
36 Simulation Technologies in Networking and Communications
the real critical point: second order
= 0.1435 versus rst order
= 0.1667. Paradoxically, the
rst-order approximation gives an upper bound on
for small network loads when the probability
of message generation λ < 0.8λ
c
, while the second-order approximation provides a lower bound on
for all λ.
The real behavior of λ
act
differs dramatically from both rst-order and second-order predictions
once λ approaches the critical region (λ > 0.85λ
c
) (see Figure 2.4). Evidently, this fact is due to the
emergence of a long-range order, which is not reected in both approximate t ...