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Pre-print
Mathematical Analysis of Wavelength-Based QoS Management in Optical Burst
Switched Networks
Ali Rajabi 1, Aresh Dadlani 1,2, Ahmad Kianrad 2, Ahmad Khonsari 2,1, Farzaneh Varaminian 2
1IPM School of Computer Science
Niavaran Square, Tehran, Iran.
2University of Tehran, ECE Department
North Karegar Avenue, Tehran, Iran.
{alirajabi, a.dadlani, ak}@ipm.ir, {a.kianrad, f.varaminian}@ece.ut.ac.ir
Abstract
With increase in time-critical applications over the In-
ternet, the need for differentiating services has become a
major endeavor in research communities. One promising
paradigm proposed to support such traffic diversity in the
next-generation Internet is Optical Burst Switching (OBS).
In the literature, two simple but efficient approaches namely,
threshold and wavelength-based techniques have been in-
vestigated under the resource allocation-based QoS man-
agement scheme as solutions to overcome the bandwidth
requirement in the backbone. However, to the best of our
knowledge, the wavelength-based technique has not been
analytically studied for any arbitrary number of service
classes. In this paper, we generalize the wavelength-based
technique to support any number of classes. Firstly, we
present a novel mathematical model for the wavelength-
based technique for real-time and non-real-time service
classes. The proposed model is then extended to support
any arbitrary number of classes. Simulations conducted at
the switch level validate the model.
1. Introduction
The Internet, being the leading communication in-
frastructure, has been experiencing an exponential growth
in IP traffic over the past few decades. With increase in
demand for applications such as video conferencing, voice
e-mailing and high definition television (HDTV), this grow-
ing trend is expected to continue in the years to come. In
spite of the flexibility and robustness of IP in handling In-
ternet traffic, its best effort nature limits quality of service
(QoS) provisioning in the Internet backbone. Such short-
comings as well as need for greater bandwidth have moti-
vated researchers to explore new high-speed transmission
technologies. Among various approaches such as IP-over-
ATM [1] and IP-over-SONET/SDH [2], IP-over-WDM [3]
seems to be the most efficient and feasible candidate for the
next-generation Internet backbone.
One of the most viable paradigms proposed to support
the Internet traffic over all optical WDM networks is optical
burst switching (OBS) [4] which is the result of combining
the best features of the two existing switching techniques
namely, optical packet switching (OPS) [5] and optical cir-
cuit switching (OCS) [6]. Most of the approaches suggested
for QoS provisioning in OPS can be easily adapted in OBS
with slight changes. Several protocols have been introduced
to provide QoS in buffer-less WDM networks by means of
offset-time exploitation [7] or resource reservation [8]. One
such novel protocol is the Just-Enough-Time (JET) protocol
which uses an offset-time in its one-way reservation [9]. By
extending the features of the JET protocol such as exploit-
ing delayed reservation (DR) and extra offset time, a new
prioritized protocol has been suggested to provide QoS in
OBS with two and more traffic classes [10]. In this proto-
col, a higher priority class is distinguished from a lower pri-
ority class by assigning different offset times to each class.
The offset time assigned to each class is dependent on the
average burst length of its lower class.
Another QoS provisioning model is the resource-
reservation-based QoS approach. In this approach, one
traffic class is privileged over the other by adopting some
form of reservation scheme over the available resources.
Based on the types of resources available, the resource-
reservation-based QoS scheme is investigated under two al-
ternatives namely, threshold-based and wavelength-based
techniques. In this paper, we provide a generalized model
for the wavelength-based technique examined under the
resource-reservation-based QoS scheme introduced in [11]
by extending the OBS paradigm to support any arbitrary
number of service classes. In addition, we present an an-
Pre-print
alytical model for the wavelength-based technique under
both, two-class and k-class traffics, and evaluate their per-
formance at switch level through simulation results.
The rest of the paper is structured in the following man-
ner. In Section 2, we provide an overview on OBS net-
works, followed by a concise description on the reservation-
based QoS model for the buffer-less WDM layer in Sec-
tion 3. The analytical models for the 2-class as well as its
generalized k-class scenario are provided in Section 4. Sim-
ulation results validating the proposed models, are given in
Section 5, followed by some conclusions and future works
in Section 6.
2. An overview on OBS networks
Many OBS-related issues have been investigated in the
literature [4-12]. In all these studies, optical switches have
been broadly classified into two categories namely, edge
and core switches. As depicted in Fig. 1, edge switches
are the switches that connect the optical core network to
the outside electronic world. Based on their functionality,
these edge switches can further be classified into two types:
ingress and egress edge nodes. An edge switch is said to
act as an ingress node whenever it aggregates the incom-
ing packets into optical bursts according to their destination
edge address. An egress node is any edge switch at which
data burst disassembling takes place.
