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Abstract—We study the mtrail (monitoring trail) allocation
problem in alloptical WDM mesh networks for achieving fast and
unambiguous link failure localization. The existing ILP is not
feasible for solving the problem in largesize networks. A heuristic
RCA+RCS can find feasible solutions in a shorter running time,
but it is a randomized algorithm. More importantly, RCA+RCS
suffers from the disjoint trail problem which dramatically
increases the number of required monitors in largesize networks.
In this paper, we propose a new heuristic MTA (Monitoring Trail
Allocation) to solve the problem. MTA avoids those issues in
RCA+RCS, and achieves an efficient tradeoff between monitor
cost and bandwidth cost. Compared with RCA+RCS, MTA greatly
shortens the running time and achieves a much higher solution
quality. We also show that MTA provides a flexible framework to
enable multiple possible variations for future study.
Index Terms—Failure localization, monitoring trail (mtrail),
optical networks, Wavelength Division Multiplexing (WDM).
I. INTRODUCTION
Alloptical WDM networks have played a vital role in
supporting various Internet applications with high QoS [1]. In
WDM networks, hundreds of wavelengths can be multiplexed
onto a single fiber for parallel data transmission. This improves
data transmission efficiency and cuts down the network cost as
well. But, network survivability becomes a great concern, as
even a very short service downtime can lead to huge data loss.
To minimize data loss, it is important to have a fast monitoring
scheme to localize the failed link, such that it can be bypassed
and the disrupted traffic can be recovered in a timely manner.
In upperlayer monitoring schemes [2], fault localization
time is generally long due to the complex signaling. A scheme at
the optical layer [38] can greatly simplify the required signaling
to render a much shorter localization time. In this paper, we
focus on an optical layer monitoring scheme.
Recently, several optical layer monitoring schemes using
monitoring cycles (or mcycles) [34] and trails (or mtrails) [5]
were proposed. A common feature of those schemes is to
precrossconnect some dedicated supervisory wavelengths into
a set of mcycles or mtrails. Each mcycle or mtrail is a
supervisory lightpath, and an mtrail differs from an mcycle by
taking an arbitrary (open or closed) path, instead of only a
closed path as in an mcycle. Since mcycle is a special case of
mtrail [5], it is also called mtrail hereafter. Any link failure on
an mtrail will disrupt the optical supervisory signal transmitted
in the mtrail, and thus trigger an alarm in a dedicated monitor
This work was partially supported by the 973 Program (2007CB307104),
NSFC Funds (60972030, 60872032), Fundamental Research Funds for the
Central Universities and Ph.D. Programs Foundation of Ministry of Education
of China.
equipped at the sink of the mtrail. In this way, one monitor can
be shared to monitor the health of all links on the mtrail.
To accurately localize all possible single link failures, each
link must be traversed by a distinct set of mtrails. Then, a link
failure will trigger a unique alarm code to unambiguously
identify a specific link failure, where the onoff status of each
alarm is indicated by a binary bit. In essence, this approach
codes each link using a binary system, subject to the monitoring
structure and the network topology constraints [46]. In a
wellconnected network, the number of required monitors is
close to log2E where E is the set of all the links [57]. This
greatly reduces the number of monitors compared with the
linkbased monitoring schemes. Then, fault management can be
greatly simplified by managing only a small set of monitors.
The ILP (Integer Linear Program) in [5] needs a long
running time to find an optimal mtrail solution. To shorten the
running time, a twostep heuristic RCA (Random Code
Assignment) + RCS (Random Code Swapping) is proposed in
[7]. In RCA, each link is randomly assigned a unique code. RCA
aims at ensuring the code uniqueness in advance. Then, RCS
analyzes each bit in the codes to generate one or several mtrails.
Due to the randomized nature of this algorithm, its performance
highly depends on RCA. Besides, RCS may generate multiple
disjoint mtrails in analyzing each bit (i.e., the disjoint trail
problem), which increases the number of mtrails and monitors.
In this paper, we propose a heuristic MTA (Monitoring Trail
Allocation) which removes the randomness and the disjoint trail
problem in RCA+RCS [7]. Instead of ensuring code uniqueness
first as in RCA+RCS, our idea is to ensure a valid mtrail
structure first, and then sequentially add necessary mtrails to
achieve unambiguous link failure localization. Theoretical
analysis and simulation results show that MTA can generate a
better solution in a much shorter time than RCA+RCS.
