Content uploaded by Nagao Ogino
Author content
All content in this area was uploaded by Nagao Ogino on Aug 07, 2014
Content may be subject to copyright.
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014 467
Heuristic Computation Method for All-Optical
Monitoring Trails Terminated at Specified Nodes
Nagao Ogino and Hidetoshi Yokota, Member, IEEE
Abstract—Detecting degraded optical signal quality solely at the
terminal nodes of monitoring trails is a promising approach for
reducing the fault management cost in all-optical mesh networks.
However, this approach requires that monitoring trails are routed
so that all failures can be localized using route information for
the monitoring trails where degraded signal quality is detected.
Thus, this paper proposes a novel heuristic method to compute
the least number of monitoring trails required to localize all link
failures in an arbitrary failure scenario. In particular, the proposed
method can compute the monitoring trails terminating only at
specified nodes to which monitors can be attached. This paper
verifies the effectiveness of the proposed method by comparison
with the optimum method based on an integer programming model
and an existing heuristic method. Using the proposed method, an
accurate estimate of the least number of monitoring trails and
their routes can be computed quickly, even for practical large-scale
networks.
Index Terms—All-optical mesh network, failure localization,
heuristic optimization method, monitoring trail computation,
multiple-link failures, specified terminal nodes.
I. INTRODUCTION
ALL-OPTICAL networks can avoid electronic bottlenecks
and increase data transmission rates. They can also reduce
the network costs of optoelectronic regenerators and the oper-
ational costs of power consumption [1], [2]. Although fast fault
localization is indispensable for reliable all-optical network
operation, fault detection and localization are more complex
because detecting fault-caused degradation of signal quality is
difficult in the optical layer [3]. Clearly, all link failures can
be localized by supervising each link. However, this approach
increases the required number of monitors to the total number
of links in the managed all-optical network. Furthermore, the
attachment of monitors to all the nodes for supervising all
the links is fundamentally difficult due to various operational
constraints [4]. In order to solve the above problems, an inves-
tigation was carried out to localize link failures by detecting
degraded signal quality solely at the terminal nodes of monitor-
ing trails (m-trails) established through the managed all-optical
networks [5], [6]. The required number of monitors, i.e., the
required number of m-trails, may be reduced by supervising
only the key m-trails, instead of having one monitor for each
Manuscript received August 9, 2013; revised October 27, 2013 and December
2, 2013; accepted December 2, 2013. Date of publication December 4, 2013;
date of current version December 25, 2013.
The authors are with the KDDI R&D Laboratories, Inc., Saitama 356-8502,
Japan (e-mail: ogino@kddilabs.jp; yokota@kddilabs.jp).
Digital Object Identifier 10.1109/JLT.2013.2294015
link. All link failures to be considered may be localized by only
the m-trails terminated at the nodes to which monitors can be
attached.
All-optical m-trails must be routed so that all considered link
failures can be localized from the route information on the m-
trails where degradation of optical signal quality is detected.
Furthermore, they must be terminated at the particular nodes to
which monitors can be connected. The optimum route computa-
tion for the m-trails that satisfy the above conditions is a difficult
problem [7]. Therefore, most of the existing studies only con-
sidered m-trails for localizing all single-link failures [8]–[13].
However, the consideration of localizing multiple-link failures is
needed for the practical network operation [14], [15]. Although
the problem to localize multiple-link failures can be formulated
using an integer programming model, solving the integer pro-
gramming model is time consuming and this approach cannot be
applied to practical scale networks [16]. Recently, two heuristic
approaches have been proposed to localize shared risk link group
(SRLG) failures including multiple-link failures. However, there
is a danger in the first approach that the required number of
m-trails increases significantly when many SRLG failures must
be localized [17]. The second approach cannot compute the m-
trails terminated at specified terminal nodes to which monitors
can be attached [18]–[21].
Thus, this paper proposes a novel heuristic method for com-
puting the appropriate m-trails to localize all link failures in an
arbitrary failure scenario. In particular, the proposed method can
compute the least number of m-trails terminating only at spec-
ified terminal nodes to which monitors can be attached. The
proposed method first reduces the number of m-trails composed
of a sequence of adjacent links using an initial code swapping
(ICS) algorithm. Next, the proposed method efficiently extends
the routes for all the m-trails not terminating at the specified
terminal nodes to which monitors can be attached. Since the
proposed method starts from the set of combinations of m-trails
to localize all considered link failures, an accurate estimate of
the least number of m-trails can be obtained quickly, even when
many multiple-link failures must be localized in all-optical mesh
networks of a practical scale.
The rest of this paper is organized as follows. Section II ex-
plains the considered fault management architecture and related
work on m-trail computation as the background of this paper.
Section III formulates the problem considered in this paper using
an integer programming model. Section IV explains in detail the
proposed heuristic method to compute the m-trails terminated
at specified nodes. The effectiveness of the proposed method
is verified using a computer simulation in Section V. Finally,
Section VI concludes this paper.
0733-8724 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
468 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
Fig. 1. An example of fault management architecture.
II. FAULT MANAGEMENT SCHEME AND RELATED WORKS
A. Fault Management Architecture
Fig. 1 shows an example of the fault management architecture
considered in this paper. The managed all-optical mesh network
is comprised of bidirectional optical links. Monitors are con-
nected to several terminal nodes to which they can be attached.
Each required monitoring trail (m-trail) is established between
a pair of monitors. Each m-trail is bidirectional and separated
into two unidirectional monitoring trails (um-trails) traversing
an identical route in the opposite direction. The optical signal
quality in each m-trail is supervised by a pair of monitors that
terminate the m-trail. Thus, the number of m-trails determines
the required number of monitors, and is reflected in the monitor
cost. Each m-trail traverses an identical link only once, though it
may pass through a particular transit node multiple times. Fur-
thermore, each m-trail may terminate at an identical terminal
node.
The centralized fault management system can compute the
optimum routes of m-trails and requests the monitors to set up
the m-trails. The monitors notify the fault management system as
to which m-trails show degradation of optical signal quality. The
fault management system localizes link failures from the route
information for the m-trails where signal quality degradation is
detected. This means that the m-trails must be routed so that
all considered link failures can be localized from their route
information. According to Lemma 1 in Appendix A, at least
two m-trails must traverse each link to distinguish all pairs of a
single-link failure and a dual-link failure from each other. Thus,
the bandwidth cost for the m-trails increases compared with
supervising each link individually while the monitor cost can be
reduced thanks to the m-trails.
B. Related Work on Monitoring-Trail Computation
The monitoring structure required to localize all single-link
failures has been a key concern [7]. The concept of a monitoring
cycle (m-cycle), whose source and destination node are identi-
cal, has been proposed. The necessary and sufficient conditions
for localizing all single-link failures by simple m-cycles from
one terminal node have been derived, and the optimum place-
ment for the minimum number of terminal nodes has also been
clarified [8]. An efficient heuristic method to compute simple
m-cycles has also been proposed [9]. The optimum computation
methods based on an integer linear programming (ILP) model
have been proposed for non-simple m-cycles and for monitor-
ing paths involving simple m-cycles [10], [11]. The concept for
a more general structure called a monitoring trail (m-trail) has
been proposed. An m-trail may have different source and des-
tination nodes and may pass through the same node multiple
times. The optimum computation for m-trails was formulated
using an ILP model [12]. Since solving a large-scale ILP model
is time consuming, a heuristic method to compute sub-optimum
m-trails has also been proposed [13].
As described above, most of the existing studies have
only considered all single-link failures. Nevertheless, localiz-
ing multiple-link failures needs to be considered for practical
network operation. Although a performance anomaly localiza-
tion method in the IP networks and the optimum sequential
probing method have been proposed to localize multiple-link
failures, these methods cannot be applied to the fault manage-
ment architecture shown in Fig. 1 [4], [5]. Recently, different
fault management architecture without control plane signaling
for notification of degraded m-trails has been proposed [22].
In this architecture, each node can localize all considered link-
failures only from on-off status of m-trails passing through the
node. This architecture was also applied to fast signaling-free
failure restoration for interrupted working lightpaths in the op-
tical layer [23], [24]. However, this architecture assumes that
monitors can be attached to every node comprising the man-
aged network.
An ILP-based optimum routes selection method has been pro-
posed to deal with a dual-link failure scenario in the fault man-
agement architecture shown in Fig. 1 [16]. However, this method
cannot be applied to practical scale networks. Two heuristic ap-
proaches have also been proposed to localize shared risk link
group (SRLG) failures including multiple-link failures. The first
approach adds a new shortest m-trail if a new m-trail is re-
quired to distinguish between a pair of SRLG failures selected
sequentially [17]. The second approach starts from a set of com-
binations of m-trails to localize SRLG failures [19]–[21]. For
example, a method based on the second approach first generates
¯
d-separable combinatorial group testing (CGT) codes to local-
ize SRLG failures with up to darbitrary links and ensures the
adjacency of links traversed by each m-trail using a greedy code
swapping algorithm [19]. Recently, heuristic methods based on
the second approach have also been proposed for the m-trails
to localize adjacent link failures and sparse SRLG failures
[20], [21].
Generally, the following three primary constraints must be
satisfied in the optimum computation problem for m-trails:
CR1: The m-trails must be able to localize all link failures
involved in the considered failure scenario;
CR2: The m-trails must be composed of a sequence of adja-
cent links different from each other;
CR3: The m-trails must terminate at specified terminal nodes
to which monitors can be attached.
