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QoS Behavior of Optical Burst Switching under Multimedia Traffic: an Analytical Approach

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Recent studies in modern telecommunication networks have convincingly revealed that IP traffic exhibits a perceptible self-similar behavior over a wide range of time scales. Adapting the traditional Poisson model can therefore lead to erroneous conclusions regarding network performance dynamics. On the other hand, with growing demand for greater bandwidth, several optical paradigms have been proposed as substitutes for the next-generation Internet backbone. Among all these approaches, optical burst switching (OBS) has been widely recognized as a suitable alternative to optical packet switching (OPS) due to its support for bursty traffic and high bandwidth granularity. Thus, devising suitable buffers so as to accurately capture the fractal behavior of multimedia traffic in such optical core switches has become a major scientific endeavor. For the first time, in this paper, we propose an analytical model with quality of service (QoS) provision at a complete OBS network level. We then study the performance of the presented model in terms of blocking probability. Using this model, we also study the impact of burst aggregation time on the total loss probability and validate its correctness through simulation results.
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QoS Behavior of Optical Burst Switching under Multimedia Traffic: an
Analytical Approach
Aresh Dadlani, Ahmad Khonsari 1,2
1University of Tehran, ECE Department
North Karegar Ave., Tehran, Iran
2IPM School of Computer Science
Niavaran Sq., Tehran, Iran
a.dadlani@ipm.ir, ak@ipm.ir
Mohammadreza Aghajani, Ali Rajabi
IPM School of Computer Science
Niavaran Sq., Tehran, Iran
aghajani@ipm.ir, alirajabi@ipm.ir
Abstract
Recent studies in modern telecommunication networks
have convincingly revealed that IP traffic exhibits a per-
ceptible self-similar behavior over a wide range of time
scales. Adapting the traditional Poisson model can there-
fore lead to erroneous conclusions regarding network per-
formance dynamics. On the other hand, with growing de-
mand for greater bandwidth, several optical paradigms
have been proposed as substitutes for the next-generation
Internet backbone. Among all these approaches, Optical
Burst Switching (OBS) has been widely recognized as a suit-
able alternative to Optical Packet Switching (OPS) due to
its support for bursty traffic and high bandwidth granular-
ity. Thus, devising suitable buffers so as to accurately cap-
ture the fractal behavior of multimedia traffic in such opti-
cal core switches has become a major scientific endeavor.
For the first time, in this paper, we propose an analytical
model with Quality of Service (QoS) provision at a com-
plete OBS network level. We then study the performance of
the presented model in terms of blocking probability. Using
this model, we also study the impact of burst aggregation
time on the total loss probability and validate its correct-
ness through simulation results.
1. Introduction
As demonstrated through various research experiments,
traffic in contemporary packet networks such as cor-
porate LANs, variable-bit-rate (VBR) video over ATM,
CCSN/SS7 and other communication systems appears to
be self-similar in nature (scale-invariant burstiness) with
long-range dependence (LRD) [1-3]. This means that traf-
fic traces of such networks show similar statistical patterns
over different time scales and look the same over a long
range of time interval. Therefore, properties of models
based on self-similar traffic are quite different from those
based on short-range dependent (SRD) processes such as
the traditional Poisson process [2].
In addition, several switching paradigms such as opti-
cal circuit switching (OCS) [4], optical packet switching
(OPS) [5] and optical burst switching (OBS) [6] have been
proposed in the literature to satisfy the ever-growing surge
of bandwidth demand due to increase in the myriad of real-
time and multimedia applications over the Internet. How-
ever, among all the proposed paradigms, OBS seems to be
the preferred option for providing quality of service (QoS)
at the optical layer and in presence of bursty traffic [7].
With the failure of modeling the behavior of the actual
LAN traffic with traditional processes, the need for equip-
ping high-speed optical networks with suitable storage sys-
tems for long-range dependent input processes has gained
growing importance. One such storage-level model with
self-similar input has been investigated in [8]. In the litera-
ture, several queuing models for optical networks have been
reported [9-11]. However, to the best of our knowledge,
none of these models have been scrutinized under multi-
media traffic at network-level. In fact, they have all been
modeled using traditional Poisson-based processes. In this
paper, we propose a novel analytical model based on the
storage-level model reported in [8] using self-similar traf-
fic model for an entire OBS network. We then analyze the
performance of the proposed model in terms of blocking
probability and justify its appropriateness through results
obtained from simulation experiments.
