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Evaluation of Network-on-Chip Architectures
the ON or the OFF state should be selected according to a distribution that
exhibits long-range dependence. The Pareto distribution [F(x) = 1 – x –α , with
1  < α < 2] is found to fit well to this kind of traffic. The duration of each
ON–OFF period is assumed to be a random variable T i (i є {ON, OFF}). The
degree of self-similarity is expressed using only a single parameter, namely,
Hurst parameter (HP). The value α at ON slot is related to HP as given below:
3 − α
HP =
ON , where 0.5 < HP <1
(4.5)
2
If the network utilization parameter is given by ρ, the α OFF parameter is
obtained as
(1− ρ α
) ON
α OFF =
(4.6)
(1− ρ α ON − ρ α ON − 1)
)
(
For a random variable U with uniform distribution on [0, 1], the following
transformation can be used to generate the random number P of time slots
during active and idle periods:
⎡
−1
⎤
P i = round αi i ∈ {ON, OFF}
(4.7)
⎣ ⎢ U ⎦ ⎥
,
The active and idle periods in each iteration is calculated as
P i
T i =
(4.8)
IR
where IR is the packet injection rate within the ON slot. The pseudocode of
the algorithm for generating a self-similar traffic is shown in Figure 4.5.
Algorithm: Generation of Self-Similar Traffic
1. Set IR, HP, ρ, and time to 0.
2. Calculate α ON from HP by using (Eq. 5.5).
3. Calculate α OFF from ρ and α ON by using (Eq. 5.6)
4. While time ≤ SIMULATION_TIME do
4.1 Generate a random number U between 0 and 1.
4.2 Calculate P ON and P OFF by using (Eq. 5.7).
4.3 Calculate T ON and T OFF by using (Eq. 5.8).
4.4 For j ← 0 to P ON do
Generate packet for the destination.
4.5 time ← time + T ON + T OFF
5. Stop
Figure 4.5
Pseudocode of the algorithm for generating self-similar traffic.