Real Time Systems Design And Analysis

Chapter 7.3.3 - Some Buffer-Size Calculations

7.3.3   Some Buffer-Size Calculations

The M/M/1 queue can also be used for buffer-size calculations by portraying
the “customers” as data being placed in a buffer. The “service” time is the time
needed to pick up the data by some consumer task. Here the basic properties of
M/M/1 queues are used to calculate the average buffer size needed to hold the
data using Equation 7.11, and the average time a datum spends in the system (its
age using Equation 7.13). For example, a process produces data with interarrival
times given by the exponential distribution 4e−4t, and is consumed by a process
at a rate given by the exponential distribution 5e−4t. To calculate the average
number of data items in the buffer, use Equation 7.11:

 

A probability distribution for the random variable determining the age of the data
can be found by using Equation 7.13:

 

 

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