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uncorrected proof
Photonic Network Communications (2006) 11:277–286
DOI 10.1007/s11107-005-7355-3
ORIGINAL ARTICLE
A novel fault detection and localization scheme for mesh
all-optical networks based on monitoring-cycles
Hongqing Zeng ·Changcheng Huang ·Alex Vukovic
Received: 25 February 2005 / Revised: 29 August 2005 / Accepted: 2 September 2005
© Springer Science + Business Media, Inc. 2006
Abstract We previously showed the feasibility of a fault1
detection scheme for all-optical networks (AONs) based on2
their decomposition into monitoring-cycles (m-cycles). In3
this paper, an m-cycle construction for fault detection is for-4
mulated as a cycle cover problem with certain constraints. A5
heuristic spanning-tree based cycle construction algorithm6
is proposed and applied to four typical networks: NSFNET,7
ARPA2, SmallNet, and Bellcore. Three metrics: grade of8
fault localization, wavelength overhead, and the number of9
cycles in a cover are introduced to evaluate the performance10
of the algorithm. The results show that it achieves nearly11
optimal performance.12
Keywords Fault detection ·Fault localization ·13
All-optical network ·Monitoring cycle ·Cycle cover14
Introduction15
Fault detection and localization are essential for providing16
continuous and reliable services in all-optical networks17
H. Zeng (B
)·C. Huang
Department of Systems and Computer Engineering,
Carleton University,
1125 Colonel By Drive,
Ottawa, ON,
Canada K1S 5B6
e-mail: hzeng@sce.carleton.ca
A. Vukovic
Communications Research Centre Canada,
3701 Carling Avenue,
P.O. Box 11490,
Stn. H Ottawa, ON,
Canada K2H 8S2
e-mail: alex.vukovic@crc.ca
(AONs) with ever-increasing data rate as well as increased 18
wavelength number and density in wavelength-division mul- 19
tiplexing (WDM) [1]. For AONs, fault detection and locali- 20
zation can be performed in either the physical or the IP layer. 21
Most routing protocols in the IP layer, e.g., OSPF or IS–IS, 22
have inherently such a functionality [2]. Unfortunately, the 23
long detection time in the IP layer (typical at seconds-level) 24
makes it difficult to achieve time-critical recovery. Thus, 25
some effective and efficient fault detection mechanisms at 26
the optical layer are required. However, existing fault detec- 27
tion and localization mechanisms for conventional networks 28
cannot be applied to AONs directly due to the lack of electri- 29
cal terminations [3]. Even some detection methods deployed 30
in optical networks with opto-electro-opto (OEO) conversion 31
cannot be transplanted to AONs, for instance the examples 32
in [4]. In the physical layer, network faults can be detected 33
by measuring the optical power, analyzing the optical spec- 34
trum, using pilot tones, or performing optical time-domain 35
reflectometry [5]. A fault detection scheme was developed 36
by assigning monitors to the sinks of each optical multiplex 37
section and optical transmission section [6]. Another scheme 38
proposed in [7] modeled all possible states of a link as a fi- 39
nite state machine (FSM). The FSM for each link keeps tracks 40
of the current state of the link by assigning a monitor to the 41
link. Ideally, all potential faults could be completely detected 42
and located by assigning a monitor to each link (channel). 43
However, it is usually not feasible to implement the monitor- 44
per-link scheme in large-scale networks because of the large 45
number of required monitors and the real-time processing of 46
a huge amount of redundant alarms. 47
Other than assigning a monitor per link, some authors 48
placed a monitor to each established lightpath [8]. Some 49
heuristics were proposed to reduce the number of required 50
monitors based on the information of redundant alarms. This 51
scheme was effective at the time it was proposed, since the 52
“PNET-0004” 2006/3/7 11:45
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278 Photonic Network Communications (2006) 11:277–286
number of lightpaths in an AON was relatively small and they53
did not change frequently once established. However, the54
number of lightpaths soars so much nowadays with the use55
of DWDM technology that this scheme will introduce huge56
cost due to the large number of required monitors. Further-57
more, most AONs currently support dynamically lightpath58
provisioning so that the monitor placement has to be dynam-59
ically re-calculated and re-located once some lightpaths are60
changed, which is not easy to fulfill in the real world.61
