Throughput or X – Throughput is defined as the rate of completions for a given system. It’s also defined as the total completions per unit time e.g. Transactions/Sec.

The equation for throughput is defined as:

  • X = C / T …………………[C = Completions in time T, T = Total time of observation]

Example: Let’s assume we observe a system for a period of 180 seconds (3 minutes) during which there are 5 customers who successfully exit the system. The system can be described as:

  • Completions or C = 5
  • Time Period of Observation or T = 180s
  • Throughput or X = C / T = 5 / 180 = 0.03 Transactions/Sec

There is also one other interesting relationship between Maximum Throughput of a system and the Average Value of Service Time. It’s denoted by the following equation:

  • Xmax <= 1 / Stavg …[Xmax= Max Value of Throughput possible, Stavg = Avg Value of Service Time ]

The above equation is one of the most fundamental and important equations with regards to system performance, also called the bottleneck equation. The bottleneck equation basically states that the Maximum Throughput is inversely proportional to the Average (System/Component) Service Time. Using the above equation you can key in the Average Service Time for your bottleneck resource (resource or component within the system that has the highest Service Time) within your system and obtain the maximum possible throughput the system can achieve.

Example: Let’s assume for the same system above the poorest performing component has a Service Time of 3s i.e. This is the component within the system with the largest Service Time.

Thus Xmax <= 1/3s = 0.33 Transactions/Sec. This particular system can never achieve a throughput more than 0.33 Transactions/Sec as long as the largest Service time within the system is 3s.

The above equation comes in very handy when validating performance testing results. The bottleneck equation is also very frequently used to perform back of the envelope calculations for bottleneck and throughput analysis.

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