The rest of the paper is organized as follows. Section II
briefly reviews the mtrail concept. Section III discusses the
existing RCA+RCS algorithm [7]. MTA is proposed in Section
IV. Section V presents simulation results to compare MTA with
RCA+RCS. We conclude the paper in section VI.
II. MTRAIL CONCEPT
A monitoring trail (mtrail) is a supervisory lightpath which
can traverse a directed link once and a node multiple times (see
Fig. 1a). If a link on an mtrail fails, the monitor at the sink of the
mtrail will alarm due to loss of the supervisory signal. Fig.1b
shows an example with three mtrails {t0, t1, t2}. If link (0, 1)
fails, monitors on t0 and t2 will alarm to generate an alarm code
[a2, a1, a0]=[1, 0, 1], where aj=1 means that the monitor on tj
Yangming Zhao , Shizhong Xu, Xiong Wang and Sheng Wang
School of Communication and Information Engineering
University of Electronic Science and Technology of China, Chengdu, P. R. China, 610054
Email: {zhaoyangming, xsz, wangxiong, wsh_keylab}@uestc.edu.cn
A New Heuristic for Monitoring Trail Allocation
in AllOptical WDM Networks
9781424456376/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
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alarms and aj=0 otherwise. With the predefined alarm code table
(ACT) in Fig.1c, the failed link (0, 1) can be localized. Other
link failures can be uniquely identified in the same way.
The objective is to minimize the monitoring cost in (1) [5]:
Monitoring Cost = monitor cost + bandwidth cost
= γ × number of monitors + cover length (1)
where the cover length is the total number of wavelengthlinks
traversed by all mtrails, and the cost ratio γ weights the cost of a
monitor over that of a supervisory wavelengthlink.
III. RCA+RCS ALGORITHM
RCA+RCS [7] is the only heuristic proposed so far for mtrail
design. In its first step RCA, each link is assigned a unique
random code. The key spirit is to ensure unique identification of
each link first. Basically, all links with alarm code bit aj=1
should be traversed by mtrail tj (see Fig. 1c). Due to the
randomized nature of RCA, it cannot ensure a proper mtrail
structure (i.e., a single connected supervisory lightpath). Then,
RCS (Random Code Swapping) is used to shape each tj (or each
alarm code bit aj for simplicity) into a valid mtrail.
The above idea is illustrated in Fig.2. In Fig.2a, a set of
decimal codes 18 is randomly assigned to the links by RCA,
with binary translations in the brackets. Then, RCS sequentially
shapes each bit a0a3. Let’s take a0 as an example, where those
links with a0=1 are denoted by the dashed lines in Fig.2a. Define
a code pair [7] as a pair of binary codes with only one bit
different. If we swap the code pair of links (0, 5) and (1, 2), a
valid mtrail can be obtained in Fig.2b. However, RCS may
swap another code pair of links (0, 1) and (2, 4). Then, two
separate mtrails will be generated as shown in Fig. 2c (i.e., the
disjoint trail problem as defined in Section I).
Another issue in RCA+RCS is that the solution quality
depends on the randomized RCA. More times we try to
reexecute the algorithm, better result we may get with high
possibility. Sometimes, simultaneously swapping multiple code
pairs can improve the solution, but is not allowed in RCS.
IV. MTA ALGORITHM
A heuristic for mtrail design may follow two possible
approaches. The first one is to ensure code uniqueness of each
link first and then shape the mtrail structures, as in RCA+RCS.
The second one is to ensure valid mtrail structures first, and
then sequentially add mtrails to achieve unambiguous link
failure localization. MTA adopts the second approach.
A. Key Definitions
Temporary Code: MTA sequentially adds mtrails to the
solution. Before the final solution is obtained, the codes
assigned to the links are called temporary codes. They are
determined by the mtrails that have already been allocated so
far. Since unambiguous link failure localization is not yet
achieved due to the insufficient number of mtrails allocated,
multiple links may have the same temporary code.
Ambiguity Set (ASc): An ambiguity set ASc contains at least
two links with the same temporary code c. If a link l is in an ASc
(i.e., l∈ ASc), we call ASc the home ambiguity set of l. In Fig.3,
we have two ambiguity sets AS1={(0,1), (1,2)} and AS2={(0,3),
(2,3)}, and the home ambiguity set of link (0, 1) is AS1.
Unambiguous Link (UAL): Whenever a link can be uniquely
identified from others by its current temporary code c (c>0), it
becomes an unambiguous link (UAL). In MTA, once a link
becomes an UAL, it remains as an UAL no matter how many
other mtails will be added to the solution in the future.