Although the first heuristic approach can satisfy all the above
constraints, there is the danger that the required number of
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 469
m-trails may increase significantly when many SRLG failures
must be localized [17]. In contrast, the second heuristic approach
cannot satisfy constraint CR3 although the required number
of m-trails can be reduced [19]–[21]. Although the proposed
heuristic method is based on a set of combinations of m-trails to
localize all considered link failures, it can satisfy all the above
three constraints. Furthermore, the proposed method is expected
to reduce the required number of m-trails since it starts from the
set of combinations of m-trails to localize link failures as in the
second approach.
III. PROBLEM STATEMENT
Although the proposed heuristic method can deal with arbi-
trary multiple-link failure scenarios, only two types of dual-link
failure scenarios are considered in this section. The first type
is all independent dual-link failure scenario, and the second
one is all simultaneous dual-link failure scenario [14], [15]. An
independent dual-link failure means that the second link fail-
ure occurs after the first link failure is localized. In contrast,
a simultaneous dual-link failure indicates that the second link
failure occurs prior to localization of the first link failure. The
above dual-link failures are important in the practical network
operation. For example, an independent dual-link failure corre-
sponds to occurrence of a single-link failure during the planned
outage of a link. In the all independent dual-link failure sce-
nario, all pairs of single-link failures must be discriminated to
localize outage of an arbitrary link. All pairs of a single-link
failure and a dual-link failure including a common failed link
must also be discriminated to detect occurrence of an arbitrary
single-link failure during the outage of an arbitrary link. Fur-
thermore, all pairs of two dual-link failures including a common
failed link must also be discriminated to localize all single-link
failures during the outage of an arbitrary link. In contrast, all
pairs of link failures with up to two arbitrary links must be
distinguished from each other in the all simultaneous dual-link
failure scenario.
The optimum m-trail computation problem to localize
multiple-link failures can be formulated using an integer pro-
gramming model. When an integer programming model is ap-
plied for computing the m-trails terminated at specified terminal
nodes, the managed network under consideration needs to be ex-
tended as shown in Fig. 2. The managed network is expressed as
a directed graph and each bidirectional link is separated into two
unidirectional links. In the same way, each m-trail is separated
into two um-trails traversing an identical route in the opposite
direction. First, a pair of virtual source and destination nodes is
added to the managed network as shown in Fig. 2(a). The virtual
source node is connected to each of the specified terminal nodes
using a virtual link, and each of the specified terminal nodes is
connected to the virtual destination node using a virtual link.
This means that each of the specified terminal nodes accommo-
dates two virtual links as one of the incoming links and one of
the outgoing links.
Furthermore, each node in the managed network is separated
into the same number of incoming and outgoing nodes as shown
in Fig. 2(b). An incoming node corresponds to an incoming uni-
Fig. 2. Extended network for the integer programming model. (a) Considera-
tion of specified terminal nodes. (b) Transformation of each node.
directional link and only accommodates the unidirectional in-
coming link. An outgoing node corresponds to a unidirectional
outgoing link and only accommodates the unidirectional outgo-
ing link. Each incoming node is connected to outgoing nodes
using internal links. As an exception, a pair of incoming and
outgoing nodes accommodating a pair of incoming and outgo-
ing links divided from one bidirectional link is not connected to
each other.
The symbols used in the integer programming model are
defined as follows:
lBidirectional link;
ul Unidirectional link;
nNode;
vs Virtual source node;
vd Virtual destination node;
ul(s)Starting node of unidirectional link ul;
ul(t)Terminating node of unidirectional link ul;
kIdentification of m-trail and um-trail:
Here, um-trail kindicates one of two um-trails divided from
m-trail k.
The constants and sets are defined as follows:
MAssumed maximum number of m-trails;
LSet of bidirectional links comprising the managed network;
UL Set of unidirectional links including virtual links and
internal links;
NSet of nodes;
nin Set of incoming links in node n;
nout Set of outgoing links in node n;
470 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
For example, the value of Mis set to the total number of
links in the managed network since m-trails aim to reduce the
required number of monitors less than the total number of links.
The variables are defined as follows:
Xl(k)Binary variable indicating whether m-trail k(1 ∼M)
traverses bidirectional link l(=1) or not (=0);
XUul (k)Binary variable indicating whether um-trail k(1 ∼
M) traverses unidirectional link ul (=1) or not (=0);
Yl1,l2(k)Binary variable indicating whether m-trail k(1 ∼
M) traverses at least one of two bidirectional links l1and l2(=
1), or neither bidirectional links l1nor l2(=0);
Zn(k)Integer variable indicating the voltage in node nfor
um-trail k(1 ∼M); Here, Zvs (k)=0.
The constraints in the ILP model are given as follows. First,
the following constraints hold as the route preservation rule:
ul∈vsout
XUul(k)≤1;
ul∈vdin
XUul(k)≤1;
ul∈nin
XUul(k)=
ul∈nout
XUul(k); ∀n=vs, vd ∈N
∀k=1∼M. (1)
The following constraint is necessary to prevent formation
of monitoring cycles not terminating at the virtual source and
destination nodes:
Zul(s)(k)+1≤Zul(t)(k)+A(1 −XUul(k));
∀ul ∈UL, ∀k=1∼M. (2)
Here, the constant Ahas a sufficiently large value. Thus, the
voltage in the terminating node of unidirectional link ul surely
becomes more than that in the starting node of unidirectional
link ul only if um-trail ktraverses unidirectional link ul.The
following constraint is necessary since each um-trail traverses
only either of two unidirectional links ul1and ul2comprising
one bidirectional link l:
XU ul1(k)+XU ul2(k)=Xl(k);
∀l∈L, ∀k=1∼M. (3)
The condition that m-trail ktraverses at least one of two
bidirectional links l1and l2is indicated as follows:
(Xl1(k)+Xl2(k)) /2≤Yl1,l2(k)≤Xl1(k)+Xl2(k);
∀l1∈L, ∀l2=l1∈L, ∀k=1∼M. (4)
When an m-trail passes through bi-directional link l1and
avoids bidirectional link l2or vice versa, two single-link fail-
ures (l1)and (l2)can be distinguished from each other. Thus,
the following constraint is necessary to localize all single-link
failures:
M
k=1
Xl1(k)(1−Xl2(k)) +
M
k=1
(1 −Xl1(k)) Xl2(k)>0;
∀l1∈L, ∀l2=l1∈L. (5)
When an m-trail avoids bidirectional link l1and passes
through bidirectional link l2, a single-link failure (l1)and a
dual-link failure (l1,l
2)can be distinguished from each other.
Thus, the following constraint is necessary to localize all pairs
of single-link and dual-link failures including a common failed
bidirectional link l2:
M
k=1
(1 −Xl1(k)) Xl2(k)>0;
∀l1∈L, ∀l2=l1∈L.
(5)
The left-hand side in the above constraint (5) corresponds to
the second term on the left-hand side in the constraint (5). This
means that the constraint (5) is satisfied automatically if the con-
straint (5) is satisfied. Thus, the constraint (5) can be substituted
by the constraint (5). The constraint (5) indicates that at least
one m-trail avoids an arbitrary bidirectional link l1and passes
through another arbitrary bidirectional link l2. This means that
a single-link failure (l1)and a dual-link failure (l2,l
3)can be
distinguished for every combination of three bidirectional links
l1,l
2,and l3. Thus, the constraint for localizing all pairs of a
single-link failure and a dual-link failure including no common
failed bidirectional link is also given by the constraint (5).
When an m-trail avoids both bidirectional links l1and l3and
passes through bidirectional link l2or an m-trail avoids both
bidirectional links l1and l2and passes through bidirectional link
l3, a pair of independent dual-link failures (l1,l
2)and (l1,l
3)
can be distinguished from each other. Thus, the following con-
straint is necessary to localize all pairs of independent dual-link
failures:
M
k=1
Yl1,l2(k)1−Yl1,l3(k)
+
M
k=1 1−Yl1,l2(k)Yl1,l3(k)>0;
∀l1∈L, ∀l2=l1∈L, ∀l3=l1,l2∈L.
(6)
When an m-trail passes through at least one of bidirectional
links l1and l2and avoids both bidirectional links l3and l4or
an m-trail avoids both bidirectional links l1and l2and passes
through at least one of bidirectional links l3and l4, a pair of
simultaneous dual-link failures (l1,l
2)and (l3,l
4)can be dis-
tinguished from each other. Thus, the following constraint is
necessary to localize all pairs of simultaneous dual-link fail-
ures:
M
k=1
Yl1,l2(k)1−Yl3,l4(k)
+
M
k=1 1−Yl1,l2(k)Yl3,l4(k)>0;
∀l1∈L, ∀l2=l1∈L, ∀l3=l1,l2∈L, ∀l4=l1,l2,l3∈L.
(7)
In all independent dual-link failure scenario, the above con-
straints (1)–(6) must be satisfied. In contrast, all the above con-
straints (1)–(7) must be satisfied in all simultaneous dual-link
failure scenario.
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 471
In both dual-link failure scenarios, the objective function to
be minimized is the required number of m-trails:
Obj =
M
k=1
ul∈vsout
XUul(k).(8)
The minimized value of the objective function indicates the
least number of um-trails, i.e., m-trails, and the optimum route
for the kth m-trail is given by the final values of Xl(k).The
terminal nodes of each m-trail can be also known from the
virtual links that the corresponding um-trail traverses.
