Joint Routing and Wavelength Allocation Subject to Absolute QoS Constraints in OBS Networks

Abstract

From the network layer perspective, the problem of burst losses is one of the most challenging problems which restrain the development of optical burst switching (OBS) networks. Indeed, OBS is a buffer-less technology and the consequent lack of guarantees for data delivery may affect significantly the quality of service (QoS) perceived by end users. To overcome these obstacles, dedicated network mechanisms and design methods are required for QoS provisioning in the network. With this end in view, in this paper, we present a traffic engineering (TE) approach to support the end-to-end traffic delivery with absolute QoS guarantees, in terms of burst losses, in an OBS network. We focus on the establishment of explicit routing paths and minimum allocation of wavelength resources in network links under the requirement that certain absolute level of burst loss probability for a given set of traffic demands is guaranteed. In this paper, we call such an off-line problem the virtual topology (VT) design problem. Since the VT design problem is NP -complete, as an alternative to the mixed integer linear programming formulation, we develop a local search heuristic algorithm to solve it. Moreover, we focus on a dynamic OBS network scenario, where the offered traffic is subject to a change. In this context, we propose an on-line VT maintenance mechanism that is responsible for traffic admission control and adaptation of the VT to traffic changes. Eventually, proposed algorithms and mechanisms for the TE-driven end-to-end QoS approach are verified both numerically and by means of network simulations for a number of network scenarios.

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Joint Routing and Wavelength Allocation subject to
Absolute QoS Constraints in OBS Networks
Mirosław Klinkowski, Pedro Pedroso, Davide Careglio, Michał Pi´ oro, and Josep Sol´ e-Pareta
Abstract—From the network layer perspective, the problem
of burst losses is one of the most challenging problems which
restrain the development of Optical Burst Switching (OBS)
networks. Indeed, OBS is a buffer-less technology and the
consequent lack of guarantees for data delivery may affect
significantly the service quality (QoS) perceived by end users.
To overcome these obstacles, dedicated network mechanisms
and design methods are required for QoS provisioning in the
network. With this end in view, in this paper we present a traffic
engineering (TE) approach to support the end-to-end traffic
delivery with absolute QoS guarantees, in terms of burst losses,
in an OBS network. We focus on the establishment of explicit
routing paths and minimum allocation of wavelength resources
in network links under the requirement that certain absolute
level of burst loss probability for a given set of traffic demands
is guaranteed. In this paper, we call such an off-line problem
the virtual topology (VT) design problem. Since the VT design
problem is NP-complete, as an alternative to the Mixed Integer
Linear Programming (MILP) formulation, we develop a Local
Search (LS) heuristic algorithm to solve it. Moreover, we focus
on a dynamic OBS network scenario, where the offered traffic
is subject to a change. In this context, we propose an on-line VT
maintenance mechanism that is responsible for traffic admission
control and adaptation of the VT to traffic changes. Eventually,
proposed algorithms and mechanisms for the TE-driven end-to-
end QoS approach are verified both numerically and by means
of network simulations for a number of network scenarios.
Index Terms—Network Design, Optical Burst Switching (OBS),
Quality of Service (QoS), Routing, Traffic Engineering (TE).
I. INTRODUCTION
O
support efficiently the transport of IP packet traffic and which
provides flexible access to the immense bandwidth of the
optical fibre and the WDM technology [2][3]. OBS achieves
sub-wavelength granularity of transmission and switching by
PTICAL Burst Switching has attracted considerable
interest as an all-optical network architecture able to
Manuscript received October 15, 2010; revised May 6, 2011; accepted
September 15, 2011. Parts of this work have been presented in [1]. This work
has been supported by the Polish Ministry of Science and Higher Education
(ref. IŁ-14300011) and by the Spanish Ministry of Science and Innovation
through the ”DOMINO” project (TEC2010-18522). Pedro Pedroso would like
to thank the Portuguese Government Entity, Fundac ¸˜ ao para a Ciˆ encia e a
Tecnologia (FCT), for the grant SFRH / BD / 36950 / 2007.
Mirosław Klinkowski is with National Institute of Telecommunications, 1
Szachowa Street, 04-894 Warsaw, Poland (e-mail: mklinkow@itl.waw.pl).
Pedro Pedroso, Davide Careglio, and Josep Sol´ e-Pareta are with the
Technical University of Catalonia, C/Jordi Girona, 1-3. 08034 Barcelona,
Catalonia, Spain (e-mail: {ppedroso,careglio,pareta}@ac.upc.edu).
Michał Pi´ oro is with the Warsaw University of Technology, 00-665 Warsaw,
Poland, and with the Lund University, P.O. Box 118, SE-22100 Lund, Sweden
(e-mail: mpp@tele.pw.edu.pl).
Copyright (c) 2011 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
assembling groups of IP packets into optical data bursts and
reserving wavelength channels in WDM links for the time
period just enough for the burst transmission.
In general, OBS is a buffer-less technology and OBS
networks belong to the class of loss networks [4]. Indeed the
bursts may contend for link resources at core switching nodes
and the contention when unresolved leads to burst losses. The
problem of burst contention is of fundamental importance in
OBS networks. A way to alleviate the problem is to make use
of wavelength converters, which allow to transmit a contending
burst on another wavelength than the one used so far [5]. By
these means, the burst is accepted as long as there are some
free wavelength resources available in the transmission link
during the burst reservation period.
The problem of burst losses has an impact on the service
quality perceived by end users. In order to guarantee certain
level of Quality (or Grade) of Service (QoS/GoS), in terms
of burst losses, wavelength resources in network links have to
be dimensioned properly [6]. The key aspect is to determine
and allocate a subset of wavelengths, from the entire set of
wavelengths available in the link, able to support offered traffic
demands [7][8]. Concurrently, bursts should be routed properly
over the network so that to avoid congestion in bottleneck
links and prevent from excessive burst losses. To the best of
our knowledge, the joint problem of routing and wavelength
allocation under QoS constraints has not been studied in
the literature; for our recent surveys on QoS mechanisms
and routing methods, the reader is referred to [9] and [10],
respectively.
In this article, we address a general problem of optimizing
routing and wavelength allocation in an OBS network subject
to given QoS constraints. To treat such a problem we take
a traffic engineering approach. In particular, we develop a
network model which is based on the non-reduced load
approximation [11] of a common OBS network loss model
[4]. The modelling assumptions result in a set of constraints
that are applied whenever routing and wavelength allocation
decisions have to be taken.
We consider that the set of routing paths and allocated
wavelengths form a Virtual Topology (VT). We focus both on
off-line routing and wavelength allocation - referred to as the
VT design problem - and on on-line VT maintenance during
the network operation. In VT design, we are looking for such
network routing that for a given offered traffic load and (strict)
absolute QoS requirements on the connection end-to-end (e2e)
burst loss probability (BLP) minimizes the number of allocated
wavelengths, i.e., the wavelength usage, in network links. We
formulate the problem as a Mixed Integer Liner Programming

