The simulation model described in part 1 is a detailed model, which has the capability to measure the response time at every resource in the model. Also this model can find out the least response time value and the highest response time value for a request. Analytic model is a simple mathematic formula based which is not suitable in all the scenarios where a detailed level of average response time prediction is required.

How Analytic model Measures performance
Analytic model requires a set of input workload parameters to calculate the performance. Following is the formula to calculate the average response time of requests in a queue model.

T= S/ (1 - λS)
* Where T is the average response time
* S is the average time spent by a request in a resource
* Λ is the average arrival rate of the requests over a period of a monitoring time

Let us revisit the inputs used in Part 1. We use the same values here, if you are able to guess at this point why the same input values are being used you can skip the last paragraph of this article.
There are three requests have been send to a resource and their responses are measured as 3, 4 and 5 seconds. The resource is being monitored for 120 seconds.

In this case S = (3+4+5)/3 = 4
* Λ = 3/120 = 0.025 (arrival rate per unit time)
* T = S/ (1-λS)/3 = 4/ (1-0.025*4) = 4.4444

Analytic model is not very accurate, it can't capture all the system behaviors, efficient than simulation model in terms of fast performance analysis and very flexible.

Now we think about our last paragraph, though the simulation models are widely used for the accuracy of measurement the in valid inputs or not validated data can lead to erroneous results which ultimately spoil the purpose of the simulation model, most of the performance analysts are intended to use analytic model to compare the results of simulation model and analytic model. It is time for you to compare our results, using simulation model the result obtained is 4 seconds and the results of the analytic model is 4.444 seconds which is more or less equal to the first one.

The first two part of this series covers the basic modeling techniques and the remaining parts would be unfolding various metrics, theories, laws used in performance engineering. Also a detailed case study based analysis of a queue model and Java applications performance issues, and performance improvement techniques would be a part of this series.

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