), N, is equal to their average arrival rate, X, multiplied by their average time in the system, R.

N = X . R (or) for easy remembrance use L = A . W

This law is very important to check whether the load testing tool is not a bottleneck.
For Example, in a shop , if there are always 2 customers available at the counter queue , wherein the customers are entering the shop at the rate of 4 per second , then time taken for the customers to leave from the shop can be calculated as

N = X. R

R = 2/4 = 0.5 seconds


A Simple example of how to use this law to know how many virtual users licenses are required:

Web system that has peak user load per hour = 2000 users
Expected Response time per transaction = 4 seconds
The peak page hits/sec = 80 hits/sec

For carrying out Performance tests for the above web system, we need to calculate how many number of Virtual user licenses we need to purchase.

N = X . R
N = 80 . 4 = 320

Therefore 320 virtual user licenses are enough to carry out the Load Test.

Kendall's Notation

In Queueing Theory , Kendall's Notation is used to describe or classify the queuing models.

A / B / C / ( D / E / F )

A - It represents the arrival pattern of the requests to the system.

B - It represents the servicing pattern the system.

C - It represents the total number of servers in the system.

D -It represents the total number of requests that can be queued in the system.

E -It represents the calling source (i.e) the customer base

F -It represents the service discipline of how the job that gets served by the system.

Example :

1. M/M/1/20/30/FIFO = markovian arrival rate , markovian service time , 1 server queuing model , maximum queue length as 20 , user base as 30 , service discipline as First In First Out (FIFO).