Real Time Systems Design And Analysis

Chapter 7.3.4 - Response-Time Modeling

7.3.4   Response-Time Modeling

The “average” response time for a process handling an interrupt request in the
absence of other competing processes can also be computed if an M/M/1 model
is assumed. In this case use Equation 7.13 to measure the average time spent in
the system by an interrupt request (the response time). For example, a process
is based on a sporadic interrupt that occurs with an interarrival rate given by
the exponential function with mean 1/λ = 5 milliseconds. A process handles the
data in an amount of time determined by the exponential function with mean
1/μ = 3 milliseconds. The mean response time for this interrupt request is seen
from Equation 7.13 to be:

 

A probability distribution for the random variable determining the mean response
time can be found by using Equation 7.14. Omitting context switching and inter-
task interference gives

 

or

 

Note that the response time will be deleteriously affected if the interrupt rate is
greater than the mean service rate.

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