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(MILP) problem and, additionally, we develop a Local Search
(LS) heuristic algorithm. Concurrently, to support network
operation, we present an on-line mechanism that is responsible
for traffic admission control and adaptation of the VT to traffic
changes. As the simulation results show, the TE-based on-line
mechanism responds to traffic changes and maintains the e2e
burst losses below certain target level for all burst flows that
are carried over the VT.
The reminder of this paper is organized as follows. In
Section II we review the literature on QoS routing in OBS
and, afterwards, we present our contributions. In Section III
we present a framework for the TE-based Absolute QoS.
In Section IV we discuss main network modelling steps. In
Section V we present a MILP formulation and the LS heuristic
algorithm for the off-line VT design problem. In Section VI
we focus on on-line VT maintenance during the network
operation. In Section VII we present numerical and simulation
results that allow us to compare the performance of proposed
methods and validate our framework. Finally, in Section VIII
we conclude obtained results.
II. RELATED WORK AND CONTRIBUTIONS
There are two general models of QoS provisioning con-
sidered in OBS networks, namely, relative QoS and absolute
QoS [9]. In the relative QoS model, the performance of a
service quality class is defined with respect to other classes
and, for instance, it is assured that the loss probability of
bursts belonging to a higher quality class is lower than the
loss probability of bursts belonging to a lower quality class.
In the absolute QoS model, a target value of a performance
metric such as, for example, an acceptable level of burst losses
is defined for a class. Although most of QoS mechanisms
proposed for OBS networks offer relative QoS guarantees
only, still absolute QoS guarantees are required by upper level
applications.
The provisioning of absolute QoS is very complicated in
OBS networks due to the lack of viable optical buffering
technologies. The solutions that allow to achieve absolute QoS
are based mainly on the use of two-way signalling [12], a burst
preemption mechanism [13], an intentional burst dropping
mechanism [14], and appropriate wavelength allocation [7][8].
For a more thorough discussion on these solutions as well as
for other references we refer to our survey [9].
The wavelength allocation (WA) approach to absolute QoS
is very attractive since it can be implemented easily in a
wavelength conversion-capable switching node. Indeed, the
mechanism is based on a logical allocation of a subset of
wavelengths, from the entire set of wavelengths in the network
link, to be accessible for bursts belonging to a given QoS class.
Upon the arrival of a burst, the wavelength reservation decision
that is taken by the node controller concerns the selection of
a wavelength from the set of allocated wavelengths. Several
wavelength allocation policies have been considered in the
literature and they differ in the way the wavelength resources
are partitioned [15]. In details, wavelengths can be either
shared between QoS classes or they are dedicated for each
individual QoS class. Moreover, the allocation is either fixed
and then it assigns particular wavelengths to a class or elastic
and in such case it specifies only the maximal acceptable
number of wavelengths that can be occupied by a class
simultaneously.
Although the WA mechanism is simple, still the key ques-
tion is how many wavelengths should be allocated in network
links so that to provide absolute QoS and, at the same time,
use the wavelength resources efficiently. For the shared-elastic
WA policy, the problem of optimized WA was studied in [7]
and [8]. The authors develop a link loss model that is used
to determine the number of wavelengths required to satisfy
certain strict burst loss probabilities for a number of QoS
classes. Since the optimization approach is very complex,
due to the nonlinearity of both the objective function and
model constraints, the authors propose a heuristic algorithm to
provide a near-optimal solution to the WA problem. Regarding
the dedicated WA policy, it involves a simpler loss model since
a QoS class does not share the wavelengths with other classes.
In this case, the Erlang B loss formula is frequently used to
estimate burst losses in a network link [7][15].
Effective network-wide QoS provisioning requires the ex-
tension of the link level QoS guarantees to the network level.
The simplest and the most common strategy considered in loss
networks assumes that the burst losses are kept below a certain
fixed level in all network links [13]. In this case, the e2e burst
loss guarantees can be achieved if the length of the longest
routing path is limited and known. An improved strategy,
which preserves from the over-provisioning of resources, is
based on the partitioning of the network into a number of
clusters and, concurrently, the application of the previous
strategy within each cluster [14]. Yet another extension to the
strategy which differ in the method the target link losses are
calculated was proposed in [7].
The network-wide QoS should be supported by network
routing and a traffic engineering method. Indeed, a properly
designed routing protocol may preserve from the selection of
overloaded links when applying proper TE rules. In general,
in OBS networks either reactive or proactive routing strategies
are considered [10]. In reactive routing, the routing decision
is taken on-line, for instance, when burst contention occurs.
Proactive routing strategies use either measurement-based or
anticipated traffic demands to optimize, usually off-line, rout-
ing decisions. In the context of absolute QoS provisioning,
proactive routing is a convenient approach since it allows
to introduce TE rules easily and, by this means, control the
distribution of traffic over the network [16].
Our recent survey on routing methods [10] shows that the
problem of routing with QoS guarantees has not been studied
widely in OBS networks. The existing solutions belong mainly
to the class of alternative (deflection) routing. These reactive-
based strategies employ adaptive methods that introduce rela-
tive QoS guarantees by the differentiation of routing decisions
with respect to the QoS class. Regarding absolute QoS, the
common assumption in the literature is of the use of shortest
path routing [7][13] and network routing has not been explored
to provide optimized solutions.
The contributions of the paper are the following. The
concept of virtualization and, in particular, the joint problem

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of routing and WA with e2e QoS guarantees has not been
considered in OBS to the best of our knowledge. Indeed,
the common solutions for the e2e QoS provisioning are
based on the shortest part routing assumption. Our framework
for the absolute QoS provisioning takes several assumptions
(as discussed in Section III) which are used to develop a
(mathematically) tractable network loss model. In this case,
the proposed optimization algorithms for off-line VT design
and on-line VT maintenance are novel. Moreover, the burst
loss models that are considered for TE differ from the models
usually applied in IP/MPLS networks (as e.g., in [17]) due
to the buffer-less transmission in OBS. Finally, the proposed
framework facilitates the control and dynamic provisioning of
resources for quality-demanding traffic in OBS.
III. TE FRAMEWORK FOR ABSOLUTE QOS
The objective of the proposed QoS framework is to provide
burst loss probability guarantees for the quality demanding
flows of bursts transmitted between pairs of source-destination
nodes in the network. We assume, such e2e BLP can be
achieved by means of a TE approach, in particular, by an
appropriate setup of routing paths, hereafter referred to as
paths, and adequate allocation of wavelengths on the links
belonging to these paths.
A. Virtual Topology
To this end, we define the Virtual Topology (VT) as a set of
explicit paths established between source-destination pairs of
nodes to route quality-demanding bursts through the network
and the set of wavelengths allocated in the links belonging to
the VT, appropriately chosen so that to satisfy some (absolute)
QoS. We consider, a (limited) number of VTs is maintained
on top of the physical OBS transport network and each VT
is dedicated to guarantee a given QoS (i.e., a given BLP
level). We assume that the wavelengths allocated to a VT are
accessible for any burst that is carried within the VT, without
respect to its origin and destination.
To alleviate the burst contention problem and to use
the transmission resources efficiently, we consider the OBS
switching nodes are capable of wavelength conversion. In
particular, within a VT a burst when transmitted can reserve
any wavelength from the set of allocated wavelengths. It is
important to distinguish the difference between the wavelength
allocation and wavelength reservation terms. The former corre-
sponds to the (logical) selection of wavelengths that are acces-
sible within a VT, the latter represents the actual assignment
of a wavelength (from the set of allocated wavelengths) to be
used to transmit a burst.
In this paper, we assume the network applies the dedicated
WA policy so that there is no sharing of wavelengths between
VTs. It is motivated by a relatively simple burst loss model
that can be derived for such policy which allows to estimate
the number of wavelengths to be allocated in the function
of offered traffic load and target BLP. Apart from that, we
assume the network operates with unsplittable (non-bifurcated)
routing. This single-path routing approach avoids the problem
of the out-of-order burst arrival [18]. Despite such choices, still
1
2
3
4
1
2
3
4
OBS
transport
network
VT1
(QoS?level) 10
-3
VT2
(QoS?level)10
-4
p1
p2
p3
p4
allocated
wavelengths
Fig. 1.Virtual Topologies in an OBS network.
the proposed framework allows to employ any other WA and
routing approach as far as appropriate TE rules for the resource
allocation within the VT design problem can be provided.
In Figure 1 we can see an example of the OBS network
with two VTs established, where two different levels of BLP
are guaranteed, respectively, 10−3and 10−4. In this network,
the burst contention will arise only within a VT and when two
or more paths are routed over the same link. This can happen
between paths p1− p2 and p3− p4 in the links connecting
nodes 2−4 and 3−2, respectively. Accordingly, thanks to the
dedicated WA for each VT, the traffic carried over a VT does
not affect the traffic carried over other VT in network links.
Eventually, we consider the best effort (BE) class of traffic
uses the spare network capacity.
B. OBS Transport Layer
At the OBS transport layer, whenever an ingress node has
a quality-demanding burst to be transmitted to a destina-
tion egress node, it selects the corresponding routing path
established within the VT with the specific QoS. Once the
data burst is ready, the node releases its control packet that
contains the information (e.g., a label) identifying the path.
After the control packet has been transmitted over the control
wavelength and the offset time has expired, the data burst is
released. Both data burst and its control packet follow the same
path within the VT.
At each intermediate node, the control packet is electrically
terminated and processed. Based on the path identifier and the
forwarding table, which contains information about VTs, the
OBS node controller identifies the VT the burst belongs to.
Accordingly, it has knowledge about the next burst hop and
the set of allocated wavelengths that the burst can access at
the output link. The controller chooses the output wavelength
based on the local resource availability.
In Fig. 2 we can see an example of the transmission of
two bursts, burst 1 and burst 2 both requiring QoS guarantees
over path 1 − 2 − 3 − 4. Node 1 sends firstly the control
packet 1 using the control wavelength λ0. Then, after the
offset time expires, burst 1 is released using currently available

