Real Time Systems Design And Analysis

Chapter 7.3.6 - Little’s Law

7.3.6   Little’s Law

An important result in queuing theory, Little’s Law, has some application in
real-time system performance prediction. Little’s Law, which appeared in 1961,
states that the average number of customers in a queuing system, Nav, is equal
to the average arrival rate of the customers to that system, rav, times the average
time spent in that system, tav [Kleinrock75]:

 

If n servers are present, then

 

where ri,av is the average arrival rate for customers to server i, and ti,av is the
average service time for server i.

Viewing each process as a server and interrupt arrivals as customers, Little’s
Law is Equation 1.2 for CPU utilization with ei = ti,av and 1/pi = ri,av. For
example, a system is known to have periodic interrupts occurring at 10, 20, and
100 milliseconds and a sporadic interrupt that is known to occur on average
every 1 second. The average processing time for these interrupts is 3, 8, 25, and
30 milliseconds. Then by Little’s Law the average number of customers in the
queue is

 

This result is the same one obtained by using Equation 1.2 for CPU utilization.

 

UNLIMITED FREE
ACCESS
TO THE WORLD'S BEST IDEAS

SUBMIT
Already a GlobalSpec user? Log in.

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.

Customize Your GlobalSpec Experience

Category: PCMCIA Memory Cards
Finish!
Privacy Policy

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.