The most common burst assembly algorithms can be
categorized into timer-based,threshold-based, and mixed
timer/threshold based. In the timer-based scheme [13], a
timer is set at the beginning of every new assembly cycle so
as to determine the transmission time of the burst into the
optical core network. After a fixed amount of time, all the
packets that have arrived during this time period are assem-
bled into a burst and transmitted through the optical core
network. In the threshold-based scheme [14], a threshold
value determines the number of packets to be aggregated
into a burst and the length of the burst. The incoming pack-
ets are stored in the packet queues at the ingress node un-
til the threshold condition is satisfied. Once the threshold
is reached, a burst is created and sent into the optical net-
work. While timer-based schemes might result in undesir-
able burst lengths, threshold-based assembly algorithms do
not guarantee on the assembly delay experienced by the in-
coming packets. Although having a higher operational com-
plexity, a mixed timer/threshold-based assembly algorithm
might provide better performance, especially under traffic
with self-similar characteristics [15].
Services such as switching-path establishment, dele-
tion and modification are provisioned by protocols known
as signaling protocols. In optical networks, there are
one-way [7][9] and two-way reservations signaling pro-
tocols [6]. In one-way reservation, a control packet re-
Optical Burst Switching Network
Network
1
Network
2
Network
3
Core Switches
Edge Switch 1
Edge Switch 2
Edge Switch 3
Figure 1. A general graphical representation
of an OBS network.
serves the required resources for the corresponding data
burst without any acknowledgement from the destination
node. On the contrary, in a two-way reservation, the con-
trol packet gathers information regarding the link and net-
work topology instead of reserving resources for the data
burst. The acknowledgement packet from the destination
node to the source node reserves resources for the corre-
sponding data burst while traversing along the reverse path.
Since one-way reservation protocols are more flexible, have
lower latency, and are more efficient compared to two-way
reservation protocols, they are mainly adopted in OBS net-
works.
Core switches are responsible for handling contention
resolution and forwarding. When an incoming control
packet enters a core switch through one of its input ports, it
undergoes an optical to electrical conversion (O/E) so that
it can be easily processed in the electrical domain. Based
on the destination information carried within the control
packet, the appropriate output link is determined and the
control packet tries to reserve one of the available wave-
lengths for its corresponding burst prior to its arrival at the
switch. If all the wavelengths are in use, then the burst is
sent into an optical buffer where it is delayed for a definite
amount of time. Since there is no optical random access-like
memory to hold such bursts, they are delayed by employing
fiber delay lines (FDLs) [16]. In case of absence of such
FDLs, the burst is immediately dropped out and considered
lost.
3. Resource allocation-based QoS management
This QoS approach is based on resource allocation and
has been reported in [11] and [12]. Although the method has
been originally investigated for OPS, it can also be applied
to OBS with slight changes. The main idea is to allocate
high priority classes with more resources than compared to
lower priority classes. For the sake of simplicity, it is as-
Pre-print
sumed in [11] that only two classes of service namely, High
(H) and Low (L) are available.
•Threshold-based approach: In this approach, a burst
belonging to class H may be delayed in an FDL for a
longer time than that of class L. In other words, if Th
and Tldenote, respectively, the maximum amount of
time that bursts of classes H and L might be delayed in
an FDL on encountering a contention in an intermedi-
ate core switch, then This set to be greater than Tl, i.e.
Th>T
l.
•Wavelength-based approach: In this approach, out of
all the Wwavelengths in a single optical fiber, Swave-
lengths are exclusively reserved for class H bursts,
while the remaining W−Swavelengths are shared
between both the classes.
4. Analytical model
In this section, we present a mathematical model for
the wavelength-based QoS management with two classes of
service. In what follows, we consider a single switch and
focus on one of its output links.
4.1. Assumptions
In this subsection, we highlight the assumptions made
hereafter in our analytical model.
•There are two service classes namely, Low (L) and
High (H) with input rates λ1and λ2, respectively.
Hereafter, unless stated, λiwill be used to denote the
input rate of service class i.
•Each optical fiber carries up to Wwavelengths where
bursts of class L are not allowed to use more than WS
wavelengths at any given time.
•No FDL is available. Although simplifying, this as-
sumption is justifiable as the common trend in develop-
ing intermediate OBS switches is to use as few FDLs
as possible and instead, try to increase the wavelength
count in the optical fibers.
4.2. The 2-class model
The aforementioned assumptions lead to a two-
dimensional birth and death process as shown in Fig. 2. The
state of the system at each time instant can be characterized
by the pair (n1,n
2)where n1and n2are the number of
bursts of classes L and H being served by the system, re-
spectively. Thus, n1≤WSand n1+n2≤W.
