Real Time Systems Design And Analysis

Chapter 7.4.2 - Variable Buffer-Size Calculation

7.4.2   Variable Buffer-Size Calculation

It is often not accurate to assume that burst periods are fixed; they will frequently
be variable. Suppose that a process produces data at a rate given by the realvalued
function p(t). Also suppose that another task consumes or uses the data
produced by the first task at a rate determined by the real-valued function c(t).
The data are produced during a burst period T = t1t2, where t1> t2 represent
the start and finish times of the burst. Then the buffer size needed at time t2 can
be expressed as

 

Note that when p(t) and c(t) are constant, Equation 7.20 becomes Equation 7.19
(see Exercise 7.9). For example, a task produces data at a rate (in bytes per
second) that is determined by the function:

 

with t representing the burst period. The data are consumed by a task at a rate
determined by the function:

 

If the burst period is known to be 1.6 seconds, what is the necessary buffer size?
Using Equation 7.20 yields,

 

If the burst period is determined by the real-valued function u(t), then for a burst
starting at time t1 and ending at t2 the necessary buffer size is

 

In the previous example, if the burst starts at a time determined by the Gaussian
distribution

 

at time t = 0, then it is will end at time u(0) = 0.053991. Recalculation of the
buffer size now yields

 

 

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