To detect and locate network faults, it is not necessary to62
put monitors on all links, lightpaths, or nodes. For example,63
some authors proposed a diagnosis method with sparse moni-64
toring nodes (multiple monitors may be required) particularly65
for crosstalk attacks, which could be considered as special66
cases of network faults in a wide sense [9, 10]. In this paper,67
we propose a general approach at the physical layer for fault68
detection and localization in AONs through decomposing the69
given network into a set of cycles, which form a cycle cover70
for the network. A spanning-tree based cycle construction71
algorithm is developed and applied to four typical example72
networks: NSFNET, ARPA2, SmallNet, and Bellcore. The73
performance of the proposed approach is evaluated in terms74
of grade of fault localization, costs, and impacts on wave-75
length utilizations.76
This paper is organized into the following sections. Sec-77
tion Monitoring-cycles and cycle construction formulation78
introduces the concept of monitoring cycles and formulates79
the problem of constructing monitoring cycles to the cy-80
cle cover problem. Section Heuristic spanning-tree (HST)81
based cycle construction proposes a heuristic spanning-tree82
based cycle construction algorithm. The proposed algorithm83
is then applied to four typical example networks in Sec-84
tion Examples and evaluations. The performance measures85
of the proposed algorithm are also evaluated. Finally, some86
conclusions are outlined in the last section.87
Monitoring-cycles and cycle construction formulation88
We previously proposed a fault detection and performance-89
monitoring scheme based on decomposing an AON into a90
set of cycles [11]. All nodes and links in the network appear91
in at least one of these cycles, which form a cycle cover of92
the network. A network monitor is assigned to one node in93
each cycle and a loopback supervisory channel is set up in94
this cycle. A cycle with a monitor and a supervisory channel95
is defined as “monitoring cycle (m-cycle)”. Network faults96
trigger alarms in m-cycles that cover the faulty source thus97
they are detectable. Depending on the type of monitors in98
the m-cycles (e.g., optical power meters, optical spectrum99
analyzers, and transceivers), various performance parameters100
of AONs can be measured, such as optical power, channel101
wavelength, optical signal-to-noise ratio, and bit error ratio.102
Flexible index thresholds can be set to determine whether a 103
network fault occurs. Such an approach reduces the number 104
of required monitors from the number of links to the number 105
of cycles in an AON. Furthermore, the loopback supervisory 106
scheme puts the transmitter and receiver together in a sin- 107
gle node of an m-cycle. Thus the source signals could be 108
used as references for received signals and the hardware and 109
software of monitoring devices could be greatly simplified. 110
More importantly, through assigning monitors to some se- 111
lected nodes and/or avoiding assigning monitors to the nodes 112
with high management expense, the cost of our fault detec- 113
tion and localization mechanism could be kept in low. 114
A meshed AON can be modeled as a finite undirected 115
graph G(V,E), where Vis the set of vertices (nodes) and E116
is the set of edges (links). Hereafter the term vertex (edge) 117
and node (link) are exchangeable in this paper. We assume 118
that such a graph is connected and it contains neither loops 119
nor multiple edges. A loop is an edge that starts and ends at 120
the same vertex. Multiple edges refer to two or more parallel 121
edges that have the same start-vertex and end-vertex. Fur- 122
thermore, an edge is a bridge of a graph if the graph becomes 123
from a connected graph to be a disconnected one after delet- 124
ing it. A bridge link is a single-failure point for the network, 125
thus it is usually avoided during the network topology design. 126
Therefore, G(V,E)is assumed to be bridgeless. 127
A cycle (denoted as c) of the graph Gis a sub-graph of 128
Gthat is connected and regular of degree two. It is often 129
identified with its edge-set. A cycle cover (denoted as C)of 130
a graph is a set of cycles in which each vertex and edge of 131
the graph appears at least in one of these cycles. According 132
to the m-cycle definition, the set of m-cycles is a cycle cover 133
for a given graph. Let C={c1,c2,...,cM}be such a set of 134
m-cycles. For an edge e∈E,letC(e)denote the number of 135
cycles in Cthat contain e, that means C(e)=|{i:e∈ci}|136