In the above integer programming model, the number of bi-
nary variables Yl1,l2(k)becomes O(|L|2M), and the numbers
of constraints (6) and (7) become O(|L|3) and O(|L|4), respec-
tively. The scale of the integer programming model becomes
vast even when the scale of the managed network under con-
sideration increases slightly. Thus, a heuristic method for com-
puting sub-optimum m-trails is a prerequisite for practical scale
networks.
IV. MONITORING TRAIL COMPUTATION METHOD
This paper proposes a heuristic computation method for the
m-trails to localize all link failures when an arbitrary link fail-
ure scenario is considered. Each link comprising the managed
network is bidirectional and the m-trails are also bidirectional.
First, an initial code matrix that represents a set of possible
combinations of m-trails traversing the links is given to the pro-
posed method. The initial code matrix only satisfies constraint
CR1 shown in Section II-B. The proposed method derives a
final code matrix that indicates the routes for a reduced num-
ber of m-trails using the proposed ICS algorithm. This process
can reduce the required number of m-trails, while satisfying con-
straints CR1 and CR2 shown in Section II-B. Next, the proposed
method extends the routes for all the m-trails to the specified
terminal nodes and establishes additional m-trails between the
specified terminal nodes as necessary. Constraint CR3shownin
Section II-B can be satisfied using this process while the other
two constraints remain to be satisfied.
A. Generation of Initial Code Matrix
An initial code matrix represents a set of possible combina-
tions of m-trails to localize the considered link failures. Each
row and column of the initial code matrix corresponds to each
link and m-trail, respectively. Each element of the initial code
matrix is set to “1” when the corresponding m-trail traverses the
corresponding link, and otherwise it is set to “0.” Each row of
the initial code matrix represents the initial code temporarily as-
signed to the corresponding link. The correspondence between
each link and an initial code assigned to the link can be deter-
mined arbitrarily.
First, an appropriate initial code matrix for the considered
link failure scenario is given to the proposed method. Vari-
ous methods to generate the initial code matrix have been pro-
posed in the realm of coding theory [18]. Aiming to explain the
proposed method, this paper considers two types of all dual-
link failure scenarios, i.e., the all independent dual-link failure
Fig. 3. Explanation of necessary and sufficient condition in Theorem 1.
(a) Nonsatisfaction of the condition. (b) Satisfaction of the condition.
scenario and the all simultaneous dual-link failure scenario.
Thus, an initial code matrix for localizing all dual-link fail-
ures including all single-link failures is given to the proposed
method. A set of m-trails and the number of m-trails traversing
a link lare denoted by the symbols Pland |Pl|, respectively.
The set Plis not empty and |Pl| is more than zero. Then, the
following theorem holds.
Theorem 1: When |Pl1|=p(≥2) and |Pl2|=|Pl3|=2, the
necessary and sufficient condition for localizing two indepen-
dent dual-link failures (l1,l
2)and (l1,l
3)is that Condition 1
and the relationship |Pl1∪Pl2∪Pl3|≥p+2hold for every
combination of three different links l1,l
2, and l3. The proof of
Theorem 1 is shown in Appendix A. Condition 1 means that no
set of m-trails traversing a link is involved in and equal to any
other set of m-trails traversing another link.
Here, let us define an initial code graph aiming to visualize
the initial code matrix. In the initial code graph, each m-trail
is represented by a vertex, and each link is indicated by a line
connecting multiple vertices that correspond to m-trails travers-
ing the link. When an edge connects two vertices in the initial
code graph, the edge indicates a link traversed by two m-trails
corresponding to the two vertices. Fig. 3 illustrates the above
necessary and sufficient condition given by Theorem 1usingthe
initial code graph. In Fig. 3, the link traversed by pm-trails is
indicated by a broken line connecting pvertices. Fig. 3(a) shows
the case where only p+1 m-trails traverse three links l1,l
2, and
l3, and the necessary and sufficient condition indicated by The-
orem 1 is not satisfied. In Fig. 3(a), two dual-link failures (l1,l
2)
and (l1,l
3)cannot be discriminated. In contrast, Fig. 3(b) shows
the case where p+2 m-trails traverse the three links and the
necessary and sufficient condition is satisfied. In Fig. 3(b), two
dual-link failures (l1,l
2)and (l1,l3)can be localized.
Furthermore, the following theorem holds.
Theorem 2: When |Pl1|=|Pl2|=|Pl3|=|Pl4|=2, the
necessary and sufficient condition for localizing two simultane-
ous dual-link failures (l1,l
2)and (l3,l
4)is that the relationship
|Pl1∪Pl2∪Pl3∪Pl4|≥5holds for every combination of four
different links l1,l
2,l
3, and l4.
The proof of Theorem 2 is shown in Appendix B.
Fig. 4 shows the above necessary and sufficient condition
visualized by the initial code graph. Fig. 4(a) shows the case
where only four m-trails traverse four links l1,l
2,l
3, and l4, and
the necessary and sufficient condition indicated by Theorem 2
is not satisfied. In Fig. 4(a), two dual-link failures (l1,l
2)and
(l3,l
4)cannot be discriminated. In contrast, Fig. 4(b) and (c)
472 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
Fig. 4. Explanation of necessary and sufficient condition in Theorem 2. (a)
Nonsatisfaction of the condition. (b) and (c) Satisfaction of the condition.
Fig. 5. Procedure to generate an initial code matrix for the all independent
dual-link failure scenario.
shows the cases where five m-trails traverse the four links and the
necessary and sufficient condition is satisfied. In Fig. 4(b) and
(c), two dual-link failures (l1,l
2)and (l3,l
4)can be localized.
However, the necessary and sufficient condition indicated by
Theorem 1 is not satisfied and two dual-link failures (l1,l
2)
and (l1,l
3)cannot be discriminated in Fig. 4(b). In contrast, the
necessary and sufficient condition indicated by Theorem 1 is
also satisfied in Fig. 4(c).
1) All Independent Dual-Link Failure Scenario: For sim-
plicity, all the links are traversed by only two m-trails in the
given initial code matrix. This means that the initial code graph
corresponding to the initial code matrix includes no cycle com-
posed of less than four edges according to Theorem 1, where the
value of pis set to 2. It is known that the complete bipartite graph
Kr,r satisfies the above condition and has the minimum number
of vertices when the number of edges is given. Thus, the initial
code matrix represented by the complete bipartite graph with
the same size of two parties is given to the proposed method.
The procedure used to generate the initial code matrix is
shown in detail in Fig. 5. The symbol |L| indicates the total
number of links in the managed network. The symbol Cis a
sufficiently large value greater than the required length of the
initial codes. In Fig. 5, one vertex is alternately added to each of
two parties in the bipartite graph. An added vertex is connected
to all the existing vertices for another party. When |L| initial
codes are generated, surplus columns on the right side of the
matrix, where all the elements are kept at “0,” are deleted. When
length of initial codes is denoted by the symbol ICL (bits), the
number of links |L| that require initial codes with a length of
Fig. 6. Procedure to generate an initial code matrix for the all simultaneous
dual-link failure scenario.
ICL bits in the above procedure is given as follows:
|L|=(ICL2−1)/4ICL:odd
|L|=ICL2/4ICL:even.
From the above expression, the possible number of links
dealt with by initial codes with a length of ICL bits becomes
O(ICL2).
2) All Simultaneous Dual-Link Failure Scenario: For sim-
plicity, all the links are traversed by only two m-trails in the
given initial code matrix. This means that the initial code graph
corresponding to the initial code matrix includes no cycle com-
posed of less than five edges according to Theorems 1 and 2.
The procedure used to generate an initial code matrix is shown
in detail in Fig. 6. The symbol |L| indicates the total number of
links in the managed network. The symbol Cis a sufficiently
large value greater than the required length of the initial codes.
In Fig. 6, each vertex in the initial code graph is added sequen-
tially and connected to the previous vertex corresponding to the
left neighboring column in the initial code matrix. When the
added vertex corresponds to an odd column, the added vertex
is furthermore connected to the existing vertices provided that
no cycle composed of less than five edges is formed. Finally,
surplus columns on the right side of the matrix, where all the
elements are kept at “0,” are deleted. In the above procedure,
the number of links |L| that require initial codes with a length of
ICL bits is given as follows when the value of ICL is a multiple
of six
|L|=(ICL/2)(ICL/6+1).
From the above expression, the possible number of links
dealt with by initial codes with a length of ICL bits becomes
O(ICL2). A set of initial codes for all simultaneous dual-link
failures has also been studied as “Moore graphs of diameter 2”
[18]. In this case, the possible number of links dealt with by
initial codes with a length of ICL bits becomes O(ICL3/2).
Thus, the procedure shown in Fig. 6 is slightly more efficient
than that based on “Moore graphs of diameter 2.”
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 473
Fig. 7. Examples of initial code matrices. (a) Managed network. (b) Initial
code matrix for the all independent dual-link failure scenario. (c) Initial code
matrix for the all simultaneous dual-link failure scenario.
Fig. 7 shows examples of initial code matrices given to the
proposed method. Fig. 7(a) shows a managed network with 16
links. The specified terminal nodes are nodes 1 and 6, which are
indicated by solid black circles. Fig. 7(b) shows an initial code
matrix for localizing all independent dual-link failures in the
managed network shown in Fig. 7(a). The initial code matrix
in Fig. 7(b) is generated by the procedure shown in Fig. 5. The
required length of initial codes is eight bits. Meanwhile, Fig. 7(c)
shows an initial code matrix for localizing all simultaneous dual-
link failures in the managed network shown in Fig. 7(a). The
initial code matrix in Fig. 7(c) is generated by the procedure
shown in Fig. 6. The required length of initial codes is 11 bits.