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path
allocated
wavelengths
1
23
4
3 s
?
5 s
?
3 s
?
control?packet?1 ( )
burst?1 ( )
??
control?packet?1 ( )
burst?1 ( )
??
control?packet?1 ( )
burst?1 ( )
??
??
??
??
control?packet?2 ( )
burst?2 ( )
??
control?packet?2 ( )
burst?2 ( )
??
control?packet?2 ( )
burst?2 ( )
??
??
??
??
offset?time
Fig. 2. Burst transmission over a VT.
wavelength λ1 from the set of three wavelengths λ1− λ3
allocated to the VT in the link connecting node 1 and 2. At
node 2, after the processing of the control packet 1, burst 1
is transmitted over λ3(wavelength available among the set of
five allocated wavelengths). At node 3, burst 1 is transmitted
over λ2. Control packet 2 follows the same path but burst 2
uses λ2, λ3, and λ2in each link respectively.
C. Control Plane
We consider a control plane layer lays on top of the OBS
transport layer and it has all means to maintain the VTs
in the network. Among other tasks, such control plane sets
up, reconfigures, and tears down (logical) routing paths as
well as it allocates wavelengths in network links. All these
tasks are performed subject to given traffic demands and QoS
requirements and with the assistance of properly defined TE
rules.
In such a scenario, the overall network intelligence is
moved to the control plane while the OBS transport layer
is only responsible for the data burst transmission and local
burst contention resolution (as explained in Section III-B).
This approach allows to maintain the fast performance of
the OBS transport layer since only simple, local and limited
decisions are required in the OBS node controller such as,
for instance, reading the forwarding table and selecting a
wavelength from a given set. Conversely, routing decisions,
congestion notifications, connection admission control, and
protection/restoration actions are moved to the control plane.
In this context, the Generalized Multi-Protocol Label
Switching (GMPLS) technology has (potentially) all the fea-
tures to realize the OBS control plane and to provide the
required functionality. GMPLS extends the concept of MPLS
which, on the other hand, has been considered as a natural
control and provisioning solution for OBS networks within
the labelled OBS (LOBS) framework [19]. Evidently, the
adaptation of GMPLS in order to control the dynamic OBS op-
eration will require extensions in the current GMPLS protocol
stack. For instance, the GMPLS control plane should allow to
allocate the wavelength resources in individual network links
and, concurrently, update such information in the forwarding
table of the OBS node controller.
The concept of VT and the separation of global network
decisions in the control layer from local node decisions in
the OBS transport layer should facilitate the interoperability
of GMPLS and OBS. Nonetheless, such extensions are out
of the scope of this paper and are left to future studies. The
reader may refer to [20] for some preliminary ideas on this
topic.
D. Dynamic network operation
During the network operation, whenever the set of traffic
demand changes, e.g., upon acceptance of a new burst flow
connection by the admission control mechanism, we assume
the control plane has all means to update the corresponding
VT adequately. The changes in the VT may concern the
increase of the number of allocated wavelengths in congested
links, the change of the routing path, or even either partial
or complete reconfiguration of the VT. Similar actions may
be taken whenever a connection is terminated. In Section VI
we present an on-line resource provisioning mechanism which
adapts the VT, by allocating wavelength resources in network
links, whenever the admitted quality-demanding burst traffic
might violate the QoS provided within the VT.
Also, the network might be equipped with a monitoring
function at the network links so that to verify the actual BLP
statistics. In case, the burst traffic profile is such that the target
BLP is not met at a particular link, the control plane may
decide to increase the number of allocated wavelengths in the
link. In [21] we study such a monitoring mechanism which
triggers WA procedures whenever unexpected traffic peaks that
affect the provided service (i.e., QoS) levels are detected.
IV. VT MODELLING
In this Section, we define a set of TE rules that are based
on analytical modelling of the OBS network and that are used
in optimizing and maintaining a VT. The network modelling
concerns the definition of routing constraints, the estimation
of burst losses, the strategy for burst loss guarantees, and the
wavelength allocation function. These assumptions result in a
set of constraints which are taken into account in the off-line
and on-line algorithms presented in Sections V and VI.
For sake of simplicity, in this work we focus on the design
of a single VT, i.e., on the provisioning of absolute QoS
guarantees with one level of BLP in the network only. Since
our approach assumes dedicated WA in network links and, in
particular, there is no sharing of wavelength resources between
QoS classes, the formulation of the VT design problem can
be extended straightforwardly to account for multiple VTs.
A. Notation
We use G = (V,E) to denote the graph of an OBS network,
where V and E denote, respectively, the set of nodes and
the set of unidirectional links. Link e ∈ E comprises We
wavelengths. Let W = max{We: e ∈ E}.
We use the so-called path-link approach [22] for the network
flow representation of the VT model. Let P denote the set of
predefined candidate paths between source s and termination t