where |•|represents the set cardinality, i.e., the number of 137
elements in a finite set. When C(e)=t, we say that the cover 138
time of edge eis tin C. The length of a cycle is the number 139
of edges it contains, denoted by len(ci)=|ci|. The length 140
of C, denoted as len(C), is the sum of all cycle lengths in 141
C. Obviously we have, 142
len(C)=
M
i=1
|ci|=
L
j=1
C(ej). (1) 143
While looking for a set of m-cycles (a cycle cover) for 144
a graph, we have to take the following considerations into 145
account: grade of fault localization, wavelength overhead due 146
to m-cycles, and cost of the required monitors. 147
Grade of fault localization 148
A network fault triggers alarms in the m-cycles in which it ap- 149
pears, but not others. Reversely, if alarms are received in some 150
uncorrected proof
Photonic Network Communications (2006) 11:277–286 279
m-cycles but no others, it implies that the potential faulty151
links are the common links of these m-cycles. Figure 1 gives152
a graph example with a cycle cover C={c1,c2,c3,c4}.153
If, for example, a fault occurs along link (1,4), it will trigger154
alarms in c1and c4, respectively, but there is no alarm in other155
m-cycles. If alarms are received in m-cycles c1and c4,but156
not in others, it implies that the potential faulty links could157
be either (1,4) or (2,4) or both, since the alarm distribution158
triggered by the fault in both links are identical, which means159
alarms in c1and c4. Generally, a binary indication bit mjcan160
be defined for m-cycle cjto indicate whether or not a fault161
occurs and thus an alarm appears in it,162
mj=1 an alarm appears in cj
0 no alarm appears in cj
;j=1,2,...,M.(2)163
The sequence of such bits for a link forms an alarm code164
(Mbits in total). Alarms are sent to a centralized network165
management unit (NMU) and alarm codes are generated in166
real time. Furthermore, for any link ei∈E(i=1,2,...,L)167
and m-cycle cj, a binary associative bit aij is defined as,168
aij =1eiis covered by cj
0eiis not covered by cj,(3)
169
where i=1,2,...,Land j=1,2,..., M. The sequence170
of associative bits of a link corresponding to all the m-cycles171
forms the associative code (Mbits in total). Once alarms172
in m-cycles are collected and an alarm code is generated,173
we can compare the alarm code bit-by-bit with the associa-174
tive code for each link. If a link’s associative code exactly175
matches the alarm code, then this link is a faulty candidate176
for the received alarm code. By matching the real-time alarm177
codes with the associative codes of all links, a faulty candi-178
date set can be established for each alarm code. Based on179
the selection of m-cycles, multiple elements may exist in180
such candidate sets. To quantitatively measure the grade of181
localization, we introduce the concept of Localization Degree182
(denote as I), which is defined as the average size of non-183
empty faulty candidate sets produced by all possible alarm184
codes. Let C={c1,c2,...,cM}be a set of m-cycles in graph
185
G. Since each alarm code consists of Mbits, the number of186
possible alarm codes is 2M−1. Let skbe the faulty candidate187
set for alarm code mk, where k=1,2,...,2M−1. Please188
note for a given AON, some alarm codes are not applicable189
and thus the corresponding faulty candidate sets are empty.190
Let Dbe the collection of all non-empty sk. Then the locali-191
zation degree can be defined as the following,192
I=sk∈D|sk|
|D|.(4)
193
In the ideal case, every candidate set has only one element194
and Iideal =1 (defined as complete localization). In build-195
ing m-cycles for fault detection, we want to minimize the196
localization degree, i.e., MIN I.197
c
2
1
3
4
7
5
6
8
10
9
c
c
c
c1
22
11
33
44
77
55
66
88
1010
99
c2
c3
c4
Fig. 1 A graph example and cycle cover
Wavelength overhead 198
In each link, some wavelength channels are reserved for m-199
cycles. These channels cannot be used for carrying user traffic 200
and therefore become an overhead. The number of reserved 201
wavelengths within a link is equal to the cover times of that 202
link in the cycle cover. Let max be the maximum num- 203
ber of wavelengths reserved for monitoring in a link and it 204
represents the worst case. Given a graph with Nvertices, L205
edges and Mm-cycles, the average number of reserved wave- 206
lengths (avg)for all edges is equal to the average cover time 207
and, 208
avg =
L
i=1
C(ei)L=len(C)L.(5) 209
To quantitatively analyze the relative overhead due to m-210
cycles, we define the average wavelength overhead per link 211