The correspondence between each link and an initial code is only
temporary in both the initial code matrices shown in Fig. 7(b)
and (c).
B. Initial Code Swapping Algorithm
Each column in the initial code matrix indicates links that
the corresponding m-trail should traverse. However, those links
may not comprise a sequence of adjacent links in the managed
network. Generally, each column in the initial code matrix in-
cludes multiple m-trail segments, each of which is composed of
a sequence of adjacent links. For example, the first column of
the initial code matrix in Fig. 7(b) includes two m-trail segments
composed of three links (1, 2), (2, 3), and (3, 6), and composed
of a single link (7, 8), respectively. Furthermore, the latter m-
trail segment does not terminate at the specified nodes 1 and
6. In total, the number of m-trail segments is 15, and only one
Fig. 8. Procedure to derive the final code matrix.
m-trail segment terminates at the terminal nodes in the initial
code matrix shown in Fig. 7(b). As another example, the third
column of the initial code matrix in Fig. 7(c) includes two m-trail
segments composed of two links (1, 7) and (1, 8), and composed
of a single link (3, 4), respectively. Furthermore, these two m-
trail segments do not terminate at the specified nodes 1 and 6. In
totally, the number of m-trail segments is 17, and none of these
m-trail segments terminate at the terminal nodes in the initial
code matrix shown in Fig. 7(c).
An initial code matrix only represents a set of possible combi-
nations of m-trails to localize the considered link failures. This
means that the correspondence between each link and an initial
code assigned to the link can be determined arbitrarily in the
initial code matrix. The initial code matrix continues to satisfy
primary constraint CR1 even if two initial codes are selected
randomly and swapped with each other. The proposed ICS al-
gorithm reduces the total number of m-trail segments, and the
number of m-trail segments not terminating at the specified
nodes, by swapping two initial codes repeatedly. The random
code swapping (RCS) algorithm has been proposed to compute
m-trails for localizing all single-link failures [13]. In the RCS
algorithm, pairs of bitwise initial codes different at only one
digit are swapped in order to restrict the affect due to the swap-
ping. However, the initial code matrix considered in this paper
includes no pair of bitwise initial codes according to Lemma 1 in
Appendix A. Thus, the ICS algorithm selects all pairs of initial
codes as the candidates of swapping. The greedy code swapping
(GCS) algorithm has also been proposed to compute m-trails
for localizing SRLG failures [19]. The GCS algorithm selects
an appropriate code for each link from a sufficient number of
CGT codes generated separately. In contrast, the ICS algorithm
premises the least number of initial codes with a short length.
Fig. 8 shows the procedure to derive the final code matrix
using the ICS algorithm. The ICS algorithm randomly selects
two candidate initial codes for swapping and actually swaps the
two initial codes if the total number of m-trail segments (P)can
be reduced by swapping, or the number of m-trail segments not
terminating at the specified nodes (P) can be reduced, while
retaining a constant total number of m-trail segments. The ICS
algorithm finishes when the ICS is not actually executed during
474 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
Fig. 9. Examples of final code matrices. (a) Final code matrix for the all inde-
pendent dual-link failure scenario. (b) Final code matrix for the all simultaneous
dual-link failure scenario.
a given number of continuous candidate initial code selections
(Th).
Each m-trail segment in the final code matrix corresponds
to an m-trail satisfying primary constraints CR1 and CR2. As
described in the following section, the total number of m-trails
in the final code matrix (P)gives the lower bound for the final
number of required m-trails. Meanwhile, the sum of the total
number of m-trails and the number of m-trails not terminating at
the specified nodes (P+P) gives the upper bound for the final
number of required m-trails. This means that the ICS algorithm
can reduce the lower and upper bounds of the final number of
required m-trails. When all the links are traversed by two m-
trails in the initial code matrix, the upper bound for the total
number of m-trail segments is given by 2|L| where the symbol
|L| denotes the total number of links in the managed network.
Meanwhile, the lower bound for the total number of m-trail seg-
ments is ICL where the symbol ICL denotes the length of initial
codes. This means that the required number of successful initial
code swaps is limited to less than {(2|L|+1)2−ICL2}/2. The
required length of initial codes is O(|L|1/2)in the two types of
all dual-link failure scenarios considered in this paper. Thus, the
required number of successful initial code swaps is limited to
O(|L|2).
Fig. 9 shows the final code matrices derived from the initial
code matrices shown in Fig. 7. Fig. 9(a) shows the final code
Fig. 10. An example of extension and addition of m-trails
matrix derived from the initial code matrix shown in Fig. 7(b).
Four initial codes pre-assigned to links (1, 2), (2, 3), (3, 6), and
(7, 8) are re-allocated respectively to links (4, 7), (1, 2), (3, 4),
and (2, 3) through the initial code swaps. Consequently, the first
column only includes an m-trail segment composed of four links
(1, 2), (2, 3), (3, 4), and (4, 7). However, one end of this m-trail
segment does not yet terminate at the specified nodes 1 and 6.
As shown in Fig. 9(a), the total number of m-trail segments
decreases from 15 to 8 and the number of m-trail segments
not terminating at the specified nodes is reduced from 14 to 3.
Fig. 9(b) shows the final code matrix derived from the initial
code matrix shown in Fig. 7(c). Two initial codes pre-assigned
to links (1, 8) and (3, 4) are re-allocated respectively to links
(2, 7) and (2, 6) through the initial code swaps. Consequently,
the third column only includes an m-trail segment composed of
three links (1, 7), (2, 6), and (2, 7). Furthermore, this m-trail
segment terminates at the specified nodes 1 and 6. As shown in
Fig. 9(b), the total number of m-trail segments decreases from
17 to 11 and the number of m-trail segments not terminating at
the specified nodes is reduced from 17 to 8.
C. Extension and Addition of Monitoring Trails
To satisfy remaining primary constraint CR3, the proposed
method extends each m-trail not terminating at the specified
terminal nodes and establishes an additional m-trail between the
specified terminal nodes if necessary. Fig. 10 shows an example
of the extension of an m-trail and the addition of an m-trail. An
m-trail penot terminating at the terminal node is extended from
transit node n0to one of the specified terminal nodes tealong
the shortest route, e.g., the minimum hop route. When primary
constraint CR1 is violated by the extension of m-trail pe,the
proposed method establishes an additional m-trail pabetween
the specified terminal nodes. To avoid the violation of primary
constraint CR1, the additional m-trail patraverses along the
original route Laof m-trail peand avoids the extended route Le
of m-trail pe. The proposed method also localizes links lx(∈
Lx=L−Le−La)that the additional m-trail pamust avoid to
satisfy primary constraint CR1. Here, the symbol Lindicates the
set of all the links. The additional m-trail patraverses the original
route Laof m-trail pefrom terminal node t0and is extended
from transit node n0toward one of the terminal nodes taalong
the shortest route, e.g., the minimum hop route, avoiding the
extended route Leof m-trail peand the links lxthat the additional
m-trail pamust avoid.
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 475
Fig. 11. Procedure for extension and addition of m-trails.
Fig. 11 shows the procedure for the extension and addition
of m-trails. The proposed method sequentially deals with each
m-trail not terminating at the specified terminal nodes according
to [Step 1]through [Step 5]. If an m-trail in the final code matrix
is not terminated at the terminal nodes, the m-trail is extended
toward one of the terminal nodes along the shortest route, e.g.
the minimum hop route, at [Step 1]. Both ends of an m-trail are
extended when both of its two edge nodes are not the terminal
nodes. Next, at [Step 2], it is determined whether constraint CR1
remains to be satisfied or not by examining the distinguishability
of pairs of link failures involved in the considered failure sce-
nario. The pairs of link failures to be examined can be limited
on a basis of necessary conditions that the pairs of link failures
indistinguishable from each other must satisfy. When constraint
CR1 is not satisfied, an additional m-trail that traverses the orig-
inal route of the extended m-trail and avoids the extended route
of the extended m-trail is considered at [Step 3]. Next, links that
the additional m-trail must avoid are localized by examining
the distinguishability of pairs of link failures involved in the
considered failure scenario at [Step 4]. The pairs of link failures
to be examined can be restricted again on a basis of necessary
conditions that the pairs of link failures indistinguishable from
each other must satisfy. Finally, an additional m-trail is actually
established between the specified terminal nodes at [Step 5].
If the additional m-trail cannot be established, the procedure
returns to [Step 1] and the m-trail is extended toward another ter-
minal node. In practice, necessity of executing [Step 1] through
[Step 5] more than once is small because nodes with a small
degree must be the terminal nodes. For example, nodes with a
degree of k(<4) must be the terminal nodes in the dual-link
failure scenario [17]. Since the transit nodes generally have a
large degree in contrast to the terminal nodes, possibility that
a route can be found toward the terminal node is expected to
be large. The maximum number of required additional m-trails
corresponds to the number of m-trails not terminated at the spec-
ified terminal nodes in the final code matrix. Thus, the sum of
the total number of m-trails and the number of m-trails not ter-
minating at the specified terminal nodes in the final code matrix
gives the upper bound for the final number of required m-trails.
Meanwhile, the number of m-trails in the final code matrix gives
the lower bound for the final number of required m-trails.
When m-trail peis extended to one of the specified terminal
nodes, two link failures F1and F2are assumed to become
indistinguishable from each other. When the symbols P1and
P2indicate sets of m-trails traversing links involved in failures
F1and F2prior to the extension of m-trail pe, the following
expression holds from the assumption:
P1=P2→P1∪{pe}=P2.