Fragment: MTA may need to connect multiple links or short
paths to produce a new mtrail. Each of them is defined as a
fragment. Let Fj ={ fk
mtrail tj where fk
denote the relationship by l∈ fk
Residue Topology: Let G(V, E) be the network topology
where V is the set of all the nodes and E is the set of all the links.
For a given set of links L⊆ E, a residue topology G(V, E)L is
obtained by removing L from G(V, E).
j } be a set of fragments used to generate an
j is the kth fragment. If a link l is a part of fk
j, l∈Fj and fk
j, we
j ⊆ Fj.
B. MTA Mechanism
Fig. 4 shows the main flowchart and Fig.5 gives the details of
MTA. In Step 1, we put all the links in a special ambiguity set
AS0, which is a set of links that have not yet been traversed by
any allocated mtrails. When MTA ends up in Step 4 (see Fig. 5),
AS0 must be a null set Φ. This is because each link must be
traversed by at least one mtrail in the final solution. Otherwise,
a failure at this link cannot be detected by any mtrail [5].
In Fig. 5, Step 2 adds a new mtrail tj to the solution based on
a set of fragments Fj ={fk
generally consists of some linkdisjoint fragments. In Step 2.2,
the end nodes of those linkdisjoint fragments are connected
using some shortest paths in the residue topology G(V, E)Fj to
6(0110)
8(1000)
j}. Fj is found in Step 2.1 and it
Fig. 1. Fast link failure localization using mtrails.
2
0
3
1
4
(b) An mtrail solution
t1
t0
t2
(0,1) 1 0 1 5
(0,2) 1 1 1 7
(0,3) 1 0 0 4
(1,2) 0 1 1 3
(1,3) 1 1 0 6
(2,4) 0 0 1 1
(3,4) 0 1 0 2
t2 t1 t0
Link
(c) Alarm code table
Decimal
(a) mtrail
d
s
a
b
c
e
f
Transceivers
1(01)
1(01)
2(10)
2(10)
1
0
2
3
4
5
0
1
3
2
(a) (b)
(c)
Fig.2. Mechanism of RCA+RCS and the disjoint trail problem.
2(0010)
7(0111)
)
1(0001)
3(0011
4(0100)
6(0110)
8(1000)
5(0101)
Fig.3 Example of ambiguity sets
t0
1
0
2
3
4
5
2(0010)
7(0111)
)
1(0001)
3(0011
4(0100)
6(0110)
8(1000)
5(0101)
1
0
2
3
4
5
2(0010)
7(0111)
)
1(0001)
3(0011)
4(0100)
5(0101)
t1
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produce a valid mtrail structure. Since several linkdisjoint
fragments may traverse a common node, the mtrail generated
may also pass through a node multiple times.
In particular, Step 2.1.1 initializes Fj to a null set Φ, and Step
2.1.2 finds an extending node rk from which a particular
fragment fk
rk, and fragment fk
weights. Note that the maximum nodal degree is always pursued
in choosing rk and weighting the neighbouring links, as well as
extending fk
and also increases the possibility that more links can share the
same mtrail tj which reduces the number of mtrails. Also note
that the weight wl is adjusted in Step 2.1.3. Specifically, if fk
extended using a link in AS0, it is promoted by increasing wl (i.e.,
wl×C1→wl); If fk
in an ambiguity set, the mtrail tj cannot distinguish this link
from other links on fk
this is not preferred by decreasing wl (i.e., wl /C2→wl). In short,
MTA prefers to let tj pass through those links not yet traversed
by any mtrail, and extend fragments and mtrails using links
from different ambiguity sets. If a link has become a UAL, or its
home ambiguity set has more than half links in Fj, this link is not
used to extend fk
Steps 2.1.3 and 2.1.4 form an inner loop to iteratively extend a
fragment fk
to extend fk
process of extending fk
loop (Steps 2.1.22.1.5) to construct the next fragment in Fj. Fj
construction completes when every ambiguity set has at least
one link in Fj.