brought to the network by m-cycles as WOHavg =avg/F,212
where Fis the number of total available wavelengths per 213
link. To minimize the wavelength overhead, we have to min- 214
imize avg, which is equivalently to minimize the cycle cover 215
length. Consequently, m-cycle construction can also be for- 216
mulated to the least cost cycle cover problem for un-weighted 217
graphs. 218
Cost of monitors 219
Since a monitor and a dedicated supervisory channel are 220
assigned for each m-cycle, the number of required moni- 221
tors and reserved wavelengths, i.e., the number of m-cycles 222
(M=|C|), is a measure of the cost for such type of fault 223
detection and localization approaches. To minimize this cost, 224
we have to minimize the number of m-cycles, i.e., MIN |C|.225
Heuristic spanning-tree (HST) based cycle construction 226
It has been proven that cycle covers exist for each bridge- 227
less, connected, undirected graph and could be obtained in 228
uncorrected proof
280 Photonic Network Communications (2006) 11:277–286
running time O(N2)[12]. Numerous algorithms have been229
reported for constructing cycle covers, e.g., a polynomial-230
time algorithm was proposed in [13]. Unfortunately, such231
works are focused on the least-cost cycle cover problem but232
do not consider the localization degree and cycle numbers.233
We previously developed two m-cycle construction algo-234
rithms: heuristic depth-first searching and shortest path Eulerian235
matching algorithm, with a balance of all three considerations236
[11]. In this paper, we propose a heuristic spanning-tree based237
m-cycle construction algorithm for the same purpose, while238
improving the performance in terms of localization degree.239
Preliminary240
For a connected, bridgeless, simple graph G(V,E), there241
must exist a spanning-tree T. For each link e/∈T(whereby242
eis called a “chord”), it holds that if the two endpoints of e243
are n1and n2, then n1,n2∈Tand there must exist a path244
p∈Tconnecting n1,n2. Thus, link eand path pform a245
cycle. We say this cycle is generated by chord e. Each chord246
generates such a unique cycle. We also have the following247
cycle cover existence lemma [12],248
Lemma There exists at least one cycle cover for a bridgeless249
graph G(V,E).250
For a cycle ciin a graph Gwith precisely Ledges, an251
associative vector viwith Lcomponents can be assigned to252
it. The jth component vj
iof the vector vi=(v1
i,v
2
i,...,vL
i)253
is one if the jth edge of Glies in ci, and zero otherwise (please254
note the difference with the associative code defined in Sec-255
tion Grade of fault localization). Cycles c1,c2,...,cMare256
called independent if their associative vectors are linearly257
independent, where a group of vectors a1,a2,...,anare258
linearly independent if and only if i=n
i=1kiai=0 holds259
when k1=k2= ··· = kn=0.260
H. Walther has proven the following theorem in [13],261
Walther’s Theorem: Let Gbe a connected graph with L262
edges and Nvertices. Then there exist L−N+1, but no263
more independent elementary cycles.264
A cycle is called elementary cycle if no vertex is encoun-265
tered more than once when traversing it. Each cycle can be266
partitioned into elementary cycles. In this paper, a cycle refers267
to an elementary cycle268
Based on the above lemma and theorem, we claim the269
following theorem,270
New theorem: For a connected, bridgeless, simple graph271
Gwith a given spanning-tree, cycles generated by all chords272
construct a cycle cover for G.273
Proof Let Ghas Ledges, Nvertices, and the spanning-tree274
is T. Then, all edges can be partitioned into two sets: N−1275
edges in Tand L−N+1 edges not in T.276
(1) Each edge not in Tis a chord. It generates a cycle and is 277
covered by this cycle. There are L−N+1 such cycles. 278
(2) Assume that there exists an edge e∗∈Tand e∗is not
covered by any cycles generated by those chords. Be-
cause of the lemma, there must exist another cycle c0
in which e∗appears. The associative vector of c0is
a0=(a1
0,a2
0,...,a∗
0,...,aL
0), where a∗
0=1 and
corresponding to the position of edge e∗. For all other
cycles, the components at this position of the associa-
tive vectors are zero, because they do not cover edge e∗.
Thus, cycle c0is independent from all other L−N+1
cycles. Consequently, by adding c0, graph Gnow has
L−N+2 independent cycles. But Walther’s theorem
indicates that there are no more than L−N+1 inde-
pendent cycles in graph G.
In the proof, please note that a cycle cover of graph Gis 279
uniquely determined by the given spanning-tree. 280