The above expression indicates that two link failures F1and
F2become indistinguishable from each other since m-trail pe
traverses a link involved in failures F1due to its extension. The
following necessary conditions that failures F1and F2must
satisfy can be derived from the above expression:
NC1 Failure F1must include a link lecomprising the extended
route Leof m-trail pe;
NC2 Failure F1must include no link lacomprising the orig-
inal route Laof m-trail pe;
NC3 Failure F2must include a link lacomprising the original
route Laof m-trail pe;
NC4 Failure F2must include multiple links when multiple-
link failures are considered as the failure scenario.
The condition NC1 is apparently necessary from the above
expression. If the condition NC2 is not satisfied, set of m-trails
P1is invariant regardless of the extension of m-trail peand the
above expression does not hold. Thus, the condition NC2 is nec-
essary. Set of m-trails P2originally includes m-trail pefrom the
above expression. Thus, the condition NC3 is necessary. Since
P1⊂P2holds from the above expression, all m-trails passing
through links involved in failure F1traverse links involved in
failure F2. If failure F2only includes a single link, dual-link fail-
ure of the single link F2and a link involved in failure F1cannot
be discriminated from the single-link failure F2. Thus, the con-
dition NC4 is necessary. Using the above necessary conditions,
pairs of link failures to be examined at [Step 2] can be restricted.
If pairs of link failures satisfying the above necessary conditions
are distinguishable after extension of an m-trail, all pairs of link
failures are distinguishable from each other regardless of the
extension of the m-trail. In contrast, the examination at [Step 2]
is immediately finished when a pair of link failures satisfying
the above necessary conditions is found to be indistinguishable
after extension of an m-trail. In this case, an additional m-trail
is necessary and the procedure further progresses to [Step 3].
Let us consider a case where an additional m-trail pais nec-
essary since a pair of link failures F1and F2become indistin-
guishable from each other due to the extension of m-trail pe.In
this case, the following expression needs to hold after addition
of m-trail pa:
P1∪{pe}=P2→P1∪{pe} =P2∪{pa}.
The above expression means that the additional m-trail pa
must pass through no link involved in failure F1and must pass
through a link involved in failure F2. Failure F1includes a link
lecomprising the extended route Leof m-trail peaccording to
the condition NC1. Furthermore, failure F2includes a link la
476 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
comprising the original route Laof m-trail peaccording to the
condition NC3. Thus, the additional m-trail pathat traverses
the original route Laof the extended m-trail peand avoids the
extended route Leof the extended m-trail peis considered at
[Step 3]. Although the above additional m-trail pacertainly
passes through no link leinvolved in failure F1and passes
through a link lainvolved in failure F2, it may pass through a
link lx(∈Lx=L−Le−La)involved in failure F1. Each link
lxthat the additional m-trail pamust avoid can be localized
by examining the distinguishability between failures F1and F2
when the additional m-trail pais assumed to pass through the
link lx.IfapairoffailuresF1and F2is indistinguishable from
each other, the additional m-trail pamust avoid the link lx.
When failures F1and F2are indistinguishable, one necessary
condition that the pair of failures F1and F2must satisfy is added
to the conditions NC1 through NC4:
NC5: Failure F1must include a link lxcomprising neither
the extended route Leof m-trail penor the original route Laof
m-trail pe.
Based on the necessary conditions NC1 through NC5, pairs
of link failures to be examined at [Step 4] can be restricted. Ad-
ditional m-trail pacan traverse link lxif all pairs of link failures
satisfying the above five necessary conditions are distinguish-
able from each other assuming that the additional m-trail pa
traverses the link lx. In contrast, the examination is immedi-
ately finished and additional m-trail pacannot pass through link
lxwhen a pair of link failures satisfying the above five neces-
sary conditions is found to be indistinguishable from each other
assuming that the additional m-trail patraverses the link lx.At
[Step 4], all of links lx(∈Lx=L−Le−La)are sequentially
examined whether additional m-trail pacan traverse them or
not.
1) All Independent Dual-Link Failure Scenario: In the all
independent dual-link failure scenario, pairs of link failures F1
and F2satisfying the necessary conditions NC1 through NC4
are classified into the following three cases:
Case A)F1=(l1),F2=(l1,l
2):l1∈Le,l
2∈La;
Case B1) F1=(l1,l
2),F2=(l1,l
3):l1∈Le,l
2/∈La,l
3∈
La;
Case B2) F1=(l1,l
2),F2=(l1,l
3):l1∈Lx,l
2∈Le,l
3∈
La.
Only pairs of link failures F1and F2included in the above
three cases are examined at [Step 2]. Furthermore, pairs of link
failures F1and F2satisfying the necessary conditions NC1
through NC5 are given as follows:
Case C1) F1=(l1,l
2),F2=(l1,l
3):l1∈Le,l
2=lx,l
3∈La;
Case C2) F1=(l1,l
2),F2=(l1,l
3):l1=lx,l
2∈Le,l
3∈La.
Only pairs of link failures F1and F2included in the above
two cases are examined for each link lx(∈Lx=L−Le−La)
at [Step 4].
2) All Simultaneous Dual-Link Failure Scenario: In the all
simultaneous dual-link failure scenario, the following pairs of
link failures F1and F2are considered as pairs of link failures
satisfying the necessary conditions NC1 through NC4 in addition
to those for the all independent dual-link failure scenario:
Case D) F1=(l1),F2=(l2,l
3):l1∈Le,l
2∈La,l
3∈L;
Fig. 12. Examples of final computed routes for m-trails. (a) Final computed
routes for m-trails in the all independent dual-link failure scenario. (b) Final
computed routes for m-trails in the all simultaneous dual-link failure scenario.
Case E) F1=(l1,l
2),F2=(l3,l
4):l1∈Le,l
2/∈La,l
3∈
La,l
4∈L.
Only pairs of link failures F1and F2included in the above
cases A, B1, B2, D, and Eare examined at [Step 2]. Further-
more, the following pairs of link failures F1and F2are consid-
ered as pairs of link failures satisfying the necessary conditions
NC1 through NC5 in addition to those for the all independent
dual-link failure scenario:
Case FF
1=(l1,l
2),F2=(l3,l
4):l1∈Le,l
2=lx,l
3∈
La,l
4∈L.
Only pairs of link failures F1and F2included in the above
cases C1, C2, and Fare examined for each link lx(∈Lx=L−
Le−La)at [Step 4].
Fig. 12 shows the final computed routes for the m-trails that
are derived from the final code matrix shown in Fig. 9. In Fig. 12,
each column corresponds to an m-trail terminating at the spec-
ified nodes 1 and 6. Fig. 12(a) shows the final routes in the
all independent dual-link failure scenario, which are computed
from the final code matrix shown in Fig. 9(a). Three m-trails are
extended toward the specified terminal nodes, and three m-trails
are added between the specified terminal nodes since constraint
CR1 is violated by the extension of all three m-trails. Finally, the
required number of m-trails for the managed network shown in
Fig. 2(a) is 11 when the proposed method is applied. Fig. 12(b)
shows the final routes in the all simultaneous dual-link fail-
ure scenario, which are computed from the final code matrix
shown in Fig. 9(b). Eight m-trails are extended toward the spec-
ified terminal nodes, and four additional m-trails are established
between the specified terminal nodes since constraint CR1is
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 477
violated by the extension of four m-trails. Finally, the required
number of m-trails for the managed network shown in Fig. 2(a)
is 15 when the proposed method is applied.
V. EVA L U AT I O N O F PROPOSED COMPUTATION METHOD
A. Simulation Results in Small-Scale Networks
This section evaluates the proposed method in terms of small-
scale random networks with eight nodes and different node
degrees [25]. It has been shown that placement of one monitor
in each k(<d+2)-edge-connected component in the managed
network is necessary and sufficient to localize multiple-link
failures up to darbitrary links [17]. Thus, one terminal node is
specified in each k(<4)-edge-connected component involved
in the managed network in this section. This means that the
minimum terminal nodes required for the all simultaneous dual-
link failure scenario are specified in this section.
The proposed method is compared with the optimum method
and an existing heuristic method [17]. The optimum method
strictly derives the least number of m-trails by solving an integer
programming model shown in Section III. However, the small-
scale networks evaluated in this section represent the largest
network scale for which the integer programming model can
be solved in tractable time. The proposed method was executed
20 times with different random seeds for selecting pairs of initial
codes in the ICS algorithm, and the best solution was selected
for each evaluated network. The existing method was also exe-
cuted 20 times with different random seeds for selecting pairs
of link failures to be examined, and the best solution was se-
lected for each evaluated network. As will be explained in the
following section, a sufficiently improved solution can be ob-
tained empirically thanks to 20 times execution of each method.
In the proposed method, the required number of m-trails ob-
tained from the worst solution was at most 1.1 times larger than
that obtained from the best solution. Each of 20 solutions in
the proposed method was consistently better than the best so-
lution obtained from 20 times execution of the existing method
in every evaluated network. Furthermore, repetition of [Step 1]
through [Step 5] for the extension and addition of m-trails was
unnecessary in every execution of the proposed method.
Tables I–IV show the simulation results of m-trail computa-
tion. They indicate the average value calculated from each set
of five evaluated networks with an identical node degree. Each
table shows the required number of m-trails computed by the
optimum method, the proposed heuristic method, and the ex-
isting heuristic method on the MPTH field. For reference, each
table also shows the average bandwidth cost for the m-trails on
the BW.AV field. The average bandwidth cost corresponds to the
average number of m-trails traversing each link and represents
the bandwidth cost required for localizing the considered link
failures.