Since Fj may consist of several linkdisjoint fragments, Step
2.2 in Fig. 5 is to connect them using some shortest paths to
ensure a valid mtrail structure. Shortest paths are computed in
the residue topology G(V, E)Fj using FloydWashall algorithm
[9], and are sequentially checked in an ascending order of their
lengths to see if it can properly connect two fragments fa, fb⊆ Fj,
subject to constraints a)d) in Step 2.2. Constraint a) means that
it is not costefficient to use a shortest path SPuv longer than γ
hops to save one monitor by connecting fa and fb (see (1));
Constraint b) says that SPuv must be able to properly connect fa
and fb into a longer fragment; Constraint c) specifies that the
new connected fragment SPuv∪fa∪fb must not fully cover all
links in an ambiguity set (otherwise it cannot divide those links
into two distinguishable subsets); Constraint d) ensures that any
j stems. Step 2.1.3 weights the neighbouring links of
j is extended in Step 2.1.4 according to the
j. This gives more possible routes in extending fk
j,
j is
j is extended using a link which is not the first one
j which are in the same ambiguity set, and
j by setting its weight to zero.
j. If no more links with a positive weight can be used
j, or the length of fk
j completes, and MTA turns to the outer
j has reached E/2, then the
directed link is not traversed by an mtrail more than once. Since
Step 2.2 may not be able to connect all fragments into a single
mtrail tj, we set tj as the longest fragment in the updated Fj.
After a new mtail tj is added in Step 2, we can update the
ambiguity sets and ACT in Step 3. If all the links have become
UAL and AS0=Φ, stop the algorithm and return ACT; Otherwise
Step 1: Initialize ambiguity set AS0
Step 2: Add a new mtrial
Step 3: Update ambiguity set and ACT
End: Return ACT and the final solution
Fig.4. The main flowchart of MTA.
Step 4: Have all the links been
uniquely identified and AS0=Φ?
N
Y
MTA Algorithm
Input: a network topology G(V, E) and a cost ratio γ.
Output: a set of mtrails for unambiguous single link failure localization.
Step 1: Initialize ambiguity set AS0:
Define AS0 as a set of links that have never been traversed by any
mtrail. Set E→AS0 (i.e., initialize AS0 to the set of all the links E). Mark
all the links in E as nonUAL. Let j be the index of the mtrails to be
added. Set 0→j.
Step 2: Add a new mtrail tj:
2.1) Find a fragment set Fj for tj:
2.1.1) Initialize Fj :
Define Fj ={fkj} as a set of fragments fkj that should be chosen
from G(V, E) to produce tj. Set 0→k and initialize Fj to a null set
Φ by setting Φ→fkj and Φ→Fj.
2.1.2) Find an extending node rk for fkj:
For each ASc generated so far (including AS0), if ASc∩Fj
=Φ, construct a subgraph of G(V, E) from ASc. In all the
subgraphs obtained, find an extending node rk of fkj as the node
with the maximum nodal degree (ties are broken by randomly
choosing one from multiple peers).
2.1.3) Weight neighbouring links of rk :
In residue topology G(V, E)Fj, weight each neighbouring
link l of rk using the nodal degree wl of the other end node of l.
Let C1 and C2 be two predefined large constants, and AS be the
home ambiguity set of l (i.e., l ∈ AS). If AS=AS0, set
wl×C1→wl. If there is another link l’ ∈AS ∩ Fj, set wl /C2→wl.
If l is an UAL, or AS ∩ Fj ≥AS/2, set 0→wl.
2.1.4) Extend fragment fkj:
In residue topology G(V, E)Fj, let lmax be the neighbouring
link of rk with the maximum positive weight wl as calculated in
Step 2.1.3 (ties are broken by randomly choosing one from
multiple peers), and r’k be the other end node of lmax. Set r’k→rk
and lmax∪fkj→ fkj (thus lmax also becomes a link lmax∈ Fj).
Repeat Steps 2.1.3 and 2.1.4 until no more links with positive
weight can be further added to fkj, or  fkj = E /2.
2.1.5) Loop control to construct another fragment in Fj:
If ASc ∩ Fj ≠ Φ for all ASc, go to Step 2.2; Otherwise set
k+1→k and go to Step 2.1.2 to construct the next fragment.
2.2) Connect linkdisjoint fragments in Fj to produce tj:
Let SPuv be the shortest path between nodes u and v in the
residue topology G(V, E)Fj. Use FloydWashall algorithm to
compute SPuv between all node pairs u, v∈G(V, E)Fj, and sort
those shortest paths in an ascending order of their lengths. In the
same order, sequentially check whether each SPuv can be used to
properly connect two linkdisjoint fragments (say faj, fbj) in Fj. If
a) SPuv≤γ,
b) SPuv can properly connect faj and fbj into a new fragment,
c) ASc ⊄ (SPuv∪faj∪fbj) for all ASc, and
d) SPuv∩(faj∪ fbj)= Φ,
set SPuv∪faj∪fbj→faj and Fjfbj→Fj. After all SPuv have been
checked, set tj as the longest fragment in Fj and go to step 3.