Heuristic spanning-tree (HST) based cycle construction 281
Among the numerous existing cycle building algorithms, the 282
spanning-tree based ones are fast, simple, and flexible. 283
Breadth-first and depth-first spanning-trees (BFST and 284
DFST) are well known and have been in common use for a 285
long time. Numerous algorithms to generate such spanning- 286
trees have been intensively studied [15]. Figure 2 gives three 287
spanning-trees for an example graph and m-cycles gener- 288
ated by corresponding chords. Numbers of cycles in the cov- 289
ers generated by various spanning-trees are the same for the 290
graph. By enumerating the faulty candidates for all possi- 291
ble alarm codes, we find that their localization degrees are 292
also the same (I=1). However, the figure shows that the 293
average cover time (i.e., the average wavelength overhead) 294
per link is smaller for the cover generated by BFST than 295
by DFST. Furthermore, the average cover time might be de- 296
creased by including nodes with large degrees in the tree 297
(comparing Fig 2 b and c). This observation leads us to 298
choose BFST and apply a heuristic rule of putting the large- 299
degree nodes into the spanning-tree as early as possible while 300
generating the spanning-tree for constructing a cycle cover. 301
6
5
41
32
(a)
6
5
41
32
(c)
6
5
41
32
(b)
6
5
41
32
(a)
66
55
4411
3322
6
5
41
32
(c)
66
55
4411
3322
6
5
41
32
(b)
66
55
4411
3322
Fig. 2 Spanning-tree and cycle cover. (a) DFST: max cover time =
5/link, average cover time =2.3/link. (b) BFST (rooted from random
nodes): max cover time =5/link, average cover time =1.9/link. (c)
BFST (rooted from the node with maximum degree): max cover time
=2/link, average cover time =1.5/link
uncorrected proof
Photonic Network Communications (2006) 11:277–286 281
Fig. 3 m-Cycles obtained by
HST for (a) NSFNET; (b)
ARPA2; (c) SmallNet; (d)
Bellcore (links in spanning-trees
are in dark)
8
141
13
12
10
11
2
3
4
5
6
7
9
NSF NET: 14 nodes , 21 links
c
1
: 1 – 2 –3– 1
c
2
: 1 – 4 –5– 6–3– 1
c
3
: 4 –1 0 –13– 12– 6–5 –4
c
4
: 7 – 8 –2– 3–6– 5–7
c
5
: 8 – 9 –13 –12– 6–3 –2– 8
c
6
: 9 –1 1 –6–1 2–1 3–9
c
7
: 9 –1 4 –12– 13– 9
c
8
: 1 0–14 –12– 13– 10
8
141
13
12
10
11
2
3
4
5
6
7
9
8
14
13
12
10
11
6
9
SFNET: 14 nodes, 21 links
c
1
: 1 – 2 –3– 1
c
2
: 1 – 4 –5– 6–3– 1
c
3
: 4 –1 0 –13– 12– 6–5 –4
c
4
: 7 – 8 –2– 3–6– 5–7
c
5
: 8 – 9 –13 –12– 6–3 –2– 8
c
6
: 9 –1 1 –6–1 2–1 3–9
c
7
: 9 –1 4 –12– 13– 9
c
8
: 1 0–14 –12– 13– 10
ARPA2: 21 nodes, 25 links
14
1
2
3
4
5
6
7
891011
12
13
15 16
17 18
19 20
21
c
1
: 4 – 5 –6–3–2–1–4
c
2
: 7 – 8 –1 –2–3–6– 7
c
3
: 13–14 –12–11–10–9–8–13
c
4
: 15–16 –14–12–11–10–9–8
–1–2–3 –6–15
c
5
: 20–21 –18–17–11–12–14
–16–19 –20
ARPA2: 21 nodes, 25 links
14
1
2
3
4
5
6
7
891011
12
13
15 16
17 18
19 20
21
14
1
2
3
4
5
6
7
891011
12
13
15 16
17 18
19 20
21
c
1
: 4 – 5 –6–3–2–1–4
c
2
: 7 – 8 –1 –2–3–6– 7
c
3
: 13–14 –12–11–10–9–8–13
c
4
: 15–16 –14–12–11–10–9–8
–1–2–3 –6–15
c
5
: 20–21 –18–17–11–12–14
–16–19 –20
(c)
(b)
(a)
SmallNet: 10 nodes, 22 links
1
10
2
34
5
6
7
89
c
1
: 1 – 2 –7–1 c
10
: 6 –1 0 –7 – 6
c
2
: 1 – 6 –7–1 c
11
: 8 – 9 –7– 8
c
3
: 2 – 3 –9–7– 2 c
12
: 8 –1 0 –7 – 8
c
4
: 2 – 8 –7–2 c
13
: 9 –1 0 –7 – 9
c
5
: 3 – 4 –9–3
c
6
: 3 – 8 –7–9– 3
c
7
: 4 – 5 –9–4
c
8
: 5 – 6 –7–9– 5
c
9
:5 –1 0 –7– 9–5
mallNet: 10 nodes, 22 links
1
10
2
34
5
6
7
89
1
10
2
34
5
6
7
89
c
1
: 1 – 2 –7–1 c
10
: 6 –1 0 –7 – 6
c
2
: 1 – 6 –7–1 c
11
: 8 – 9 –7– 8
c
3
: 2 – 3 –9–7– 2 c
12
: 8 –1 0 –7 – 8
c
4
: 2 – 8 –7–2 c
13
: 9 –1 0 –7 – 9
c
5
: 3 – 4 –9–3
c
6
: 3 – 8 –7–9– 3
c
7
: 4 – 5 –9–4
c
8
: 5 – 6 –7–9– 5
c
9
:5 –1 0 –7– 9–5
(d)
Bellc ore : 15 no des , 28 links
1
2
3
45
6
7
8
9
10
11
12
13
14
15
chord
chord chord
chord
chord
chord
c
1
: 1 – 9 –8–2–1 c
11
: 9 –10 –2–8–9
c
2
: 1 –10 –2–1 c
12
: 9 –11 –2–8–9
c
3
: 3 –13 –2–3 c
13
: 12–13 –2–8–12
c
4
: 4 – 5 –6–3–4 c
14
: 12–14 –6–3–2–8–12
c
5
: 4 –13 –2–3–4
c
6
: 6 – 7 –8–2–3–6
c
7
: 6 –12 –8–2–3–6
c
8
: 5 –15 –6–5
c
9
:7 –12 –8–7
c
10
: 8 –11 –2–8
ellco re: 15 nod es, 28 links
1
2
3
45
6
7
8
9
10
11
12
13
14
15
c
1
: 1 – 9 –8–2–1 c
11
: 9 –10 –2–8–9
c
2
: 1 –10 –2–1 c
12
: 9 –11 –2–8–9
c
3
: 3 –13 –2–3 c
13
: 12–13 –2–8–12
c
4
: 4 – 5 –6–3–4 c
14
: 12–14 –6–3–2–8–12
c
5
: 4 –13 –2–3–4
c
6
: 6 – 7 –8–2–3–6
c
7
: 6 –12 –8–2–3–6
c
8
: 5 –15 –6–5
c
9
:7 –12 –8–7
c
10
: 8 –11 –2–8
uncorrected proof
282 Photonic Network Communications (2006) 11:277–286
A heuristic spanning-tree (HST) based cycle construction302
algorithm is then given below,303
1. Initial: for a graph G, label the degrees of all nodes; set304
the spanning-tree T=null; select the node with the305