1) All Independent Dual-Link Failure Scenario: Tables I and
II show the simulation results of m-trail computation in the
all independent dual-link failure scenario. Table I shows the
results obtained from the final code matrix prior to the extension
and addition of m-trails. This means that Table I shows the
results in the case where all the nodes can be terminal nodes
TAB L E I
SIMULATION RESULTS IN ALL INDEPENDENT DUAL-LINK FAILURE SCENARIO
(TERMINAL NODES ARE NOT SPECIFIED)
TAB L E II
SIMULATION RESULTS IN ALL INDEPENDENT DUAL-LINK FAILURE SCENARIO
(MINIMUM TERMINAL NODES ARE SPECIFIED)
for m-trails. However, terminal nodes in the existing method
are identical to those at which the m-trails terminate in the final
code matrix of the proposed method. This is because all m-
trails only traverse one link in the existing method if all the
nodes can be terminal nodes. As shown in Table I, the proposed
heuristic method can correctly estimate the least number of m-
trails obtained using the optimum method, except for the case
where the average node degree is 2.5. The average bandwidth
cost in the proposed method is always 2.0 owing to the initial
codes generated by the procedure in Fig. 5. The required number
of m-trails in the existing method is identical to the total number
of links, and the average bandwidth cost approaches 1.0 when
the average node degree is reduced. This is because most of
the nodes become terminal nodes in the final code matrix of
the proposed method and most of the m-trails computed by the
existing method traverse only one link when the average node
degree is small.
Table II shows the final computed results in the case where
the minimum terminal nodes are specified. As shown in
Table II, the proposed heuristic method can correctly estimate
the least number of m-trails obtained using the optimum method,
except for the case where the average node degree is 2.5. The
average bandwidth cost in the proposed method is also identical
to that in the optimum method. As the average node degree in-
creases, the ratio of specified terminal nodes to the entire nodes
decreases and more extensions and additions to the m-trails are
necessary. This means that the average bandwidth cost increases
from 2.0 with the increase in the average node degree. The re-
quired number of m-trails in the existing method is reduced
from the number of links when the average node degree is 3.0
and 3.5. This is because more m-trails computed by the exist-
ing method traverse multiple links due to the restriction of the
available terminal nodes.
478 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
TABLE III
SIMULATION RESULTS IN ALL SIMULTANEOUS DUAL-LINK FAILURE SCENARIO
(TERMINAL NODES ARE NOT SPECIFIED)
TAB L E IV
SIMULATION RESULTS IN ALL SIMULTANEOUS DUAL-LINK FAILURE SCENARIO
(MINIMUM TERMINAL NODES ARE SPECIFIED)
2) All Simultaneous Dual-Link Failure Scenario: Tables III
and IV show the simulation results of m-trail computation in the
all simultaneous dual-link failure scenario. Table III shows the
results obtained from the final code matrix, assuming that all
the nodes can be terminal nodes. In the existing method, termi-
nal nodes for m-trails are specified identically to the proposed
method. As shown in Table III, the proposed heuristic method
can correctly estimate the least number of m-trails obtained us-
ing the optimum method, except for the case where the average
node degree is 2.5. The average bandwidth cost in the proposed
method is always 2.0 owing to the initial codes generated by the
procedure in Fig. 6. Table IV shows the final computed results
in the case where the minimum terminal nodes are specified.
As shown in Table IV, the proposed heuristic method can also
estimate the least number of m-trails correctly, except for the
case where the average node degree is 2.5. The average band-
width cost in the proposed method is also identical to that in
the optimum method. Clearly, the required number of m-trails
in the all simultaneous dual-link failure scenario is larger than
that in the all independent dual-link failure scenario.
B. Simulation Results in Large-Scale Networks
This section evaluates the proposed method in terms of large-
scale random networks with different numbers of nodes (N)and
average node degrees [25]. The proposed method is compared
with the existing heuristic method [17]. A terminal node is speci-
fied in each k (<4)-edge-connected component in the managed
network. The number of continuous unsuccessful code selec-
tions (Th) to finish the ICS algorithm in the proposed method
was set at approximately twice the total number of link pairs
in the managed network. The proposed and existing methods
were each executed 20 times with different random seeds, and
the best solutions were selected for each evaluated network. In
Fig. 13. Simulation results in the all independent dual-link failure scenario.
Terminal nodes are not specified for m-trails. (a) Required number of m-trails.
(b) Average bandwidth cost for m-trails.
the proposed method, the required number of m-trails obtained
from each of 20 solutions followed a distribution with a coef-
ficient of variation of about 0.025 in every evaluated network.
The least number of m-trails obtained from the best solution
approximately corresponds to the 5th percentile of this distribu-
tion. The required number of m-trails obtained from the worst
solution was about 1.1 times larger than that obtained from the
best solution. All the 20 solutions in the proposed method were
consistently better than the best solution obtained from 20 times
execution of the existing method in every evaluated network.
Repetition of [Step 1] through [Step 5] for the extension and
addition of m-trails was unnecessary in every execution of the
proposed method. A CPU with a clock rate of 2.13 GHz and
2 GB of memory were used in the evaluation.
Fig. 13–16 show the simulation results of m-trail computa-
tion. They show the results obtained from the proposed method
and the existing method using solid lines and broken lines, re-
spectively. Each plot in those figures indicates the average value
calculated from each set of ten evaluated networks with an iden-
tical number of nodes and average node degree.
1) All Independent Dual-Link Failure Scenario: Figs. 13 and
14 show the simulation results in the all independent dual-link
failure scenario. Fig. 13 shows the results obtained from the final
code matrix prior to the extension and addition of m-trails. This
means that Fig. 13 shows the results in the case where all the
nodes can be terminal nodes for m-trails. In the existing method,
terminal nodes for m-trails are specified identically to the pro-
posed method. As shown in Fig. 13(a), the required number of
m-trails can be greatly reduced from the total number of links in
the proposed method. As the average node degree increases, it
is easier for the ICS algorithm to ensure the adjacency of links
traversed by each m-trail. This causes the required number of
m-trails to increase only slowly with the increase in the average
node degree. In contrast, the required number of m-trails in the
existing method is almost identical to the total number of links
since the ratio of the terminal nodes to all the nodes is large. As
shown in Fig. 13(b), the average bandwidth cost in the proposed
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 479
Fig. 14. Simulation results in the all independent dual-link failure scenario.
Minimum terminal nodes are specified for m-trails. (a) Required number of m-
trails. (b) Average bandwidth cost for m-trails. (c) Ratio of pairs of link failures
to be examined to all pairs of link failures.
method is kept at 2.0 according to the initial codes assigned to
the links. Although the average bandwidth cost in the existing
method approaches 1.0, it increases slightly as the number of
nodes and the average node degree increase. This is because
the ratio of the terminal nodes can be reduced as the number of
nodes and the average node degree increase.
Fig. 14 shows the final computed results in the case where the
minimum terminal nodes are specified. As shown in Fig. 14(a),
the required number of m-trails (P)can be reduced from the
total number of links (|L|) in the proposed method. In contrast,
the required number of m-trails in the existing method is almost
identical to the total number of links. As shown in Fig. 14(b),
the average bandwidth cost (bw) is almost independent of the
total number of nodes. In the proposed method, the increase in
the average bandwidth cost is mitigated by the increase in the
average node degree. This is because the increase in the average
length of the m-trails (pl) becomes slower as the average node
degree increases.
Fig. 14(c) shows the ratio (R)of pairs of link failures to be
examined to all the pairs of link failures when m-trails are ex-
tended and added in the proposed method. The number of pairs
of link failures to be examined for the all independent dual-link
failure scenario is given by O(Ppl2|L|), which can be known
from cases B1, B2, C1, and C2 in Section IV.C-1). By replacing
pl with |L|bwP −1, this can be expressed as O(|L|3bw2P−1).In
contrast, the number of all the pairs of link failures is given by
O(|L|3) in the all independent dual-link failure scenario. Thus,
the ratio (R)can be given by O(bw2P−1). When the average
node degree is constant, the required number of m-trails (P)is
almost proportional to the total number of links (|L|) as shown
in Fig. 14(a). Meanwhile, the average bandwidth cost (bw)is
almost identical as shown in Fig. 14(b). Thus, the ratio (R)can
be given by O(|L|−1). This means that the ratio (R)is reduced
as the total number of nodes (N)increases where the average
node degree is constant, as shown in Fig. 14(c).
When the total number of nodes (N)is constant, the required
number of m-trails (P)is almost proportional to the total number
of links (|L|) as shown in Fig. 14(a). When the total number of
nodes (N)is constant and the average node degree is not large,
the ratio (R)can be given by O(|L|) since the average bandwidth
cost (bw) can be regarded as O(|L|), as shown in Fig. 14(b).
This means that the ratio (R)increases as the average node
degree increases. Nevertheless, the ratio (R)decreases when the
average node degree is fairly large, as shown in Fig. 14(c). This
is because the increase in the average bandwidth cost (bw) tends
to saturate when the average node degree is larger, as shown in
Fig. 14(b). The proposed method can greatly restrict the pairs
of link failures to be examined while the existing method needs
to examine all possible pairs of link failures.
In the all independent dual-link failure scenario, the number of
pairs of link failures to be examined is given by O(|L|3bw2P−1).
