Utilization or U – Utilization of any system is defined as the Ratio of Busy Time to Total Time of Observation. Utilization is a ratio that generally refers to how busy or free the resources within a given system are. Utilization can also be used to refer to how busy or free are components within a given system instead of the system as a whole.

 

The following equations are used to describe Utilization:

  • U = Bt / T   …………………………. [ Bt = Busy Time, T = Total Observed Time Interval ]

The above equation describes utilization as the ratio of Busy Time to Total Observed Time.

Example: Let’s assume we are viewing a system for a period of 180 seconds during which it remains busy for 100 seconds.

  • The Utilization of the system is calculated as follows:
  • We know : U = Bt / T   …………………………. [ Bt = Busy Time, T = Total Observed Time Interval ]
  • Utilization (U) = 100/180 = 0.55

The Utilization thus for this system is 0.55.

In addition to the equation above Utilization can be described as:

  • U = X * St   …………………………. [ X = Throughput, St = Service Time ]

The above equation describes Utilization as the product of Throughput and Service Time. As mentioned earlier the above equation can be applied to either the system as a whole or at a resource level within a given system.

Example: Let’s assume we are viewing a system for a period of 180 seconds during which it remains busy for 100 seconds. The Service Time for a transaction is 2s. The throughput of the system is calculated as follows:

  • U = X * St
  • X = U / St = 0.55 / 2 = 0.275 Transactions/Sec

The equation provided below is very similar to the previous equation but with one subtle difference i.e. the addition of Average Number of Servers (of CPU’s in our case).

  • Uavg =  [ X * St ] / M …………….. [ Uavg = Average Utilization, X = Throughput, St = Service Time, M = Average Number of Servers  ]

On a system with multiple servers (CPU’s) the average utilization is obtained by dividing the overall system utilization by the total number of servers (CPU’s) present.

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