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International Journal on Advances in Telecommunications, vol 5 no 3 & 4, year 2012, http://www.iariajournals.org/telecommunications/
IV. SYSTEM MODEL OF A MULTI-RATE OCDMA PON
WITH QOS GUARANTEES
In OCDMA networks, QoS differentiation can be realised
by the utilization of codewords with different weights. To this
end, we assume that the PON supports K = T · F serviceclasses:
F service-classes are differentiated by the data rate,
while each one of these F service-classes supports T different
QoS levels that express different values of the BER at the
receiver. We also consider that the PON assigns (L, Wt, λa, 1)
codewords to service-class t, t = 1, ..., T . Calls of these T
service-classes require the same number bf,t (f = 1, ..., F )
of codewords, while they are differentiated by the weight
Wt. The received power per bit “1” of service-class f, t is
denoted as I f,t
unit , while the received power that corresponds
to a call of service-class f, t is at most Iact f,t = bf,t · I f,t
unit .
The traffic parameters of service-class f, t are denoted as
(λf,t, µ −1
1,f,t , µ−1
2,f,t , vf,t). To simplify the presentation of these
parameters we use one notation for the service-classes; we
denote that the parameters of service-class k (k = 1, . . . , T ·F )
are I k unit
= If,t
unit , Ik act = I f,t
act, bk = bf,t, λk = λf,t,
µ −1
ik = µ−1
i,f,t and vk = vf,t.
In order to determine the LBP of service-class k, we use
the following relation, which is based on (6):
lbk(n 1 k )=P
1−lbk(n 1 k )=P
IN
Imax
IN
Imax
·F
>1−T
x=1
·F
≤1−T
x=1
n1 bx·I
x
x
unit
Imax
n 1 k
bx·I x
unit
Imax
x,k
Pinterf where the probability of interference P x,k
P x,k
interf
− Ik
act ⇔ Imax
− Ik
act
Imax
(33)
between two
interf
codewords with weights Wx and Wk is a function of the hit
probability [26]:
px,k = WxWk
2L
(34)
The probability of interference of a codeword of a serviceclass
k assigned to a new arriving call and a codeword
of service-class x can be calculated by following the same
procedure that was used in order to derive (3):
TABLE I
ANALYTICAL VS SIMULATION CBP RESULTS FOR THE 1ST APPLICATION
EXAMPLE.
Arrival CBP 1 st service-class CBP 2 nd service-class
Rate Analysis Simulation Analysis Simulation
(calls/sec) (%) (%) (%) (%)
0.10 0.187 0.183±6.80E-03 0.023 0.023±3.66E-03
0.11 0.309 0.316±1.44E-02 0.041 0.043±3.40E-03
0.12 0.487 0.490±1.65E-02 0.070 0.066±5.93E-03
0.13 0.731 0.715±2.12E-02 0.112 0.110±5.76E-03
0.14 1.056 1.061±2.44E-02 0.172 0.175±8.67E-03
0.15 1.473 1.488±2.91E-02 0.252 0.249±5.15E-03
0.16 1.993 1.995±2.55E-02 0.356 0.3625±4.76E-03
0.17 2.624 2.637±3.89E-02 0.488 0.4789±8.11E-03
0.18 3.371 3.355±5.55E-02 0.648 0.6548±1.17E-02
0.19 4.237 4.118±2.79E-01 0.839 0.8239±5.46E-02
0.20 5.220 5.213±6.16E-02 1.061 1.0773±1.94E-02
P k,x 1 Wx · Wk
interf =
Wx 2L
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= Wk
2L
(35)
The LBP lbk(j) can be calculated by using (8), where the
variable x can be calculated through (33) as follows:
x = 1 − T ·F
k=1 (n1 k
x = 1 − T ·F
k=1 (n1 k
bk·I k
unit
Imax
bk·I k
unit
Imax
x = 1 − ( j1
Imax · T ·F
k=1
· P k
Ik
interf ) − Imax ⇔
· P k
interf
) − bk·I k
unit
Imax ⇔
k (Pinterf · Ik k
bk·Iunit unit ) − Imax
(36)
For the case of the multi-rate OCDMA PON with QoS
differentiation the distribution of active and passive calls is
given by (10), where the upper bound of the summations that
refers to the total number of service-classes has to be changed
(from K) to T ·F . The same change has to be applied in (26),
(30) and (31) in order to calculate the CBP, the BBP and the
link utilization, respectively.
V. EVALUATION
We evaluate the proposed analytical models through simulation.
To this end we simulate the OCDMA PON of Fig.1 by
using the Simscript II.5 simulation tool [27]. The simulation
results are mean values from 6 runs with confidence interval
of 95%. The resulting reliability ranges of the simulation
measurements are small and, therefore, we present them only
in tables; in figures we provide only mean values. We consider
two application examples. In the first example, which is
simpler for clarification, we assume that the OCDMA PON
supports K=2 service-classes that are only differentiated by
the data rate, without QoS differentiation. The PON utilizes
the (211,4,1,2) codewords, which result in a maximum number
of 105 codewords. Based on the analysis presented in
[28] and considering a typical value of BER=10−6 , the total
number of codewords is reduced to C1 for Iunit = 0.4µW.
The traffic description parameters of the two service classes
are (b1, b2) = (7, 2), (µ −1
11 , µ−1 12 ) = (0.8, 1.0), (µ−1 21 , µ−1 22 ) =
(1.1, 1.4), (v1, v2)=(0.9, 0.95). We assume that the maximum
received power is equal to 4 µW, while the total number of
TABLE II
ANALYTICAL VS SIMULATION BBP RESULTS FOR THE 1ST APPLICATION
EXAMPLE.
Arrival BBP 1 st service-class BBP 2 nd service-class
Rate Analysis Simulation Analysis Simulation
(calls/sec) (%) (%) (%) (%)
0.1 6.65E-03 6.5E-03 ± 5.53E-04 8.25E-04 8.69E-04±1.7E-04
0.11 9.91E-03 1.1E-02 ± 1.22E-03 1.27E-03 1.41E-03±1.8E-04
0.12 1.40E-02 1.4E-02 ± 1.27E-03 1.85E-03 1.81E-03±2.4E-04
0.13 1.88E-02 1.9E-02 ± 1.21E-03 2.56E-03 2.43E-03±2.8E-04
0.14 2.43E-02 2.4E-02 ± 1.09E-03 3.42E-03 3.48E-03±3.5E-04
0.15 3.04E-02 2.9E-02 ± 1.10E-03 4.40E-03 4.36E-03±3.3E-04
0.16 3.69E-02 3.7E-02 ± 1.01E-03 5.52E-03 5.78E-03±5.3E-04
0.17 4.37E-02 4.4E-02 ± 1.86E-03 6.74E-03 6.62E-03±3.4E-04
0.18 5.05E-02 5.1E-02 ± 2.55E-03 8.06E-03 8.24E-03±6.9E-04
0.19 5.73E-02 5.7E-02 ± 1.33E-03 9.47E-03 9.60E-03±5.6E-04
0.2 6.38E-02 6.3E-02 ± 1.49E-03 1.10E-02 1.11E-02±5.7E-04
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