Response Time Theory – Tutorial I

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Response Time Theory – Tutorial I

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Introduction : Response Time Theory model is an elementary form of Queuing Theory model which ideally should be used to obtain a sense of direction with regards to system behavior. You want to avoid using Response Time Theory models to accurately forecast system performance for a given workload and make investment decisions based on the outcome.

You can learn more about Response Time Theory here – Link.scalability_graph_RT

Types Of Models : There are various ways we could classify systems i.e. open or closed, stable or unstable, etc., but for purposes of this conversation we’ll stick to classification between CPU based systems or IO based systems for purposes of simplicity when performing modelling using the Analytical models. CPU based systems are systems which is defined by the following characteristic –

  • Single or multiple Service Counters or CPU’s
  • Single Queue for the entire system

IO based systems are defined by the following characteristic –

  • Single of multiple Service Counters of IO Devices
  • Single Queue per device

Your choice of a CPU or IO model completely changes the Queuing Characteristics of the system. So be careful and select the appropriate type of system. Please note for IO model’s CPU = 1 irrespective of value entered. This assumes that you are modelling for a single IO device.

Let’s Look At An Example : Let’s review the results for the Response Time Theory model using the above inputs.

  • Throughput or X (TPS) = 10
  • Service Time (S) in Seconds = 0.2
  • Number of CPU’s (M) = 4

The resulting plots for this model are:

  • Utilization (%) v/s Throughput (TPS)
  • Queue Length (Q) v/s Throughput (TPS)
  • Response Time (Sec) v/s Throughput (TPS)

Interpreting Results : Let’s review the results for the Response Time Theory model using the above inputs.

The model computes the behavior of the system for an assumed gradual increase in Throughput (X). These resulting values are then plot on the graphs presented to you.

Utilization (%) v/s Throughput (TPS) – The resulting graph very clearly tells us that at 21 TPS you’ll be at 97% utilization. In any sphere of life when dealing with systems i.e. a bank with tellers as processors and customers lining up for services or  a fast food store with counters as processors and customers lining up for service, you avoid getting into the Zone of Non Linear Performance. Technically speaking the Zone of Non Linear Performance (ZNLP) is typically the entire region past 75% utilization. You’ll note from the graphs below that once a system has entered the Zone of Non Linear Performance the “Request Queues” begin to increase in size and the Transaction Response times increase.

Queue Length (Q) v/s Throughput (TPS) – The resulting graph tells us that at 21 TPS you are at a queue length of 35. As we’ve mentioned before, the Zone of Non Linear Performance (ZNLP) is typically the entire region past 75% utilization. As a system moves through the Zone of Non Linear Performance the “Request Queues” begin to increase in size and the Transaction Response times increases gradually.

Response Time (Sec) v/s Throughput (TPS)  – The resulting graph tells us that at 21 TPS you will see a response time of ~2 seconds. As we’ve mentioned before, the Zone of Non Linear Performance (ZNLP) is typically the entire region past 75% utilization. As a system moves through the Zone of Non Linear Performance the “Request Queues” begin to increase in size and the Transaction Response times increases gradually. When a system enters the Zone Of Non Linear Performance (ZNLP) the requests are arriving at a rate faster than the systems ability to service them as a result we start noticing an increase in response times. It’s also worth noting that when a system has high utilization levels and is within the ZNLP the service times haven’t really changed. It’s the exponential increase in Queue Time (Qt) or Waiting Time (Wt) which is responsible for the exponential increase in overall Response Times.

Analytical Modelling Solution: VisualizeIT offers access to a bunch of Analytical Models, Statistical Models and Simcropped-visualize_it_logo__transparent_090415.pngulation Models. Access to all the Analytical (Mathematical) models is free. We recommend you try out the Response Time Theory models at VisualizeIT and drop us a note with your suggestions, input and comments.

Conclusion : On any system you want to avoid getting into the Zone Of Non Linear Performance (ZNLP) i.e. > 75% Utilization. This applies not just to IT (Information Technology) systems but generally systems across the board i.e. a bank with tellers as processors and customers lining up for services or  a fast food store with counters as processors and customers lining up for service.

Response Time Theory is based on the fundamental laws of Performance (Details of which are available at this Link). Use Response Time theory to get a quick sense of direction with regards to where you are headed when designing a system. You should considering using Response Time Theory to obtain a quick sense check on the approach you are taking or have considered taking. Avoid using Response Time Theory to make fundamental design decisions. That’s where some of the more complex models come in.

 

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