maximum degree as the root. Add all links to Tthat are306
incident to the root.307
2. For each node ni∈T, update its degree label with the308
number of links that are incident to niand connect ni
309
with nodes not in T.310
3. Select the node with the maximum degree label in T.311
Add all links to Tthat are incident to the selected node312
and connect it with nodes not in T.313
4. Repeat steps 2–3 until all node-degree labels are zero.314
Now Tis a spanning-tree of G.315
5. Given T, construct the cycles for all chords. They form316
a cycle cover and are the required m-cycles.317
For fault localization based on m-cycles obtained by the318
HST algorithm, each chord appears in a unique m-cycle and319
thus it can be completely localized if faults occur upon such320
edges. Most edges in Tare also completely localizable for321
topologies of real telecommunication networks, although it322
is not guaranteed all the time. Therefore, the lower bound323
ratio of localizable links is324
(localizable link)% =L−N+1
L=1+1L−2¯
d,(6)
325
where
d=2NLis the average node degree of graph326
G. This lower bound shows that the ratio of localizable links327
in a graph is in inverse proportion to the average node degree.328
It implies that the HST algorithm has better performance in 329
terms of localization degree for more complex networks. 330
Examples and evaluations 331
In this section, the HST based cycle construction algorithm is 332
applied to four typical example networks (NSFNET, ARPA2, 333
SmallNet, and Bellcore). The network topologies, spanning- 334
trees, and m-cycles obtained by the HST algorithm are shown 335
in Fig. 3. The performance of the algorithm is evaluated in 336
terms of localization degree, cost, and wavelength 337
overhead. 338
Tables 1–4 enumerate all possible alarm codes and corre- 339
sponding faulty candidate sets for the four example networks, 340
respectively. Table 5 summarizes these localization results 341
and compares them with the heuristic depth-first searching 342
(HDFS) and the shortest-path Eulerian matching (SPEM) 343
algorithms reported in [11]. The comparison shows that the 344
HST algorithm has much better performance than the HDFS 345
and SPEM algorithms in terms of fault localization degree. 346
Further analyses indicate that the HST algorithm performs 347
even better in terms of localization degree for graphs with 348
larger average node degrees. More specifically, for graphs 349
with average node degree larger than 3.0, the localization 350
degrees of the HST algorithm are very close to the ideal 351
case (Iideal =1). This observation implies that such fault 352
detection and localization approaches are suitable for com- 353
plex networks (with large average node degree), and thus are 354
scalable. 355
Tabl e 1 Fault localization
results: NSFNET — HST Alarm code Fault candidate
c1c2c3c4c5c6c7c8
00000000Null
1 10–14
1 9–14
1 1 12–14
1 6–11, 9–11
1 8–9
1 1 1 9–13
1 5–7, 7–8
1 1 2–8
1 4–10
1 1 10–13
1 1 1 6–12
1 1 1 1 1 12–13
1 1–4
1 1 1 3–6
1 1 4–5
1 1 1 5–6
11–2
1 1 1 2–3
1 1 1–3
Others N/A
uncorrected proof
Photonic Network Communications (2006) 11:277–286 283
Tabl e 2 Fault localization
results: ARPA2 — HST Alarm code Fault candidate
c1c2c3c4c5
00000 Null
1 11–17, 16–19, 17–18, 18–21, 19–20, 20–21
1 6–15, 15–16
1 1 14–16
1 8–13, 13–14
1 1 8–9, 9–10, 10–11
1 1 1 11–12, 12–14
1 6–7, 7–8
1 1 1–8
1 1–4, 4–5, 5–6
1 1 1 1–2, 2–3, 3–6
Others N/A
Tabl e 3 Fault localization
results: SmallNet — HST Alarm code Fault candidate
c1c2c3c4c5c6c7c8c9c10 c11 c12 c13
0000000000 0 0 0 Null
1 9–10
1 8–10
1 8–9
1 6–10
1 5–10
1 1 1 1 7–10
1 5–6
1 4–5
1 1 1 5–9
1 3–8
1 3–4
1 1 4–9
1 2–8
1 1 1 1 7–8
1 2–3
1 1 1 1 1 1 7–9
1 1 1 3–9
1 1–6
1 1 1 6–7
11–2
1 1 1 2–7
1 1 1–7
Others N/A
The cost of the proposed scheme is measured by the num-356
ber of required monitors and reserved wavelengths for the357
m-cycles. The cost of the wavelengths is evaluated by avg,358
max, and WOHavg , as described in Section Monitoring-359
cycles and cycle construction formulation. In Table 6, the360
maximum and average numbers of reserved wavelengths in361
the network links are summarized and compared with the362
HDFS/SPEM algorithms. It shows that the numbers of both363
maximum and average reserved wavelengths for the m-cycles364
obtained by HST algorithm are larger than when performing365
HDFS and SPEM. This is the payment for the benefit in366
localization degree. Nevertheless, with DWDM technology,367
the number of wavelengths in a single link tends to become368
larger. For example, it was reported already in 2001 that 432 369