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nodes, where s,t ∈ V and s ̸= t. Each path p ∈ P is identified
with a subset of network links, i.e., p ⊆ E. Adequately, subset
Pe⊆ P identifies all paths that go through link e. Let δ =
max{δp : p ∈ P} be the length of the longest path in the
network, where δpis the length (in hops) of path p.
Let D denote the set of demands with QoS guaran-
tees, where each demand corresponds to a pair of source-
termination nodes. Let Pd ⊆ P denote the set of candidate
paths supporting demand d; P =∪
and a burst belonging to demand d can follow one of them.
According to [23], we assume that the traffic is characterized
by a Poisson process. Let hd= λd/µ denote the offered traffic
load for demand d ∈ D, where λdis the arrival rate and µ−1
is the mean burst holding time; for convenience, we consider
hp= hdfor p ∈ Pd. Let ρp∈ R+and ρe∈ R+denote the
offered load to path p ∈ P and the offered load to link e ∈ E,
respectively.
We maintain the following assignment of indices: e =
1,...,|E|, p = 1,...,|P|, d = 1,...,|D|, which identify,
respectively, links, paths, and demands, and w is used to count
wavelengths in link e.
d∈DPd. Each subset Pd
comprises a (small) number of paths, e.g., k shortest paths,
B. Routing
We assume that the network applies source-based routing,
i.e., the path to be followed by a burst is determined in
the source node. For all burst belonging to demand d the
selection of path p from set Pd is performed according to
decision variable xp, also referred to as the routing variable.
In this paper, we consider unsplittable (non-bifurcated/single-
path) routing, which allows to avoid out-of-order burst arrivals.
Therefore, the routing variables are binary variables and,
consequently, a burst flow is routed over path p iff xp = 1
and there is only one path p ∈ Pdsuch that xp= 1. These
assumptions result in the following routing constraints:
∑
Note that multi-path routing can be modelled easily by
assuming real-valued variables xp∈ ⟨0,1⟩,p ∈ P.
Finally, traffic ρpoffered to path p ∈ Pdis calculated as
ρp= xphd.
p∈Pdxp= 1,∀d ∈ D, and xp∈ {0,1},∀p ∈ P.
(1)
(2)
C. Burst losses
To treat the QoS provisioning problem analytically, a burst
loss model has to be developed so that to estimate the level
of burst losses in network links. A common OBS network
loss model is based on the reduced load approximation, which
applies the Erlang fixed-point calculation [4]. However, due to
its computational complexity, we assume a simplified model
based on the non-reduced load calculation [11]. In this model,
to estimate traffic load ρe offered to link e, we sum up the
traffic load ρp offered to each path p ∈ P that crosses this
link:
ρe=∑
The use of such approximation is justified by its accuracy,
particularly under low overall burst losses (below 10−2) [11].
p∈P:p∋eρp=∑
p∈P:p∋exphp,
∀e ∈ E.
(3)
The burst loss probability Lp along path p ∈ P can be
calculated as
Lp= 1 −∏
where we account for blocking probabilities Bein all links e
that belong to path p. This approximation is based on general
assumption that burst blocking events occur independently in
network links.
The blocking probability Λdof a burst belonging to demand
d ∈ D can be calculated as a weighted sum of path loss
probabilities. Hence, using (2) we have
∑
hd
The main difficulty of the above model is the calculation of
losses Bein network links, which depends highly on the burst
traffic model. Under the common in the literature assumption
of i.e.d burst arrivals, i.i.d burst durations, together with the
assumption of the full wavelength conversion capability in
network nodes and the dedicated WA policy, the Erlang B-
loss formula can be used to estimate the probability a burst is
lost in link e ∈ E:
Be(ρe,ce) =
∑ce
number of provided (allocated) wavelengths ce.
Remark: In the optimization problem in Sec. V-B we
rely on numerical approximations of function Beand its in-
verse. Therefore, any other dimensioning function that counts
for different burst traffic characteristics can be represented
straightforwardly in the formulation.
e∈p(1 − Be),
(4)
Λd=
p∈PdρpLp
=∑
p∈PdxpLp.
(5)
(ρe)ce/ce!
k=1(ρe)k/k!,
(6)
where Be is a function of offered traffic load ρe and the
D. BLP guarantees
In the framework defined in Section III, we assume that all
the bursts routed within VT are delivered with certain absolute
BLP guarantees. In particular, for each demand d ∈ D the
following constraints should hold:
Λd≤ Be2e,
where Be2edenotes the acceptable e2e BLP within the VT.
Constraints (7) may bring some difficulties when involved
into the optimization problem due to the nonlinearity of Λdin
the function of x (see (5)). In order to simplify the problem, an
alternative solution is to replace (7) by a set of more restrictive,
but treatable inequalities representing constraints on acceptable
burst blocking probabilities in network links. A particular, yet
convenient, case is when the BLP is kept below certain fixed
level Blinkat each link. In this paper we take such an approach
and, similarly as in [13], we consider Blinkto be equal to:
Blink= 1 −(1 − Be2e)1/δ.
It can be shown easily that the burst loss guarantees given by
(7) are satisfied in OBS with unsplittable routing. Using (1)-
(5), a proof consists in showing that if Be≤ Blink,∀e ∈ E,
then for each p ∈ P we have Lp ≤ Be2eand, since
for the active path q (i.e., such that xq = 1) we have
∀d ∈ D.
(7)
(8)

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Λd=∑
In the reminder of the paper, we assume Blinkis a fixed
value, the same for each link, and determined by the QoS
objectives given by Be2eand calculated according to (8).
p∈PdxpLp= Lq, it results in Λd≤ Be2e, what ends
the proof.
E. Wavelength Allocation
The last modelling step concerns the definition of the dimen-
sioning function F (·) that for given traffic load ρedetermines
the minimum number of wavelengths to be allocated in link
e so that to meet given Blinkrequirements on the BLP. Such
an estimation is given by a discontinuous, step-increasing
function
F (ρe) =⌈B−1(ρe,Blink)⌉,
where B−1(ρe,Blink) is the inverse of the Erlang B Loss
formula (6) extended to the real domain [24], and ⌈·⌉ is
the ceiling function; note that B−1(·) is (strictly) concave.
Because Blinkis a predetermined parameter, for simplicity of
presentation we skip it from the list of arguments of function
F (·).
It is convenient to define awas the maximal load supported
by w wavelengths given target blocking probability Blink,
i.e., aw = B−1(w,Blink). Note that the inverse function
B−1(w,Blink) is expressed with respect to w and Blink, on
the contrary to the inverse function used in (9).
Although there is no close formula to calculate the inverse
of (6), still we can use a line search method (see e.g., [25]) to
find the root ρ∗of function f(ρ) = Blink− B(ρ,w) so that
to approximate the value of awby aw= ρ∗for each index w,
where 0 < w ≤ W; obviously, a0= 0.
Vector a = (a0,...,aW) can be further used to determine
F (ρe) according to the following simple algorithm:
(9)
Algorithm 1 Wavelength Allocation (WA)
1: while aw< ρe& w ≤ Wedo w + +
2: if w ≤ Wethen return F ← w else return infeasibility
Algorithm 1 is a polynomial time algorithm of complexity
O(W). It is applied in the Local Search heuristic in Section
V-C and in the online resource provisioning in Section VI.
Eventually, the number of allocated wavelengths in link e ∈
E must not exceed the total number of available wavelengths
We. This capacity constraint results in the upper bound on the
offered load ρmax
e
= aWeand can be represented as:
ρe≤ ρmax
V. OFF-LINE VT DESIGN
In this Section, we address the off-line VT design problem
where a set of traffic demands is given. Such a problem
concerns a variety of network scenarios, for instance, when-
ever the VT has to be rebuilt after a failure or an update in
the network, or if there is some information available about
admitted, estimated, or long-term traffic demands [7][13] that
might be used to establish the VT, or if the VT is already
operating in the network but its resource allocation needs to
be re-optimized.
e
,
∀e ∈ E.
(10)
A. VT design optimization problem
In the off-line VT design problem we focus on the opti-
mization of the resource (i.e., wavelength) allocation in the
network. The motivation is that when minimizing the resources
allocation for the VT, there is more resources left to be used for
other classes of traffic. To this end, we define two wavelength
usage functions, namely:
1) the overall wavelength usage in the network, given by
U1(x) =∑
U2(x) = max{F(ρe(x)) : e ∈ E},
where F(·) is the wavelength allocation function defined by
(9) and ρe(x) is the link load function defined by (3).
Note that routing vector x = (x1,...,x|P|) determines the
distribution of traffic over the network and thus the traffic load
offered to network links. Consequently, in order to minimize
the usage of wavelengths in network links, x should be
optimized. Taking into account the modelling assumptions
introduced in Section IV, the off-line VT design problem can
be formulated as a non-convex optimization problem:
e∈EF(ρe(x)), and
2) the wavelength usage in the most congested link,
minimize
x
subject to
Φ(x) = f(U1(x),U2(x))
(NLP)
(1) and (10),
(11a)
where Φ(x) is a function of U1(x) and U2(x).
The difficulty of formulation NLP relies in the fact that there
is no close formula to express F (·) since no such formula
exists for the inverse of the Erlang function B−1(·). A way to
solve the problem is to substitute function F(·),e ∈ E with its
piecewise linear approximation and reformulate problem NLP
as a MILP problem.
B. MILP problem formulation
For a single link e ∈ E, whenever ρe ≤ ρmax
piecewise linear approximation of F(·) can be expressed as
F(ρe) = min{w : aw≥ ρe}, or by means of a 0-1 integer
linear programming (ILP) formulation:
∑
subject to
uew≥ ue(w+1), w = 1,...,We− 1, (12b)
u ∈ {0,1}We,
where u = (ue1,...,veWe) are decision (binary) variables and
bw= aw− aw−1for each w = 1,...,We.
In ILP1, variable uewis active whenever wavelength w in
link e is allocated and, as a result, F is the sum of all active
uew. In constraint (12a), each active variable uew increases
load budget by bwso that to achieve a value greater or equal
to ρe. Thanks to ordering constraints (12b), first F∗variables
ueware active and, therefore, we have∑
Formulation ILP1 is analogous to formulation (4.3.25) in
[22]. In [22], there is yet another formulation considered for
concave dimensioning functions, namely (4.3.24), which may
be used for modelling F(·). Although both formulations might
not be computationally equivalent [26], still they provide the
e
, the
minimize
u
F =
∑
w=1,...,Weuw
w=1,...,Weuewbw≥ ρe,
e
(ILP1)
(12a)
(12c)
w=1,...,Weuewbw=
aF∗ − a0= aF∗ ≥ ρe, where F∗is the solution to ILP1.