When the number of nodes increases under the constant average
node degree, the required number of m-trails (P)is proportional
to the total number of links (|L|) and the average bandwidth cost
(bw) is almost identical. Thus, the number of pairs of link failures
to be examined is given by O(|L|2). As shown in Section IV-B,
the computational complexity of the ICS algorithm is given by
O(|L|2). Finally, the computational complexity of the proposed
method becomes O(|L|2) in the all independent dual-link failure
scenario. In practice, the total computational time required for
executing the proposed method was approximately 300 s in the
largest evaluated networks with 100 nodes and 300 links. The
computational time required for the ICS algorithm was 200 s
and the computational time for the extension and addition of
m-trails was 100 s. Although the proposed method includes
the ICS algorithm, the total computational time required for the
proposed method was almost identical to the computational time
for the existing method thanks to the restriction of pairs of link
failures to be examined.
2) All Simultaneous Dual-Link Failure Scenario: Figs. 15
and 16 show the simulation results in the all simultaneous dual-
link failure scenario. Fig. 15 shows the results obtained from the
final code matrix, assuming that all the nodes can be terminal
nodes. In the existing method, terminal nodes for m-trails are
480 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
Fig. 15. Simulation results in the all simultaneous dual-link failure scenario.
Terminal nodes are not specified for m-trails. (a) Required number of m-trails.
(b) Average bandwidth cost for m-trails.
Fig. 16. Simulation results in the all simultaneous dual-link failure scenario.
Minimum terminal nodes are specified for m-trails. (a) Required number of m-
trails. (b) Average bandwidth cost for m-trails. (c) Ratio of pairs of link failures
to be examined to all pairs of link failures.
specified identically to the proposed method. Fig. 15 shows
the characteristics similar to Fig. 13. The required number of
m-trails in the proposed method can be greatly reduced from
the total number of links. Furthermore, it increases slowly with
the increase in the average node degree. The average bandwidth
cost in the proposed method is kept at 2.0 according to the initial
codes assigned to the links.
Fig. 16 shows the final computed results in the case where
the minimum terminal nodes are specified. Fig. 16 shows the
characteristics similar to Fig. 14. As shown in Fig. 16(a), the
required number of m-trails in the all simultaneous dual-link
failure scenario is clearly larger than that in the all indepen-
dent dual-link failure scenario shown in Fig. 14(a). However,
the required number of m-trails (P)in the proposed method can
be reduced from the total number of links (|L|). As shown in
Fig. 16(b), the average bandwidth cost (bw) is almost indepen-
dent of the total number of nodes. In the proposed method, the
average length of the m-trails (pl) increases slower and the in-
crease in the average bandwidth cost is mitigated as the average
node degree increases.
Fig. 16(c) shows the ratio (R)of pairs of link failures to
be examined to all the pairs of link failures when m-trails are
extended and added in the proposed method. The number of
pairs of link failures to be examined in the all simultaneous
dual-link failure scenario is given by O(Ppl2|L|2), which can
be known from cases Eand Fin Section IV-C.2. By replacing
pl with |L|bwP −1, this can be expressed as O(|L|4bw2P−1). In
contrast, the number of all the pairs of link failures is given by
O(|L|4) in the all simultaneous dual-link failure scenario. Thus,
the ratio (R)can be given by O(bw2P−1), and this result is
identical to that in the all independent dual-link failure scenario.
This means that the ratio (R)is reduced as the total number of
nodes (N)increases under the constant average node degree, as
shown in Fig. 16(c). Furthermore, the ratio (R)first increases
and later decreases as the average node degree increases under
the constant total number of nodes (N). The proposed method
can greatly restrict the pairs of link failures to be examined.
In the all simultaneous dual-link failure scenario, the num-
ber of pairs of link failures to be examined is given by
O(|L|4bw2P−1). When the number of nodes increases under the
constant average node degree, the required number of m-trails
(P)is proportional to the total number of links (|L|) and the
average bandwidth cost (bw) is almost identical. Thus, the num-
ber of pairs of link failures to be examined is given by O(|L|3).
Finally, the computational complexity of the proposed method
becomes O(|L|3) in the all simultaneous dual-link failure sce-
nario since the computational complexity of the ICS algorithm
is given by O(|L|2). In practice, the computational time required
for executing the proposed method was approximately 500 s in
the largest evaluated networks with 100 nodes and 300 links.
The computational time required for the ICS algorithm was
300 s and the computational time for the extension and addition
of m-trails was 200 s. Although the proposed method includes
the ICS algorithm, the total computational time required for the
proposed method was almost identical to the computational time
required for the existing method.
OGINO AND YOKOTA: HEURISTIC COMPUTATION METHOD FOR ALL-OPTICAL MONITORING TRAILS TERMINATED AT SPECIFIED NODES 481
VI. CONCLUSION
This paper proposed a novel heuristic method for computing
the least number of monitoring trails (m-trails) required to lo-
calize all link failures involved in an arbitrary failure scenario.
When an appropriate initial code matrix is given for the con-
sidered failure scenario, the proposed method can compute the
m-trails terminating at specified terminal nodes to which moni-
tors can be attached. This paper evaluated the proposed method
in terms of two types of all dual-link failure scenarios. The ade-
quacy of the proposed method was clarified by comparison with
the optimum computation method based on an integer program-
ming model. Using the proposed method, an accurate estimate
of the least number of m-trails and their routes can be computed
quickly even for practical large-scale networks.
APPENDIX
A. Proof of Theorem 1
Clearly, the necessary and sufficient condition for distinguish-
ing all single-link failures is that Pl1and Pl2are not empty and
the relationship Pl1=Pl2holds for every pair of links l1and
l2. Furthermore, the following lemma is known to give the nec-
essary and sufficient condition for discriminating a single-link
failure and a dual-link failure [17], [19].
Lemma 1: The necessary and sufficient condition for dis-
criminating all pairs of single-link and dual-link failures be-
comes that no set of m-trails traversing a link is involved in
and equal to any other set of m-trails traversing another link
(Condition 1).
This also means that at least two m-trails must traverse each
link. The following lemma can be derived concerning the num-
ber of m-trails traversing the links.
Lemma 2: The sufficient condition for localizing two arbitrary
independent dual-link failures (l1,l
2)and (l1,l
3)is that the rela-
tionship Min (|Pl1|+|Pl2|,|Pl1|+|Pl3|)≤|Pl1∪Pl2∪Pl3|
holds for every combination of three different links l1,l
2,and
l3when Condition 1 is satisfied.
Proof: Without loss of generality, the relationship |Pl1|+
|Pl2|≤|Pl1|+|Pl3| can be assumed. In this case, the relation-
ship |Pl1∪Pl2|≤|Pl1|+|Pl2|≤|Pl1∪Pl2∪Pl3|holds from
the assumed relationship. When the relationship |Pl1∪Pl2|<
|Pl1|+|Pl2|holds, at least one path traverses link l3and
neither links l1nor l2since the relationship |Pl1∪Pl2|<
|Pl1∪Pl2∪Pl3|holds. Thus, two dual-link failures (l1,l
2)
and (l1,l
3)can be discriminated. When the relationship
|Pl1∪Pl2|=|Pl1|+|Pl2|holds, no path traverses both links
l1and l2. If all paths passing through link l2traverse link l3,
Condition 1 is not satisfied. Thus, at least one path traverses link
l2and does not traverse link l3. This path does not also traverse
link l1since it traverses link l2. This means that the two dual-
link failures (l1,l
2)and (l1,l
3)can be distinguished from each
other.
Finally, the following theorem can be derived from Lemma 1
and Lemma 2.
Theorem 1: When |Pl1|=p(≥2) and |Pl2|=|Pl3|=2,
the necessary and sufficient condition for localizing two inde-
pendent dual-link failures (l1,l
2)and (l1,l
3)is that Condition
1 and the relationship |Pl1∪Pl2∪Pl3|≥p+2hold for every
combination of three different links l1,l
2,and l3.
Proof: The above condition is sufficient according to Lemma
2. Furthermore, Condition 1 is necessary according to Lemma 1.
If |Pl1∪Pl2∪Pl3|=p+1holds, link l2is traversed by one of
ppaths passing through link l1and an additional path avoiding
link l1when Condition 1 is satisfied. In the same way, link l3
is traversed by one of ppaths passing through link l1and the
additional path avoiding link l1. When a dual-link failure (l1,l
2)
occurs, all the ppaths and the additional path incur damage.
When a dual-link failure (l1,l
3)occurs, all the ppaths and the
additional path also incur damage. This means that two dual-
link failures (l1,l
2)and (l1,l
3)cannot be discriminated. Thus,
the condition |Pl1∪Pl2∪Pl3|≥p+2is also necessary.
B. Proof of Theorem 2
The following lemma holds concerning the number of m-trails
traversing the links.
Lemma 3: The sufficient condition for localizing two ar-
bitrary simultaneous dual-link failures (l1,l
2)and (l3,l
4)is
that the relationship Min (|Pl1|+|Pl2|,|Pl3|+|Pl4|)+1≤
|Pl1∪Pl2∪Pl3∪Pl4|holds for every combination of four dif-
ferent links l1,l
2,l
3,and l4.
