In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual nodes to be determined. Mitrani notes "if the network is stable, the traffic equations are valid and can be solved."[1]
In a Jackson network, the mean arrival rate
λi
\gammai
λi=\gammai+
m | |
\sum | |
j=1 |
pjiλj.
This can be written in matrix form as
λ(I-P)=\gamma,
and there is a unique solution of unknowns
λi
\gammai
In a Gordon–Newell network there are no external arrivals, so the traffic equations take the form (for i = 1, 2, ..., m)
λi=
m | |
\sum | |
j=1 |
pjiλj.
. Harrison . Peter G. . Peter G. Harrison . Patel . Naresh M. . Performance Modelling of Communication Networks and Computer Architectures . Addison-Wesley . 1992 . 0-201-54419-9 . registration .