Step 3: Update ambiguity sets and ACT:
Recompute the temporary code of each link based on the mtrails {t0,
t1, …, tj} allocated so far. Put any link with a temporary code c into ASc
and those links not traversed by any mtrail into AS0. Mark each link with
a distinct temporary code as an UAL. Update ACT accordingly.
Step 4: Loop control for unambiguous link failure localization:
If every link in E has become an UAL and AS0=Φ, stop and return
ACT; Otherwise, set j+1→j and go to Step 2 to add another mtrail.
Fig. 5 Details of MTA algorithm.
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go to Step 2 to add another mtail until unambiguous link failure
localization is achieved, as stipulated in Step 4.
Fig. 6 shows an example of MTA based on the network in Fig.
2, where we set γ=5 and C1=C2=10. Compared with the optimal
ILP result, which requires a monitoring cost of 32 (4 monitors
and 12 cover length), MTA requires 34 (4 monitors and 14 cover
length) which is within a gap of only 6.25% to optimality.
C. Theoretical Analysis and Discussions
Compared with conventional monitoring schemes which
require at least O(E) monitors, the mtrail scheme only requires
O(log2E) mtrails/monitors (in wellconnected networks) [57].
MTA has indeed pursued this logarithmic nature. MTA ensures
that at least one link is chosen from each ambiguity set to
construct a new mtrail tj (see Step 2.1.5 in Fig. 5), and tj must
not fully cover all links in any ambiguity set (see constraint c) in
Step 2.2). It means that each mtrail tj intends to divide every
ambiguity set into two distinguishable subsets (if all fragments
fk
intends to divide each ambiguity set into two subsets with
almost equal size. This is because MTA will never use more
than half links in any ambiguity set to extend a fragment (see
Step 2.1.3), and it connects them using some other links. So, an
mtrail intends to split each ambiguity set half to half. This
directly follows the binary coding principle which makes the
required number of mtrails/monitors close to log2E.
In addition to potentially saving monitors as analyzed above,
MTA also intends to save supervisory wavelengths. Examples
include that MTA does not extend a fragment using any UAL
(but the UAL can still be used to connect fragments in Step 2.2),
and shortest paths are used to connect fragments, etc. Besides,
the tradeoff between monitor cost and bandwidth cost is also
taken into account, because MTA never uses a shortest path
more than γ hops to connect two fragments for saving one
monitor, as formulated in constraint a) in Step 2.2.
Unlike the randomized RCA+RCS [7], MTA runs in a
deterministic manner. It does not need to be reexecuted many
j can be properly connected into tj in Step 2.2). Besides, MTA
times for a good solution, and this greatly shortens the running
time. The time complexity of MTA is dominated by Step 2.2,
where it needs at most O(V3) time to compute allpairs shortest
paths, O(V2logV) time to sort those shortest paths, and
O(V2E2) time to connect fragments. This results in a time
complexity of O(V3+V2E2) to generate an mtrail. Since a
solution may consist of at most O(E) mtrails, in the worst case
the time complexity of MTA is at most O(V3E+V2E3).
By ensuring valid mtrail structures and sequentially adding
them to the solution, MTA removes the disjoint trail problem in
RCA+RCS. In largesize networks, this saves a lot of mtrails,
and makes the design more scalable in terms of minimizing the
number of monitors and the fault management efforts.
MTA provides a flexible framework where one can easily try
many variations in different steps. For example, we can easily
modify MTA by randomly choosing half links from each
ambiguity set and connecting them using shortest paths. Then,
the algorithm will be randomized which can gradually improve
the solution by many times of tries. Another example is that, if
distancerelated costs instead of hopcounts are used as the link
cost metric, we can easily modify the weighting in Step 2.1.3 to
take it into account, which is very hard to achieve in RCA+ RCS.
We will studies similar issues in our future work.
V. SIMULATION RESULTS
The simulation is carried out on a computer with DuoCore
1.86 GHz intel CPU using C++ in visual studio 2005. To
compare MTA with RCA+RCS [7], we set γ=5000 as in [7] to
minimize the number of mtrails. In Figs. 79, each performance
point is obtained by averaging the results over hundreds of
randomly generated topologies. Due to the randomized nature of
RCA+RCS, we report its best result over 100 tries for each
topology whereas MTA is run only once.