wavelengths could be multiplexed into a single fiber [16, 17]. 370
In current commercial DWDM systems, it is easy to boost the 371
number of available wavelengths in a fibre to 192 or above 372
[18]. Even for a small number of available wavelengths per 373
link, e.g., F=64, the wavelength overhead for the HST 374
algorithm is small (around 3%, see Table 6). Such overhead 375
has trivial impact on network utilization, if it is not negligible. 376
The cost of monitors is weighted by the number of moni- 377
tors for the m-cycles, i.e., the number of m-cycles (denoted 378
as M). For comparing with the monitor-per-link case, a cost 379
gain is calculated as G=(L−M)/L, where Lis the 380
number of links. The cost gains of the HST algorithm are 381
uncorrected proof
284 Photonic Network Communications (2006) 11:277–286
Tabl e 4 Fault localization
results: Bellcore — HST Alarm code Fault candidate
c1c2c3c4c5c6c7c8c9c10 c11 c12 c13 c14
0000000000 0 0 0 0 Null
1 6–14, 12–14
1 12–13
1 9–11
1 9–10
1 8–11
1 1 2–11
1 7–12
1 5–15, 6–15
1 6–12
1 1 1 1 8–12
1 6–7
1 1 7–8
1 4–13
1 4–5
1 1 5–6
1 1 1 1 3–6
1 1 3–4
1 3–13
1 1 1 2–13
1 1 1 1 1 2–3
1 1–10
1 1 2–10
11–9
1 1 1 8–9
1 11 111112–8
1 1 1–2
Others N/A
Tabl e 5 Comparison of
localization degree Network example Avg. node degree Algorithm Localization degree Max candidate set size
NSFNET 3.00 HST 1.105 2
HDFS 1.50 3
SPEM 3.00 7
ARPA2 2.38 HST 2.500 6
HDFS 3.13 6
SPEM 5.00 8
SmallNet 4.40 HST 1.000 1
HDFS 1.47 3
SPEM 3.67 6
Bellcore 3.73 HST 1.077 2
HDFS 2.15 6
SPEM 4.67 8
Tabl e 6 Comparison of
wavelength overhead
max :the maximum number of
wavelengths reserved for
monitoring in a link avg :the
average number of reserved
wavelengths for all links
WOHavg :average wavelength
overhead per link. It is
calculated as
WOHavg =avg /F,whereFis
the number of total available
wavelengths per link. In this
table WOHavg is calculated for
F=64
Network example Algorithm max avg WOHav g(%)
NSFNET HST 5 1.90 2.97
HDFS 3 1.57 2.45
SPEM 2 1.24 1.94
ARPA2 HST 3 1.60 2.50
HDFS 3 1.36 2.13
SPEM 2 1.20 1.88
SmallNet HST 6 1.95 3.05
HDFS 3 1.55 2.42
SPEM 2 1.18 1.84
Bellcore HST 8 1.96 3.06
HDFS 3 1.43 2.23
SPEM 2 1.14 1.78
uncorrected proof
Photonic Network Communications (2006) 11:277–286 285
Tabl e 7 Comparison of cost
gains
M:the number of m-cycles
M:the number of extra
monitors for achieving complete
fault localization
G:cost gain over the
monitor-per-link method
G:revised cost gain over the
monitor-per-link method under
the complete fault localization
Network example Algorithm MG(%)MM+MG(%)
NSFNET HST 8 61.9 2 10 52.4
HDFS 6 71.4 7 13 38.1
SPEM 4 80.9 15 19 9.5
ARPA2 HST 5 80.0 15 20 20.0
HDFS 4 84.0 16 20 20.0
SPEM 4 84.0 18 22 12.0
SmallNet HST 13 40.9 0 13 40.9
HDFS 8 63.6 7 15 31.8
SPEM 4 81.8 16 20 9.1
Bellcore HST 14 50.0 2 16 42.9
HDFS 6 78.6 15 21 25.0
SPEM 5 82.1 21 26 7.1
compared in Table 7 with HDFS and SPEM for the exam-382
ple networks. Because the monitor-per-link approach always383
achieves complete localization, for a fair comparison, we384
add some extra monitors for those links that cannot be fully385
localized under the HST algorithm to achieve complete local-386
ization. For example, a straightforward method would be the387
following one. If there are K2 links in a faulty candidate388
set, we assign K−1 extra monitors to K−1 of those K389
links. More efficient methods might be applied for achieving390
complete localization, e.g., using extra m-cycles. Therefore,391
the HST algorithm still has good cost gains, although the M392
values of HST are larger than HDFS and SPEM. Denote the393
number of extra monitors as M, the complete localization394
can be achieved and the cost gain calculation is revised as,395
G=(L−(M+M))L.(7)396
Revised cost gains obtained from the four example networks397
are also compared in Table 7. Again, the average node de-398
gree affects the cost gain. For graphs whose average node399
degree is 3.0 or above, the cost gain for HST is 40–52%.400
For the worst case, ARPA2, it still achieves a cost gain no401
less than 20%. Such results show that under a fair compar-402
ison, the cost gains of HST are better than those of HDFS403
and SPEM.404
The fault detection scheme in [8], as described in Section405
Introduction, placed a monitor per path. In a N-node net-406
work, typically each node has to communicate with all the407
others. Thus, the number of potential paths is N(N−1).Even408
with 50% savings of monitors (in maximum) by applying409
the proposed heuristic optimization algorithm, the number of410