1 , W-11 , 1
0 , 1 0 , W
2
O
2
O
2
O
2
O
2
P
2
2
P
2
3
P
2
P
W
1
P
1
O
1
O
1
P
2
P
2
O
2
O
2
2
P
2
O
2
1
P
W
1
2
P
1
O
2
P
2
2
P
W
2
O
2
O
1
O
1
O
1
3
P
1
P
Ws
2
O
2
O
2
P
2
P
WsW
0 , 0 0 , 2
1 , 0
2 , W-22 , 0
WS , 0 WS , W-WS
Figure 2. The Markov model for the 2-class
QoS scheme.
Let πij be the steady state probability of having iand j
bursts of classes L and H, respectively, in the system. De-
riving the detailed balance equation with respect to iand j
yields:
πij =ρi
1
i!
ρj
2
j!π00,0≤i≤WS,0≤j≤W−i, (1)
in which ρi=λi/μiand μiis the service rate for i=1,2.
From equation (1) and the normalization condition, we get:
π−1
00 =
WS
i=0
W−i
j=0
ρi
1
i!
ρj
2
j!.(2)
Blocking probability can be derived from the system size
distribution as follows. For class H, an incoming burst is
lost when it finds all wavelengths busy serving other bursts.
Thus, the associated probability, PH,is:
PH=
i+j=W
i≤WS
πij =π00
W!
W
j=W−WSW
jρW−j
1ρj
2.(3)
In the case when both classes are equally prioritized, i.e.
WS=W, equation (3) reduces to:
PH=π00
W!(ρ1+ρ2)W.(4)
On the other hand, a class L burst is lost not only when
all the wavelengths are busy, but also when the number of
Pre-print
other class L bursts, already being served in the system, has
reached the threshold WS. Thus for WS<W,PLcan be
expressed as:
PL=
i+j=W
i≤WS
πij +
W−1
j=0
πWSj
=π00 ⎛
⎝
1
W!
W
j=WW
jρW−j
1ρj
2+ρWS
1
WS!
W−1
j=0
ρj
2
j!⎞
⎠,
(5)
where W=W−WS.ForWS=W,PLis the same as
PHas obtained in equation (4). Finally, if we define PTas
the total fraction of bursts that are lost, then we have:
PT=λ1
λ1+λ2
PL+λ2
λ1+λ2
PH.(6)
4.3. Generalization to k-class model
In this section, we generalize the 2-class model to sup-
port any arbitrary number of service classes (k≥2).Let
λiand μi(0 ≤i≤k−1) denote, respectively, the ar-
rival and service rates of bursts of some class Si. Also, let
Libe the maximum number of wavelengths for class Si.
Without loss of generality, it is assumed that Li≤Ljwhen
i<jand the output fiber carries Lk−1wavelengths, which
is same as the number of wavelengths for class Sk−1.Fig.3
demonstrates the case where k=nand each class exploits
two extra wavelengths with respect to its lower class, i.e.
Lj=Lj−1+2(1≤j≤k−1), and L0=2. The state
of the system at each time instant can be fully characterized
by a k-tuple (n0,n
1,...,n
j,...,n
k−1), where the jth ele-
ment denotes the number of bursts of class Sjbeing served
(1 ≤j≤k−1). Writing the detailed balance equation
with respect to (n0,n
1,...,n
k−1), we get:
π(n0,...,n
k−1)=π0
k−1
j=0
ρnj
j
nj!,n
j≤Lj,
k−1
j=0
nj≤Lk−1,
(7)
in which π0is the probability of the system being empty.
The normalization condition yields:
π−1
0=
γ0
n0=0
γ1
n1=0
···
γk−1
nk−1=0
⎛
⎝
k−1
j=0
ρnj
j
nj!⎞
⎠,(8)
where γj(0 ≤j≤k−1) is given as:
γj=⎧
⎪
⎨
⎪
⎩
min Lj,L
k−1−j−1
l=0 nl;(0 <j≤k−1)
L0;j=0 (9)
Any burst with priority greater than or equal to that of class Si
b
i
A burst of class Si
i
bnbnbn
Ȝ1
bnbnbnbn
Ȝ2
b
j
jb
j
j
Ȝm-2j-1
j j
b
j
Ȝm-2(j-1)
11 1 b1
Ȝm
b1
1 1
b1
Ȝm-1
2b2
2
Ȝm-3
2 2
b2
Ȝm-2 b2
W1
W
Wn
Wj
2
Figure 3. An example of the k-class model for
k=nservice classes with Lk−1=m=2k.
Over here, λiis used to represent wavelength
i(1 ≤i≤m).
AclassSjburst fails to get service if it either finds, at
the instant of arrival, all wavelengths busy or the number of
class Sjbursts already in system reaching the threshold Lj.