Page 7

7
same linear programming relaxations and bounds when used
with a MILP solver and the branch-and-bound method [27].
Indeed, our numerical experiments (not reported here) show
there is no particular gain when using one formulation or the
other. Hereafter, we make use (arbitrarily) of formulation ILP1.
Eventually, taking account all network links and introducing
routing variables, problem NLP can be reformulated as a MILP
problem. Below we present a MILP formulation with a mutli-
objective function, where the primary optimization objective is
to minimize the overall wavelength usage and the secondary
objective is to minimize the wavelength usage in the most
congested link, i.e., Φ(x) = αU1(x) + U2(x):
minimize
x
subject to
∑
ρe≤ ρmax
∑
uew≥ ue(w+1),∀e ∈ E,w = 1,...,We− 1,
Φ = α
∑
∑
w=1,...,Weuewbw≥ ρe,
∑
e∈EFe+ G
(MILP)
w=1,...,Weuew= Fe,
p∈Pdxp= 1,
p∈P:p∋ehpxp= ρe,
e
,
∀e ∈ E,
(13a)
(13b)
(13c)
(13d)
(13e)
∀d ∈ D,
∀e ∈ E,
∀e ∈ E,
∀e ∈ E,
(13f)
(13g)
(13h)
(13i)
Fe≤ G,
u ∈ {0,1}We,Fe∈ Z+,
x ∈ {0,1}|P|,ρ ∈ R|E|
∀e ∈ E,
∀e ∈ E,
+,G ∈ Z+;
where variables Fe and G represent the wavelength usage,
respectively, in link e and in the most congested link, ρ =
(ρ1,...,ρ|E|
is selected so that to give absolute priority to the overall
wavelength usage objective. The introduction of the secondary
objective will result in more balanced wavelength allocations.
Constraints (13a) count the allocated wavelengths in net-
work links. (13b) are the routing constraints. (13c) are aux-
iliary constraints of the non-reduced load calculation. (13d)
are the link capacity constraints. (13e) and (13f) result from
the 0-1 IP representation of function F (·). In particular, the
number of wavelengths allocated in link e should be such that
the maximum traffic load it can support (calculated as the
sum of active load segments bw) is greater or equal to offered
traffic load ρe. Besides, (13f) are ordering constraints, i.e., if
w wavelengths are utilized so w − 1 wavelengths are utilized
as well. Constraints (13g) are used to obtain the wavelength
allocation in the most congested link. Finally, (13h) and (13i)
are the variable range constraints.
As discussed in Section IV-E, the wavelength allocation
function F (·) comes from a concave dimensioning function.
Therefore, by applying similar arguments as in Section 4.3.3
in [22], the optimal routing solutions of MILP will be non-
bifurcated with highly unbalanced wavelength allocations in
network links. Indeed, the marginal cost of allocating a new
wavelength on the already occupied link is lower than on the
empty link due to the character of F (·).
Note that MILP is a variant of the well-known discrete
cost multicommodity flow (DCMCF) problem [22], which was
shown to be very difficult [26].
)
are auxiliary variables representing the traffic
load offered to links, and weighting factor α = W + 1
C. Local Search heuristic
As an alternative to the MILP approach, here we propose a
local search (LS) heuristic algorithm. Typically for this kind
of algorithms, the heuristic starts with a feasible solution and
it searches for improved solutions in consecutive iterations. At
each iteration a number of solutions neighboring to the so far
best solution is checked.
In the proposed algorithm we assume a neighboring solution
is achieved by means of a flip operation which concerns
a permutation of active routing paths of selected demands.
The heuristic makes use of the method proposed in [28] for
generating neighboring solutions. According, at each iteration
very long sequences of flips are considered, even while it
appears to be making things worse, in the hope that some
neighboring solution will allow to escape from the traps of
the local optimum. In the following, we discuss the algorithm
details.
Similarly as in MILP, the objective of LS is to improve
the wavelength usage defined by function Φ(x), where x =
(x1,...,x|P|
to network links and, as a consequence, the number of allo-
cated wavelengths, as discussed in Section IV. Accordingly,
Φ(x) = f(F(ρe(x))). To compute F (ρe) we apply Algorithm
1, which searches for the lowest w such that aw ≥ ρe(x).
Notice that the routing vector which results in link overload
will lead to infeasibility. In such case, we assume Φ(x) = ∞.
Let the single-flip neighborhood of routing vector x with
respect to demand d, denoted as ⌈x⌋d(q), be such vector ˆ x that
ˆ xp= 0 if xp= 1,p ∈ Pd, then ˆ xq= 1 for some q ∈ Pd,q ̸=
p, and ˆ xr= xrfor the rest of paths r ∈ P,r ̸= p,r ̸= q. Let
Ω be the set of demands that have not been yet the subject of
the flip operation during the algorithm performance; initially
Ω = D.
A feasible solution x0to start with can be found by solving
the following ILP problem:
)
is the routing vector. Clearly, Φ is a function
of x since x determines unambiguously traffic load offered
minimize
x
subject to
0
∑
x ∈ {0,1}|P|.
(ILP2)
p∈Pdxp= 1,
p∈P:p∋ehpxp≤ aWe,
∀d ∈ D,
(14a)
(14b)
(14c)
∑
∀e ∈ E,
Since the objective function of ILP2 is constant, either a
feasible routing vector that satisfies both routing (14a) and
link capacity (14b) constraints is found or a notification that
such solution does not exist is returned by the solver.
At each iteration, the main routine of the LS algorithm
generates |D| neighboring solutions. Solution xk, where
k = 1,...,|D|, is obtained as the best, among all possible
q ∈ Pd,d ∈ Ω and with respect to the usage Φ, single-flip
neighborhood xk = ⌈xk−1⌋d(q)of the vector xk−1 found
in the previous iteration. When a neighborhood is found,
the demand d that is the subject to the flip operation is
excluded from Ω. When Ω is empty, the algorithm selects,
among all xk, vector x∗such that it minimizes the usage, i.e.
x∗∈ {xk: Φ(xk) ≤ Φ(xm),0 ≤ k ≤ |D|,0 ≤ m ≤ |D|}.
If Φ(x∗) < Φ(x0), a new iteration is started with x0= x∗