Proof: Without loss of generality, it is assumed that the rela-
tionship |Pl1|+|Pl2|≤|Pl3|+|Pl4| holds. In this case, the rela-
tionship |Pl1∪Pl2|≤|Pl1|+|Pl2|<|Pl1∪Pl2∪Pl3∪Pl4|
holds from the above sufficient condition. Because the relation-
ship |Pl1∪Pl2|<|Pl1∪Pl2∪Pl3∪Pl4|holds, at least one
path traverses neither link l1nor l2and traverses either link l3
or l4. Thus, two dual-link failures (l1,l
2)and (l3,l
4)can be
distinguished from each other.
The following theorem can be derived from Lemma 3.
Theorem 2: When |Pl1|=|Pl2|=|Pl3|=|Pl4|=2, the
necessary and sufficient condition for localizing two simultane-
ous dual-link failures (l1,l
2)and (l3,l
4)is that the relationship
|Pl1∪Pl2∪Pl3∪Pl4|≥5holds for every combination of four
different links l1,l
2,l
3,and l4.
Proof: The above condition is sufficient according to Lemma
3. When |Pl1∪Pl2∪Pl3∪Pl4|=4holds, let us denote the
four m-trails passing through four links l1,l
2,l
3,and l4by
p1,p
2,p
3,and p4respectively. When link l1is traversed by m-
trails p1and p2and link l2is traversed by m-trails p3and p4,
all the four m-trails p1,p
2,p
3,and p4incur damage due to the
dual-link failure (l1,l
2). When link l3is traversed by m-trails
p2and p3and link l4is traversed by m-trails p4and p1, all the
four m-trails p1,p
2,p
3,and p4also incur damage due to the
dual-link failure (l3,l
4). This means that two dual-link failures
(l1,l
2)and (l3,l
4)cannot be discriminated. Thus, the condition
|Pl1∪Pl2∪Pl3∪Pl4|≥5is necessary.
ACKNOWLEDGMENT
The authors would like to thank Dr. Nakajima, President and
CEO, and Dr. Ano, Executive Director of KDDI R&D Labora-
tories, Inc., for their encouragement throughout the study.
482 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 3, FEBRUARY 1, 2014
REFERENCES
[1] M. W.Maeda, “Management and control of transparent optical networks,”
IEEE J. Sel. Areas Commun., vol. 16, no. 7, pp. 1008–1023, Sep. 1998.
[2] K. Sato, “Recent developments in and challenges of photonic networking
technologies,” IEICE Trans. Commun., vol. E90-B, no. 3, pp. 454–467,
Mar. 2007.
[3] C. Mas, I. Tomkos, and O. K. Tonguz, “Failure location algorithm for
transparent optical networks,” IEEE J. Sel. Areas Commun, vol. 23, no. 8,
pp. 1508–1519, Aug. 2005.
[4] P. Barford, N. Duffield, A. Ron, and J. Sommers, “Network performance
anomaly detection and localization,” in Proc. IEEE INFOCOM, Apr. 2009,
pp. 1377–1385.
[5] Y. Wen, V. W. S. Chan, and L. Zheng, “Efficient fault diagnosis algo-
rithms for all-optical WDM networks with probabilistic link failures,” J.
Lightwave Technol., vol. 23, no. 10, pp. 3358–3371, Oct. 2005.
[6] N. J. A. Harvey, M. Patrascu, Y. Wen, S. Yekhanin, and V. W. S. Chan,
“Non-adaptive fault diagnosis for all-optical networks via combinatorial
group testing on graphs,” in Proc. IEEE INFOCOM, May 2007, pp. 697–
705.
[7] B. Wu, P.-H. Ho, K. L. Yeung, J. Tapolcai, and H. T. Mouftah, “Optical
layer monitoring schemes for fast link localization in all-optical networks,”
IEEE Commun. Surveys Tuts., vol. 13, no. 1, pp. 114–125, Jan./Apr. 2011.
[8] S. S. Ahuja, S. Ramasubramanian, and M. Krunz, “Single-link failure
detection in all-optical networks using monitoring cycles and paths,”
IEEE /ACM Trans. Netw., vol. 17, no. 4, pp. 1080–1093, Aug. 2009.
[9] B. Wu, K. L. Yeung, B. Hu, and P.-H. Ho, “M2-CYCLE: An optical layer
algorithm for fast link failure detection in all-optical mesh networks,”
Elsevier Comput. Netw., vol. 55, no. 3, pp. 748–758, Feb. 2011.
[10] B. Wu, K. L. Yeung, and P.-H. Ho, “Monitoring cycle design for fast
link failure localization in all-optical mesh networks,” IEEE J. Lightwave
Technol., vol. 27, no. 10, pp. 1392–1401, May 2009.
[11] N. Ogino and H. Nakamura, “All-optical monitoring path computation
based on lower bounds of required number of paths,” in Proc. IEEE Int.
Conf. Commun., Jun. 2011, pp. 1–6.
[12] B. Wu, P.-H. Ho, and K. L. Yeung, “Monitoring trail: On fast link fail-
ure localization in all-optical WDM mesh networks,” IEEE J. Lightwave
Technol., vol. 27, no. 18, pp. 4175–4185, Sep. 2009.
[13] J. Tapolcai, B. Wu, and P.-H. Ho, “On monitoring and failure localization
in mesh all-optical networks,” in Proc. IEEE INFOCOM, Apr. 2009,
pp. 1008–1016.
[14] S. S. Lumetta and M. Medard, “Towards a deeper understanding of link
restoration algorithms for mesh networks,” in Proc. IEEE INFOCOM,
Apr. 2001, pp. 367–375.
[15] M. Clouqueur and W. D. Grover, “Availability analysis of span-restorable
mesh networks,” IEEE J. Sel. Areas Commun., vol. 20, no. 4, pp. 810–821,
May 2002.
[16] W. Ni, C. Huang, J. Wu, Q. Li, and J. M. Savoie, “Optimizing the moni-
toring path design for independent dual failure,” in Proc. IEEE Int. Conf.
Commun., Jun. 2012, pp. 3056–3060.
[17] S. S. Ahuja, S. Ramasubramanian, and M. Krunz, “SRLG failure localiza-
tion in optical networks,” IEEE Trans. Netw., vol. 19, no. 4, pp. 989–999,
Aug. 2011.
[18] W. H. Kautz and R. C. Singleton, “Nonrandom binary superimposed
codes,” IEEE Trans. Inf. Theory, vol. 10, no. 4, pp. 363–373, Oct. 1964.
[19] J. Tapolcai, P.-H. Ho, L. Ronyai, P. Babarczi, and B. Wu, “Failure lo-
calization for shared risk link groups in all-optical mesh networks using
monitoring trails,” IEEE J. Lightwave Technol., vol. 29, no. 10, pp. 1597–
1806, May 2011.
[20] P. Babarczi, J. Tapolcai, and P.-H. Ho, “Adjacent link failure localization
with monitoring trails in all-optical mesh networks,” IEEE /ACM Trans.
Netw., vol. 19, no. 3, pp. 907–920, Jun. 2011.
[21] P. Babarczi, J. Tapolcai, and P.-H. Ho, “SRLG failure localization with
monitoring trails in all-optical mesh networks,” in Proc. IEEE 8th Int.
Workshop Des. Reliable Commun. Netw., Oct. 2011, pp. 188–195.
[22] J. Tapolcai, P.-H. Ho, L. Ronyai, and B. Wu, “Network-wide local
unambiguous failure localization (NWL-UFL) via monitoring trails,”
IEEE /ACM Trans. Netw., vol. 20, no. 6, pp. 1762–1773, Dec. 2012.
[23] J. Tapolcai, P.-H. Ho, P. Babarczi, and L. Ronyai, “On achieving all-optical
failure restoration via monitoring trails,” in Proc. IEEE INFOCOM,Apr.
2013, pp. 380–384.
[24] J. Tapolcai, P.-H. Ho, P. Babarczi, and L. Ronyai, “On signaling-free
failure dependent restoration in all-optical mesh networks,” IEEE /ACM
Trans. Netw., to be published.
[25] B. M. Waxman, “Routing of multipoint connections,” IEEE J. Sel. Areas
Commun., vol. 69, no. 9, pp. 1617–1622, Dec. 1988.
Nagao Ogino (M’96) received the B.E., M.E., and Dr. Eng. degrees from the
University of Tokyo, Tokyo, Japan, in 1977, 1979, and 1982, respectively. He
joined the Research and Development Laboratories of Kokusai Denshin Denwa
Company Ltd. (currently KDDI Corporation), Tokyo, Japan, in 1982. Since
1982, he has been engaged in research on ATM networks, intelligent networks,
and telecommunication software engineering. He was a Supervisor of the Adap-
tive Communications Research Laboratories at the ATR Institute, Kyoto, Japan,
from 1996 until 2000, where he was engaged in research on multiagent-based
adaptive communication systems. He is currently an R&D Manager of the Com-
munications Network Planning Laboratory at KDDI R&D Laboratories, Inc.,
and a Guest Professor at the University of Electro-Communications, Tokyo,
Japan. His current interests include traffic engineering and optimization in fu-
ture network.
Hidetoshi Yokota received the B.E., M.E., and Ph.D. degrees from Waseda
University, Tokyo, Japan, in 1990, 1992, and 2003, respectively. He began
working for KDDI R&D Laboratories, Inc., Japan, in 1992. From 1995 to 1996,
he was with SRI International, in Menlo Park, CA, USA, as an International
Fellow. He received the IEICE Young Engineer Award, the IPSJ Yamashita
SIG Research Award, and the IPSJ Best Paper Award in 1998, 2005, and 2006,
respectively. His current research interests include mobile communications and
software defined networks. He is also involved with several standardization
activities including 3GPP, NFV, and IETF.
