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Real Time Systems Design And Analysis

Chapter 7.3 - Application Of Queuing Theory

7.3   APPLICATION OF QUEUING THEORY

The classic queuing problem involves one or more producer processes called
servers and one or more consumer processes called customers. Queuing theory
has been applied to the analysis of real-time systems this way since the mid-
1960s (e.g., [Martin67]), yet it seems to have been forgotten in modern realtime
literature.

A standard notation for a queuing system is a three-tuple (e.g., M/M/1). The
first component describes the probability distribution for the time between arrivals
of customers, the second is the probability distribution of time needed to service
each customer, and the third is the number of servers. The letter M is customarily
used to represent exponentially distributed interarrival or service times.

In a real-time system, the first component of the tuple might be the arrival
time probability distribution for a certain interrupt request. The second component
would be the time needed to service that interrupt’s request,. The third
component would be unity for a single processing system and >1 for multiprocessing
systems. Known properties of this queuing model can be used to predict
service times for tasks in a real-time system.

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