Hence, the associated probability is:
Pj
l=
σ=Lk−1|
nj=Lj
π(n0,...,n
k−1),σ =
k−1
l=0
nl.(10)
5. Simulation results and discussion
We conducted simulation experiments in the Ptolemy en-
vironment [17] to validate the formulas obtained in the pre-
ceding section. A single optical switch with just one output
link and Poisson arrival process was simulated under dif-
ferent data sets. In the following scenarios, the dotted lines
denote the analytical results. Hereafter, we use the notations
PH,PL, and Pclassless to denote the blocking probabilities
of classes H, L, and the classless system, respectively. The
classless system is defined to be a single-class system with
traffic intensity equal to the sum of the traffic intensities of
classes L and H, and total number of wavelengths equal to
those available to class H in the prioritized system.
Fig. 4 validates equation (1) for W=2,WS=1and
ρ1=2.0. For the sake of clarity, blocking probabilities of
states (0,2) and (1,1) have been ignored. It can be observed
that with increase in the amount of ρ2, the probability of be-
ing in state (1, 0) decreases, and for ρ2>2, this probability
falls below the curve for state (0,1).
Pre-print
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3
Traffic Intensity of Class H
Blocking Probability
State (0, 0) State (0, 1) State (1, 0)
Figure 4. Validation of equation (1) for W=2,
WS=1,andρ1=2.0.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3
Traffic Intensity of Class H
Blocking Probability
Class L Loss Class H Loss Classless Loss
Figure 5. Blocking probability comparison of
class L, class H, and classless systems for
W=5,WS=3,andρ1=3.0.
In Fig. 5, the impact of increasing the traffic intensity of
class H on the blocking probability of both classes has been
studied for W=5,WS=3and ρ1=3.0. It is observed
that even for ρ2<ρ
1, class H bursts suffer lesser loss than
class L. Blocking probabilities of both classes increase as
ρ2sweeps the values in the range [0.0,3.0]. In order to
demonstrate service differentiation, Pclassless has also been
depicted as a function of ρ2. As can be seen, PHlies below
Pclassless, while PLis above it, implying that bursts of class
H are prioritized to those of class L.
Fig. 6 demonstrates the blocking probability of both
classes, along with that of classless system, in terms of W.
In this figure, ρ1=3.0,ρ2=2.0, and WS=3.Not
surprisingly, with increase in the number of available wave-
lengths (W),PHdecreases and for W>8, this value
actually approaches 0. Although WSis fixed to 3, PL
also decreases with increase in Wsince in this case, class
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
02468101
Number of Wavelengths
Blocking Probability
2
Class L Loss Class H Loss Classless Loss
Figure 6. Blocking probability comparison of
class L, class H, and classless systems for
WS=3,ρ1=3.0,andρ2=2.0.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5
Traffic Intensity of Class 2
Blocking Probability
Class 0 Loss Class 1 Loss
Class 2 Loss Classless Loss
Figure 7. Blocking probability comparison of
classes 0, 1, 2, and classless systems for
L0=1,L1=3,L2=5,ρ0=1.5,andρ1=2.5.
L bursts have better chance in utilizing their set of wave-
lengths (WS)more effectively. As in the preceding scenar-
ios, Pclassless falls between PHand PL.
Fig. 7 depicts three different classes with traffic inten-
sities ρ0,ρ1, and ρ2, respectively. In this case, classes 0,
1 and 2 are allocated 1, 3 and 5 wavelengths, respectively.
Traffic intensities of classes 0 and 1 are taken to be 1.5 and
2.5, respectively. The blocking probabilities of all classes
are depicted as a function of ρ2. As can be observed, the
blocking probability of class 0 lies above that of the class-
less system, while the blocking probability of class 2 falls
below the classless curve. Class 1 bursts experience more
loss compared to the classless system for ρ2<1.5.But
as ρ2increases, both systems experience the same blocking
probability. Results obtained from simulation meet closely
with those obtained from equation (10).
Pre-print
6. Conclusions
In this paper, we presented a simple, yet highly accurate
analytical model for the wavelength-based quality of ser-
vice (QoS) provisioning scheme in optical burst-switched
(OBS) networks. The proposed model has been studied for
the classical 2-class traffic service case and then extended
to support any arbitrary number of service classes. Through
simulation results, we demonstrated the influence of multi-
ple service classes on the performance of a single switch in
terms of blocking probability. In all simulation scenarios, a
classless traffic has also been examined to exhibit the ser-
vice differentiation of traffic classes. Numerical results re-
vealed that service classes with more allocated wavelengths
experience lesser loss compared to classless systems, while
those with lesser wavelengths suffer great losses.
The next step of this research is to extend the work to
cover the impact of fiber delay lines (FDLs) as well. Doing
so would allow us to model a complete network of switches
and study the relevant performance dynamics at a network-
level.
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