Page 8

8
and Ω = D, otherwise, the algorithm terminates. Algorithm 2
presents the pseudo-code of LS.
An upper bound on the computation time of the main
routine of LS is given by O(W |E||D||P|), where W |E|
is the bound on the number of iterations at the worst-case
improvement (one per iteration) of the cost function, |D| is
the number of generated neighboring solutions, and |P| is an
upper bound on the number of single-flip candidates that are
considered in the search for a neighboring solution. Although
the complexity of this routine is polynomial in time, still the
feasibility problem ILP2 is NP-complete (see Proposition 4.2
in [22]). Nevertheless, as the results in Section VII-A show,
LS performs quickly.
Algorithm 2 Local Search (LS) Heuristic
Require: P, D
Ensure: x∗, Φ
1: x∗← solution of ILP2
2: if x∗is infeasible then
3:
return infeasibility
4: else
5:
repeat
6:
x0← x∗, Ω ← D
7:
for k = 1 to |D| do
8:
Φk← ∞
9:
for all demand d ∈ Ω do
10:
for all path q ∈ Pdsuch that xq= 0 do
11:
ˆ x ← ⌈xk−1⌋d(q)(where flip is defined as:
ˆ x ← xk−1, ˆ xq← 1, and ˆ xp← 0, where p is
the active path for demand d in xk−1)
12:
if Φ(ˆ x) ≤ Φkthen
13:
xk← ˆ x, Φk← Φ(ˆ x), dk← d
14:
end if
15:
end for
16:
end for
17:
Ω ← Ω\{dk}
18:
end for
19:
x∗← argminx∈{x1,...,x|D|}Φ(x)
20:
until Φ(x0) ≤ Φ(x∗)
21:
return x∗← x0, Φ ← Φ(x0)
22: end if
VI. ON-LINE VT MAINTENANCE
In this Section, our focus is on the e2e QoS provisioning for
quality-demanding burst traffic in a dynamic network scenario.
We assume that the QoS guarantees are achieved with the aim
of a VT which is maintained in the network.
We consider that the clients of the OBS network, such
as IP networks, send requests and notify the control plane
of the OBS network regarding the volume of the quality-
demanding data traffic which they are going to offer to the
network. In order to meet the QoS objectives and satisfy
the e2e BLP requirements for the traffic supported within
the VT, we assume there are admission control mechanisms
implemented in the network. Such mechanisms should react
both to the changes in the offered traffic load that are notified
to the control plane - we will refer to it as the Flow Admission
Control (FAC) mechanism - and during the burst assembly
process performed at the edge node - referred to as the
Admission Control (AC) mechanism. FAC is responsible for
admitting data flows from the clients of the OBS network
under the condition there are wavelength resources available
so that the traffic might be accommodated either within the
current VT or after its modification. Concurrently, AC should
take care that any excessive traffic which arrives at the OBS
ingress node and which does not comply the FAC agreement
either is sent through the OBS network as the best effort traffic
or is dropped at the ingress node.
In the following discussion, let ˜ x = (˜ x1,..., ˜ x|P|) be the
routing vector which determines single routing paths that are
used between source-termination nodes in the VT. Also, let
˜h = (˜h1,...,˜h|D|) be the vector of the burst traffic load which
is actually admitted to the VT. Without loss of generality,
we consider that the VT is already established and operating
in the network. In particular, the routing vector is obtained
either with the assistance of off-line optimization algorithms
presented in Section V or by some other method (e.g., the
shortest path algorithm). Eventually, let˜F = (˜F1,...,˜F|E|) be
the wavelength allocation vector which represents the number
of wavelengths allocated in network links within the VT. Here,
we assume that˜F is a function of vectors ˜ x and˜h (i.e.,
˜F = f˜ x,˜h
) and is determined using the model presented
in Section IV-E.
In the considered here on-line VT maintenance mechanism,
under a request of augmentation of offered burst load for
demand d (i.e., between a pair of source-termination nodes)
by volume h+
steps:
1) Letˆh = (˜h1,...,˜hd+ h+
traffic vector resulting from the actually admitted traffic
and the new burst flow request. LetˆF = f
a wavelength allocation vector required to support the
augmented traffic;
2) If at least one element of vectorˆF exceeds the link
capacity (i.e., ∃ˆFe,e ∈ E :ˆFe> We) then reject the
request
3) Else ifˆF =˜F then accept the request (˜h ←ˆh) and
maintain the VT without changes
4) Else accept the request (˜h ←ˆh) and increase the
allocation of wavelengths in the VT whenever necessary
(i.e.,˜F ←ˆF).
The control plane should also act whenever it is notified
about a diminishment of the burst flow load offered to demand
d by volume h−
mechanism:
1) Letˇh = (˜h1,...,˜hd− h−
traffic vector after the reduction of the actually admitted
traffic by h−
allocation vector required to support the diminished
traffic;
2) Accept the request (˜h ←ˇh);
3) IfˇF =˜F then maintain the VT without changes
4) Else reduce the allocation of wavelengths in the VT
()
d, the FAC mechanism performs the following
d,...,˜h|D|) be an augmented
(
˜ x,ˆh
)
be
d. In this case we consider the following
d,...,˜h|D|) be a diminished
d. Let ˇF = f(˜ x,ˇh)
be a wavelength

