Little's Law on Performance Test

Little's Law, as a part of Queuing theory, which was introduced to me by Wilson Mar about 2 years ago. We can make use of it to help performance test planning and modeling.

I also would like to usually calculate the arrival rate of system :

L = λW
λ = L/W

Where,
W = Average response time + Think time
L = Virtual Users we simulate in load generation tool

After calculating the arrival rate λ , I will compare arrival rate λ with Throughput X to see if the system can catch up the incoming load, if not, then start tuning it!

One example:

W =(0.352 + 0); -- which means no think time for test
L = 8;

then,
λ = L/W = 8/(0.352 + 0) = 22.73

Meanwhile, get Throughput measured by load generation tool
Throughput = 22
Not that bad currently :)

Some Update after several years I met with such an elegant equation, following results are what i have worked with my perf team to prove the Little's law:

Little's Law for Finding Response Time: 

MeanResponseTime(AVG) = MeanNumberInSystem(VUs) / MeanThroughput(TPS)

Assumptions:

• Stable system, in the long terms
• No Obvious System Bottlenecks
• Similar Actions in the system

Test And Measurement -- Get XXX Pages: 

VUs	AVG(ms)	90%(ms)	TPS	Calculated VUs using Little's Law
1	58	72	16.98	0.99
12	74	108	161.63	11.96
25	83	121	297.99	24.73
50	138	209	360.67	49.77
75	197	349	379.59	74.78
100	261	492	381.21	99.50
125	326	636	381.80	124.71

Predicting and Modeling: 

• Find relations between VU and Avg Response Time By Curve fitting:

y = 0.0067x2 + 1.3698x + 53.613

• Response Time Validation: 

Vus	Predict Result	Test Result
35	109.7	101
65	170.9	172
90	231.1	238
110	285.3	290

• Find relations between VU and Throughput By Curve fitting:

y = 82.39ln(x) + 7.8124

• Throughput Validation: 

Vus	Predict Result	Test Result
35	300.7	342.61
65	351.7	376.35
90	378.5	374.49
110	395	377.74