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Response Time Theory
The Response Time model is a simple way of calculating the overall Queue Length and Queuing Time for a given system for a given set of workload conditions. The Response time Model is generally used for back of the envelope calculations and to get a sense of direction.
We don’t recommend using Response Time models to make investment or major architectural design decisions. For more detailed performance modelling when validating architectural decisions or investment decisions we would recommend investing in building thorough Queuing Theory models. Queuing Theory is slightly more complex, requires a bit more effort but can have significantly more payoff especially with regards to the increase of accuracy when compared to Response Time Theory models.
To be able to use the Response Time model at minimum you would need to know two of the three variables mentioned below:
- Uavg – Average System Utilization
- X – System Throughput
- St – Service Time
M is always assumed to be known since it’s the number of CPU’s (also called Servers when referring to performance models) within the system. This is a design assumption and is assumed to be a known quantity.
- M – Number of Servers
Let’s take a look at all of the equations that we would use for Response Time Theory:
- Uavg = [ X * St ] / M …………….. [ Uavg = Average Utilization, X = Throughput, St = Service Time, M = Number of Servers ]
- Rt = St / [ 1 – Uavg * M ]……….. [ Rt = CPU Response Time, Uavg = Average Utilization, St = Service Time, M = Number of Servers ]
- Rt = Qt + St ……………………….. [St = Service Time, Rt = Response Time, Qt = Queuing Time ]
- Qt = Rt – St……………………… [ Rt = CPU Response Time, Qt = Queuing Time, St = Service Time ]
- Q = X * Qt ………………………….. [ Q = Queue Length, Qt = Queuing Time, St = Service Time ]
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Modelling Solution: VisualizeIT offers access to a bunch of Analytical Models, Statistical Models and Simulation Models. Access to all the Analytical (Mathematical) models is free. We recommend you try out the Analytical models at VisualizeIT which are free to use and drop us a note with your suggestions, input and comments. You can access the VisualizeIT website here and the VisualizeIT modelling solution here –VisualizeIT.