Page 9

9
(a)
(d)
(b)(c)
Fig. 3.Networks: a) SIMPLE6, b) RING9, c) TORUS9, d) NSF14.
whenever necessary (i.e.,˜F ←ˇF).
In Section VII-B we evaluate this VT maintenance mecha-
nism in a simulation environment of a dynamic OBS network.
Apart from modifying the number of wavelengths, more
advanced on-line mechanisms shall involve routing decisions
and, for instance, the selection of alternative single paths.
In this case, it will be advantageous, with respect to the
wavelength usage, to rely the joint routing and wavelength
assignment decisions on a modified version of optimization
algorithms discussed in Section V. Moreover, additional fea-
tures, such as fairness in the burst flow admission, might be
taken into account in FAC. Such extensions are left out of the
scope of this paper.
VII. PERFORMANCE RESULTS
A. Evaluation of off-line VT design algorithms
Here we compare the performance of off-line VT design
algorithms presented in Section V, namely, MILP and LS.
The results are obtained for SIMPLE6 (6 nodes, 16 links),
RING9 (9 nodes, 12 links), and TORUS9 (9 nodes, 36 links)
network topologies (see Figure 3). In the analyzed scenarios
we consider: each demand has |Pd| ∈ {2,4} candidate paths
(the shortest paths), each network link has W ∈ {16,32,64}
wavelengths, and Be2e= 10−3, which is an acceptable level
for the TCP traffic carried over OBS (e.g., see [29]). We use
IBM ILOG Cplex v.12.2 [30] on an Intel i3 2.27GHz 2GB
computer to solve MILP problems.
We consider non-uniformly distributed traffic matrices. Each
matrix is built by going through all demands (i.e., node pairs
s,t ∈ V with s ̸= t) and randomly generating, with equal
probability, an integer number md: 1 ≤ md≤ 10. Then, hd=
ρWmd|V|(∑
and ρ = 1 then the matrix is uniform and each node generates
to the rest of nodes the traffic load that occupies the entire
link (i.e., W wavelengths). The results are averaged over 10
randomly generated matrices.
We report both the overall wavelength usage (U1), the usage
in the most congested link (U2), the computation time (T), and
the difference in the usage (∆U1and ∆U2).
d∈Dmd
)−1, where ρ is a load factor introduced
to scale the volume of traffic. Note that if md= 1,∀d ∈ D
TABLE II
WAVELENGTH USAGE VS. NETWORK TOPOLOGY; LS ALGORITHM,
|Pd| = 2.
RING9 TORUS9Difference
W
ρ
16
0.2
32
0.3
16
0.2
32
0.3
16
0.2
32
0.3
U1
U2
247.2
15.2
490
30.4
222
10.2
396.7
19.5
11%
49%
23%
56%
1) Optimality: In Table I, in both SIMPLE6 and RING9
networks, the LS heuristic provides near-optimal solutions
that differ only slightly from the MILP ones. In most cases,
the difference in the primary optimization objective, i.e., the
overall wavelength usage (∆U1), is below 0.5%. It means
that the overhead in the wavelength allocation is below 0.5%
in average when optimizing the VT with LS (i.e., only 1
additional wavelength is required if 200 wavelengths are
allocated). This optimality gap is a bit higher (up to 2.3%)
in the scenario with lower number of wavelengths (W = 16).
Note that the secondary objective, i.e., the most congested link
usage (∆U2), is lower for LS in some scenarios.
2) Computation times: The computation times of the LS
algorithm range from several milliseconds for SIMPL6 to
about 200 milliseconds for TORUS9, and take some seconds
for a larger NSF14 network (not reported in Tables; depicted
in Figure 3). Except the dependency on the topology, no
particular dependency on other problem parameters has been
observed.
Although the solution of MILP can be found in a short
time in SIMPLE6, still it is time consuming even for relatively
small networks such as RING9 and TORUS9. It takes about 1
hour to solve MILP for RING9 if the number of wavelengths
is high (W = 64) and the offered load is low (ρ = 0.1).
For TORUS9, there is a difficulty even for a low number of
wavelengths (W = 16).
Another issue is the high memory usage that have
been observed for some problem instances for which the
Branch&Bound (B&B) tree of the MILP solver is not being
reduced significantly due to rather poor lower bounds obtained
in the solver. For instance, for TORUS9 with W = 32, ρ = 0.3
(not reported in Tables) the memory used to store the nodes
of the B&B tree is about 1GB after only 400 seconds of the
algorithm performance.
3) The impact of the number of candidate paths: In Table I,
when increasing the number of candidate paths |Pd| from 2 to
4, we can observe the wavelength usage increases as well. The
reason is that the length of the longest path in the extended
set of candidate paths is longer and, therefore, the value of
Blinkdecreases (see the modelling details in Section IV).
Consequently, more wavelengths are required to accommodate
given traffic demands.
4) The impact of topology: In Table II, we present the
wavelength usage results for two distinct network topologies,
namely, for a RING network and a highly connected TORUS
network, and the same traffic demand sets. The evaluation
shows that the overall wavelength usage is lower in the

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10
TABLE I
PERFORMANCE COMPARISON OF OFF-LINE ALGORITHMS IN TERMS OF WAVELENGTH USAGE (U1AND U2) AND TIME COMPLEXITY (T).
ScenarioMILP LSMILP vs LS
Wρ
|Pd|
U1
U2
T [sec.]
U1
U2
T [msec.]
∆U1
∆U2
SIMPLE6
16
16
32
32
32
64
64
64
0.1
0.3
0.3
0.4
0.4
0.3
0.5
0.5
2
2
2
2
4
2
2
4
86.8
160
237
289.9
296.1
378
548.2
558.3
10.7
15.6
27.5
28.5
28.6
42.8
56.3
58.2
1.25
2.07
6.16
5.03
26.8
17.5
10.0
76.6
88.8
161.6
238.3
290.8
297.3
378.6
549.8
558.7
10.1
15.5
27.1
28.4
29.8
41.2
55.4
58.7
7.9
6.3
3.1
4.6
20.3
6.4
1.5
28.1
2.3%
1.0%
0.5%
0.3%
0.4%
0.2%
0.3%
0.1%
−5.6%
−0.6%
−1.5%
−0.4%
4.2%
−3.7%
−1.6%
0.9%
RING9
16
64
64
0.2
0.1
0.3
2
2
2
246.9
371.9
785.7
15.3
23.1
49.8
25.6
3620
37.2
247.2
372.1
785.7
15.2
23.3
50
96.8
77.9
40.8
0.1%
0.1%
0%
−0.7%
0.9%
0.4%
TORUS9
16
16
0.1
0.2
2
2
160.6
218.5
6.6
9.4
1532
6787
165.5
222
7.1
10.2
201.4
154.7
3.1%
1.6%
7.6%
8.5%
highly-connected TORUS network what is an expected result
since the routing paths are shorter than in the RING network
and less link resources are occupied by transmitted bursts.
Accordingly, there may be more traffic with quality guarantees
accommodated within the VT in such a network than in a
weakly-connected network.
B. Dynamic network operation & on-line VT maintenance
In this subsection, we evaluate the performance of the on-
line VT maintenance mechanism in an OBS network with
dynamic traffic changes.
The results are obtained for NSF14 (|V| = 14 nodes, |E| =
42 links) network topology (see Figure 3). We consider that
each network link has W = 32 wavelengths.
Let the total network load (E), expressed in Erlangs, be
defined as the total traffic load that is offered by all nodes,
where each node generates traffic load that occupies ρ percents
of the link capacity, i.e., E = ρW |V|. For instance, for
ρ = 0.5, W = 32, and |V| = 14, we have 224 Erlangs of
the total network load. In the evaluation, we consider that
25% of E is the quality-demanding (HP, or High Priority)
traffic and the rest 75% is served as best-effort (BE) traffic.
The VT is initially dimensioned, using the LS algorithm
presented in Section V, to accommodate 70% of the HP traffic,
which comes from a static matrix of uniformly distributed
traffic demands that does not change during the simulation.
The remaining 30% corresponds to the requests of dynamic
traffic flows offered to the network. Such burst flow requests
arrive in average at every¯λ−1= 500 seconds and have
a mean duration of ¯ µ−1= 600 seconds for each pair of
source destination nodes. Accordingly, the average inter-arrival
time of the burst flows offered to the network is equal to
¯λ−1/(|V|(|V| − 1)) ≈ 2.74 seconds. The source and desti-
nation nodes for arriving burst flows are selected according to
a uniform distribution. The network either admits or rejects the
burst flow requests with the assistance of the VT maintenance
Fig. 4.
Erlangs.
Burst Loss Probabilities for a given demand vs. Time; E = 224
mechanism presented in Section VI. The e2e BLP of the HP
traffic supported by the VT is on the level of 10−4. If not
mentioned differently, the network load is equal to E = 224
Erlangs.
The burst loss probabilities are calculated in a cumulative
way, i.e., taking into account all bursts offered and lost in the
network until a given instant of time. The results are obtained
with a full burst preemption mechanism implemented, which
is presented in [31]. In this mechanism, we consider that the
BE bursts are allowed to use unoccupied wavelengths that are
allocated to the VT HP and be preempted whenever a HP burst
needs these resources. The simulations are executed using the
ad-hoc JAVOBS simulator [32].
In Figure 4, we present BLP results for the HP and BE
traffic obtained as a function of time. These temporal samples
are taken for a period of 7200 seconds for an (arbitrary) pair
of source-destination nodes (i.e., demand) in the network. The
VT is adapted whenever a new traffic flow arrives such that
it cannot be satisfied using the current allocated resources.
The BLP threshold is accomplished with respect to the HP
traffic. They show some small variations in HP BLP that take
place in the network due to the arrivals and departures of burst

