Real Time Systems Design And Analysis

Chapter 7.3.7 - Erlang’s Formula

7.3.7   Erlang’s Formula

Another useful result of queuing theory is Erlang’s Loss Formula. Suppose there
are m servers (or processes) and arriving customers (interrupts). Each newly
arriving interrupt is serviced by a process, unless all servers are busy (a potential
time-overloaded condition). In this, case the customer (interrupt) is lost. If it
is assumed that the average service (process) time is μ and the average arrival
time (interrupt rate) is λ, then the fraction of time that all servers are busy (a
time-overloaded condition) is given by

 

This result dates back to 1917 [Kleinrock75].

Applying Erlang’s Formula to the previous example gives m = 4, λ = 380,
and μ = 16.5; then

 

This means there is a potential for time overloading 83.4% of the time. Based
on the average time-loading figure of 98% and the rate-monotonic theorem, this
seems reasonable.

 

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