required monitors is still O(N2). Clearly, the m-cycle based411
approach achieves significant cost gains in all examples com-412
pared to either the monitor-per-link or the monitor-per-path413
case.414
Conclusion415
In mesh AONs, network faults can be detected and located416
by decomposing them into monitoring-cycles (m-cycles). We417
formulated the m-cycle construction as a cycle cover prob- 418
lem with certain constraints. A heuristic spanning-tree (HST) 419
based m-cycle construction algorithm has been developed 420
and evaluated in terms of localization degree, wavelength 421
overhead, and cost gain. The proposed HST algorithm has 422
been applied to four typical networks (NSFNET, ARPA2, 423
SmallNet, and Bellcore) and compared to the previously re- 424
ported algorithms, HDFS and SPEM. The comparison results 425
show that the performance of localization degree for HST 426
algorithm is better than HDFS and SPEM. Analyses indicate 427
that the average node degree of a network plays an impor- 428
tant role in the performance of m-cycle based fault detection 429
and localization approaches. The fact that m-cycle based ap- 430
proaches can achieve better performance in networks with a 431
larger average node degree implies that such approaches are 432
suitable for complex networks and thus scalable. 433
The HST algorithm introduces more monitors than in 434
HDFS and SPEM. However, in a fair comparison of achiev- 435
ing complete localization, it has better cost gains than HDFS 436
and SPEM. Additionally, all the three m-cycle construction 437
algorithms have good cost gains over either monitor-per-link 438
or monitor-per-path case. Finally, the wavelength overheads 439
due to m-cycles are negligible in all approaches. Therefore, 440
the HST algorithm is effective and cost-efficient. 441
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Hongqing Zeng received the B. Eng.
degree in Electrical Engineering from Huaz-
hong University of Science and Technology,
Wuhan, P.R. China, in 1990. He received the
M.Sc. degree in Electrical Engineering from
Wuhan University, Wuhan, P.R. China, in
1995. He worked for Industrial and Commer-
cial Bank of China from 1995 to 2000 as a
research engineer. He wasa research engineer
499
from 2002 to 2004 in the Broadband Network Technologies Research500
Branch of Communications Research Center, Ottawa,Canada. Currently501
he is a Ph.D. candidate in Electrical Engineering, in the Department of502
Systems and Computer Engineering, Carleton University, Ottawa, Can-503
ada. His research interest is optical communication networks.504
Dr. Changcheng Huang received B. Eng. in
1985 and M.Eng. in 1988 both in Electronic
Engineering from Tsinghua University, Beij-
ing, China. He received a Ph.D. degree in
Electrical Engineering from Carleton Univer-
sity, Ottawa, Canada in 1997. He worked for
Nortel Networks, Ottawa, Canada from 1996
to 1998 where he was a systems engineering
specialist. From 1998 to 2000 he was a systems engineer and network
architect in the Optical Networking Group of Tellabs, Illinois, USA.
Since July 2000, he has been with the Department of Systems and Com-
puter Engineering at Carleton University, Ottawa, Canada where he is
currently an associate professor. Dr. Huang won the CFI new oppor-
tunity award for building an optical network laboratory in 2001. He is
currently an associate editor of IEEE Communications Letters.
505
Dr. Alex Vukovic has ove r 20 years i n
research and technology development lead-
ership in optical communications, network
architecture and thermal management ac-
quired at university, industry, and research
laboratories. Alex’s contributions involve
over 60 journal and conference papers, pat-
ents, white papers, technology roadmaps and
book chapters. In addition, Alex is an inter-
nationally recognized speaker, conference
chair, invited university lecturer, member of
numerous international research lecturer, member of numerous inter-
national research committees, industry program reviewer, scientific
committee chairman, keynote speaker and scientific authority. For his
achievements, Nortel Networks presented him with a Gold Award.
506
Currently at the Communications Research Centre (Ottawa, 507
Canada), Alex’s focus is on research leadership to verify and validate 508
network concepts and key building blocks for next generation commu- 509
nication networks. He is also an Adjunct Professor at the University of 510
Ottawa. Alex earned his M.Sc. and Ph.D. degrees from the University 511
of Belgrade, Yugoslavia, in 1987 and 1990, respectively. 512