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Fig. 5.
Erlangs.
Maximum and Average Burst Loss Probabilities vs. Time; E = 224
Fig. 6. Burst loss probability vs. Total Network Load.
traffic flows. We observe that the changes in the offered HP
traffic load do not have a significant impact on the BE BLP
results, which vary between 4.2 · 10−2and 4.9 · 10−2. This
is achieved thanks to the burst preemption mechanism which
allows to make use of the VT resources for the BE bursts.
In Figure 5, we present the BLP results and the overall
wavelength usage results obtained as a function of time. The
samples are taken again for a period of 7200 seconds. In the
Figure, the HP BLP metric represents the largest observed
e2e BLP among all the demands at each time step. Since the
observed results are below the level of 10−4, it shows that for
each demand the e2e guarantees are satisfied. The BE BLP
represents the average e2e BLP with respect to the BE traffic.
Although it can be hardly observed in the logarithmic scale, the
BE BLP results vary slightly. The overall wavelength usage,
which is expressed as a percentage of wavelengths (lambdas)
allocated to VT to the overall number of wavelengths in the
network, varies with the arrivals of quality-demanding burst
flows which cannot be served with the already allocated VT
resources. Similarly, every time a burst flow is terminated, any
excessive VT resources are released.
In Figure 6, we show the overall BLP results for the HP
and BE traffic after the performance of dynamic network
simulations. The results are obtained for different loads (E)
offered to the network. We can see that the quality guarantees
are provided for the HP traffic independently of the traffic
load. As regards the BE traffic, the BLP increases as the load
increases.
It is also worth to mention that for traffic loads above 268
TABLE III
BLOCKING PROBABILITY OF THE QUALITY-DEMANDING BURST FLOW
REQUESTS.
Load (E)224268.8313.6358.4 403.2
Blocking
0%1.6%4.23%7.5%12.42%
Erlangs we notice the blocking of some requests of dynamic
burst flows due to the lack of wavelength resources in the
network. The results for different traffic loads are presented in
Table III.
VIII. CONCLUDING REMARKS
In this paper, we present a traffic engineering approach to
the problem of end-to-end burst traffic delivery with absolute
QoS guarantees in the OBS network. In particular, we address
the off-line virtual topology design problem and the on-line
VT maintenance problem. The former concerns optimal setup
of routing paths and allocation of wavelength resources under
the requirement to guarantee certain absolute level of burst
loss probability for a set of traffic demands. Such a problem
arises whenever the VT has to be established, reconfigured,
or rebuilt. The objective of the latter is to adapt the VT
dynamically during the network operation and according to
traffic changes. We take several simple assumptions in order
to develop a treatable yet valid network model. This model
is used to formulate a set of constraints that support routing
and wavelength allocation decisions in off-line and on-line
algorithms.
For off-line VT design, we formulate a MILP problem and
we develop an LS heuristic algorithm which, as numerical
results show, is a practical and efficient alternative to MILP.
To support network operation under dynamic traffic changes,
we study a VT maintenance mechanism that is responsible
for traffic admission control and adaptation of the VT. As
the simulation results show, the TE-based on-line mechanism
responds to traffic changes and maintains the e2e burst losses
below certain target level for all burst flows that are carried
over the VT. The considered on-line VT adaptation mechanism
modifies the allocation of wavelengths only. The development
of more advance mechanisms allowing for modification of
routing paths is left for future work.
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Mirosław Klinkowski is an Assistant Professor at the Department of
Transmission and Optical Technologies at the National Institute of Telecom-
munications in Warsaw, Poland, and he is a Collaborating Researcher at the
Universitat Politecnica de Catalunya (UPC), Barcelona, Spain. He received the
M.Sc. degree from Warsaw University of Technology, Poland, in 1999 and
the Ph.D. degree from UPC in 2008. He is an author of several book chapters
and more than 65 papers presented in leading journals and conference pro-
ceedings. His research interests concentrate on algorithm design, modelling,
and optimization in communication networks.
Pedro Pedroso has graduated with distinction in Telecommunications and
Computer Engineering in 2007 at Instituto Superior das Ciencias do Trabalho
e da Empresa (ISCTE), Lisbon, Portugal and he is currently a PhD. Fellow
at the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain since
2007. His research interests include algorithm and protocol design for Future
Optical Internet Architectures.
Davide Careglio (S’05–M’06) received the M.Sc. and Ph.D. degrees
in telecommunications engineering both from Universitat Politˇ ccnica de
Catalunya (UPC), Barcelona, Spain, in 2000 and 2005, respectively, and the
Laurea degree in electrical engineering from Politecnico di Torino, Turin,
Italy, in 2001. He is currently an Associate Professor in the Department of
Computer Architecture at UPC. His research interests include algorithm and
protocol design for traffic engineering and QoS provisioning in communica-
tion networks.
Michał Pi´ oro is a professor and the head of the Computer Networks
and Switching Division at the Institute of Telecommunications at Warsaw
University of Technology (Poland), and a Full Professor at the Department of
Electrical and Information Systems at Lund University (Sweden). He received
a Ph.D. degree in telecommunications in 1979 and a D.Sc. degree in 1990,
both from the Warsaw University of Technology. In 2002 he received a
Polish State Professorship. He is an author of a well known monograph on
network optimization “Routing, Flow, and Capacity Design in Communication
and Computer Networks”, Morgan Kaufmann Publishers (2004, co-written
with Deep Medhi), and more than 150 technical papers presented in leading
journals and conference proceedings. His research interests concentrate on
modeling, design and performance evaluation of telecommunication systems,
including multi-commodity flow networks and integer programming.
Josep Sol´ e-Pareta obtained his M.Sc. degree in Telecom Engineering in
1984, and his Ph.D. in Computer Science in 1991, both from the Technical
University of Catalonia (UPC). In 1984 he joined the Computer Architecture
Department of UPC. Currently he is Full Professor with this department. He
did a Postdoc stage (summers of 1993 and 1994) at the Georgia Institute of
Technology. His publications include several book chapters and more than 100
papers in relevant research journals (> 25), and refereed international confer-
ences. His current research interests are in Nanonetworking Communications,
Traffic Monitoring and Analysis, High Speed and Optical Networking, and
Energy Efficient Transport Networks.