Step 1: Precompute the values of
[Eq. (3)], which are independent of
traffic loads. |
Step 2: Consider each single link. The values of
,
,
, and
will be used later when considering
paths with multiple links. |
for each link
do |
1. Calculate offered load
[Eq. (1)] |
2. Calculate the probability that the link has
free wavelengths,
[Eq. (5)] |
3. Calculate the probability that the link has at least
one free wavelength,
|
4. Calculate the probability
(defined in Table IV) |
5. Calculate the blocking probability of single-hop
path
between nodes
,
,
|
end for
|
Step 3: Then we consider paths with more than one link.
We need the steady-state distribution of the 5D Markov
chain, and the offered loads for the five types of
connections,
,
,
,
, and
. In this step, the values of
and
are calculated, which are used to get
and
in the next step. |
for each path
containing at least one 3R node
do |
for each 3R node
on path
, starting from the one closest to
and proceeding to the one closest to
do |
1. Calculate the values of
[Eq. (C3)],
[Eq. (C4)],
[Eq. (C7)],
[Eq. (C8)],
[Eq. (C5)],
[Eq. (C6)],
[Eq. (C9)], and
[Eq. (C10)] (in Appendix C) (The values of
,
,
,
, and
needed are those found in Steps 5 and
6 of the previous iteration, as explained in
Subsection III.C) |
2. Calculate
[Eq. (13)] and
[Eq. (14)] (where
is the corresponding outgoing link of
3R node
on path
) |
end for |
end for
|
Step 4: Now we can calculate the offered loads of the
five types of connections. Then we can get the
steady-state distribution of the Markov chain. In turn,
we can compute the values of
,
, and
, which are used in the next step to
find the value of
. |
for each pair of adjacent links on all
paths do |
1. Calculate the values of
[Eq. (6)],
[Eq. (7)],
[Eq. (11)],
[Eq. (12)], and
[Eq. (8)] |
2. Calculate the steady-state probability
[Eq. (9)] |
3. Calculate
[Eq. (A1)] based on the value of
[Eqs. (D1) and (D2)] |
4. Calculate
[Eq. (A3)] |
5. Calculate
[Eq. (A2)] |
6. Calculate
[Eq. (15)],
[Eq. (16)], and
[Eq. (17)] |
end for
|
Step 5: In this step we calculate
, which is used to find the blocking
probabilities for paths without 3R nodes. |
for each path
,
(
hops) do |
1. Calculate
[Eq. (18)] |
2. Calculate
[Eq. (4)],
(defined in Table IV),
[Eq. (C1)], and
[Eq. (C2)]. (Note that these values will
be used in Step 3 of the next iteration.) |
end for
|
Step 6: |
for each path
,
(
hops) without 3R nodes
do |
Calculate the blocking probability
|
end for
|
Step 7: Now we consider the paths with 3R nodes. In this
step, we calculate the offered loads to each 3R node’s
outgoing link
, and in turn, the probability that
there are no available OEO converters at a 3R node
. Then we can get the acceptance
probability of a path
based on
and
. |
for each path
,
containing 3R nodes
do |
for each 3R node
on the path do |
1. Calculate the offered load to 3R node
on outgoing link
;
|
2. Calculate the probability that there are no OEOs
available at the node
[Eq. (19)] (where
is the corresponding outgoing link
with node
on the path) (Note that these values
will be used in Step 3 of the next iteration.) |
end for |
1. Calculate the acceptance probability of the path
[Eq. (20)] depending on the OEO
availability at the first 3R node on the path. This
calculation is based on the values of
[Eq. (22)] and
[Eq. (23)] |
2. Calculate the blocking probability
|
end for
|
Step 8: Calculate the network blocking probability
|