A. Performance Comparison as Network Size Changes
Figs. 78 show how the number of mtrails changes in both
algorithms as the network size increases. Fig. 8 also shows the
theoretical lower bound ⎣
 log2
E
is relatively small, the performance of RCA+RCS and MTA is
very close to the lower bound, and RCA+RCS may even
outperform MTA. In this smallsize network scenario,
RCA+RCS can well explore the solution space without trying
many times, but we may turn to the ILP for optimal solution. As
the network size increases, the number of required mtrails in
RCA+RCS grows much more rapidly than MTA. This is
because RCA+RCS intrinsically suffers from the disjoint trail
problem which makes the situation worsened fast in largesize
networks, whereas MTA does not have this problem by ensuring
a valid connected optical structure for each mtrail added to the
solution. Of course, the performance of RCA+RCS may be
slightly improved by reexecuting the algorithm more (than 100)
times, but that also means a much longer running time.
Since we have to reexecute RCA+RCS 100 times for each
topology to get the performance shown in the figures, the
running time of RCA+RCS is much longer than that of MTA. In
a network with 60 nodes and an average nodal degree of 8, MTA
only needs 34 seconds, whereas RCA+RCS needs more than
900 seconds to generate a much poorer solution. If the number
⎦ 1
+
[5]. When the network size
Initialize: AS0={(0,1), (1,2), (2,3),
(3,4), (4,5), (5,0), (1,5), (2, 4)}
AS0={(0,1), (2,3), (3,4), (1,5)}
AS1={(1, 2), (2, 4), (4, 5), (0, 5)}
f00 extends through nodes
1,2,4,5 and 0; F0={ f00}
and t0=1→2→4→5→0
AS0={(0,1)
AS2={(2,3), (3,4), (1,5)}
AS1={(1, 2), (2, 4), (0, 5)}
UAL: (4,5)
f01 extends through nodes
1,5,4,3, and 2; F1={ f01}
and t1=1→5→4→3→2
UAL: (0,1)
UAL: (1,5)
AS2={(2,3), (3,4)}
UAL: (2,4)
AS5={(1,2), (0,5)}
f02externs through node
2,1,0,5,1; F2={ f02} and
t2=2→1→0→5→1
UAL:(2,3)
UAL: (3,4) UAL: (1,2)
UAL: (0,5)
f03 externs through
node 3,2,1; F0={ f03}
and t3=3→2→1
Fig.6. An example of MTA execution based
on the network in Fig. 2 with γ=5 and C1=C2=10.
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Page 5
of nodes is reduced to 30, the running time of MTA will be less
than 1 second but RCA+RCS still needs 150 seconds.
B. The Impact of Network Connectivity
The number of mtrails required may change from ⎡
ring topology to
⎡
(log6
2
+
E
Due to the diversity of the networks, it is impossible to fully
explore how this number is exactly affected by various
topologies with different network connectivity. But, we can use
Fig.9 to show how MTA and RCA+RCS are affected, where
two values 8 and 4 of average nodal degree are considered. As
the average nodal degree decreases, more mtrails are required
although there are less links in the network. This is because
mtrails cannot be very freely routed in a sparsely connected
network, which greatly limits the advantage of using mtrails. In
Fig. 9, MTA always outperforms RCA+RCS in largesize
networks. Besides, network connectivity has a slightly less
impact on MTA than on RCA+RCS.
⎤ 2 / E
for a
⎤ ) 1
+

for a fully meshed topology [7].
VI. CONCLUSION
We studied fast and unambiguous link failure localization in
alloptical WDM mesh networks using the optical layer mtrail
structures. An efficient heuristic MTA (Monitoring Trail
Allocation) was proposed to find highquality mtrail solutions
in largesize networks with a very short running time. MTA
minimizes the monitoring cost with operable tradeoff between
monitor cost and bandwidth cost. Unlike the randomized
RCA+RCS, MTA runs in a deterministic manner. MTA first
ensures a valid structure of each mtrail, and then sequentially
adds necessary mtrails to achieve unambiguous link failure
localization. By avoiding the disjoint trail problem in
RCA+RCS, MTA achieves a much smaller monitoring cost. Our
numerical results demonstrated the superior performance of
MTA over RCA+RCS in both solution quality and running time.
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Fig.8. Number of monitors vs. number
of links with an average nodal degree of 8.
Fig.9. The impact of network
Fig.7. Number of monitors vs. number
of nodes with an average nodal degree of 8.
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.