The rest of the paper is organized as follows. In Sec-
tion 2, we briefly introduce the framework of an OBS net-
work. In Section 3, we specify the assumptions made in our
proposed model followed by a step-by-step analysis of the
model at three different levels of abstraction in Section 4. In
Section 5, we study the performance of the proposed model
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Optical Burst Switching Network
C3
C1
C2C4
E1E3
E2
burst
LAN/
WAN 2
packets
packets
LAN/
WAN 1
LAN/
WAN 3
Router
+
Burst Disassembler
Router
+
Burst Assembler
Switching Fabric
+
Switching Control Unit
+
Routing & Signaling Processors
Egress Node
Ingress Node
Core Node
Figure 1. A graphical representation of an OBS network comprising of three edge nodes (E1,E2and
E3) and four core nodes (C1,C2,C3, and C4).
in terms of loss probability. Finally, we summarize our con-
tributions and future works in Section 6.
2. The OBS framework
Nodes in an OBS network (OBSN) are mainly of two
types: edge and core nodes [12]. An edge node is further
classified into ingress and egress nodes. An ingress node
consists of a router and a burst assembler, while an egress
node is made up of a router and a burst disassembler. An
OBS core node is composed of a switching fabric and a con-
trol unit.
In terms of functionality, the ingress node is responsible
for collecting the incoming packets from the outside elec-
tronic world and aggregating them into bursts according to
their destination addresses. Prior to the burst transmission,
the OBS edge node creates and sends a control packet to-
wards the destination of the corresponding burst. In gen-
eral, all OBS designs include an offset time between the
transmission of a control packet and its corresponding burst.
This offset time allows the control packet to reserve the re-
quired resources along the path before the burst arrival. In
OBSNs, the two fundamental resources available for reser-
vation in the optical domain are wavelengths and fiber de-
lay lines (FDLs or optical buffers). When a control packet
reaches a core node, it is routed to the next core node based
upon the resource availability. If, at any time instant, no
free resource is available, the burst is dropped. However,
in presence of wavelength converters (WCs) and variable
FDLs, the burst loss can be reduced to a great extent. When
a burst reaches an egress edge, it is disassembled back into
packets before being transmitted into the electronic world.
As shown in Figure 1, for a burst traveling from edge 2 (E2)
to edge 3 (E3) via core nodes C2and C3,E2and E3act as
the ingress and egress nodes, respectively.
Some of the most common burst assembly algorithms
can be classified into timer-based,threshold-based, and
mixed timer/threshold-based algorithms. In the timer-based
approach, a timer is set at the beginning of every new as-
sembly cycle, determining the transmission time of the burst
into the core network [13]. After a fixed amount of time,
all the packets that arrived during that time period are as-
sembled into a burst. In the threshold-based approach, a
threshold is specified to determine the generation and trans-
mission time of a burst into the optical network [14]. The
incoming packets are stored in the prioritized queues in the
ingress node, until the threshold condition is satisfied. Once
the threshold is reached, a burst is created and sent into the
optical core. The timeout value for the timer-based schemes
should be set carefully. If the value is chosen to be too
large, the packet delay at the edge might become intoler-
able. On the other hand, if the value is too small, too many
small-sized bursts will be generated, resulting in control
overhead. While timer-based schemes might result in unde-
sirable burst lengths, threshold-based assembly algorithms
do not guarantee on the packet assembly delay. A mixed
timer/threshold-based algorithm may perform better, espe-
cially with self-similar traffic, but may experience higher
operational complexity [15, 16].
A signaling protocol is the procedure through which a
control packet reserves resources for the corresponding data
burst by guiding it through a routing path. In an optical net-
work, there are one-way and two-way reservations signaling
protocols. In one-way reservation [6], a control packet re-
serves resources along the path for the corresponding data
burst without any acknowledgement from the destination
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node. On the contrary, in a two-way reservation[17], a con-
trol packet collects link and topology information instead
of reserving resources for the data burst. The acknowledge-
ment packet from the destination node to the source node
reserves resources for the corresponding data burst while
traversing along the reverse path. Since one-way reserva-
tion protocols are more flexible, have lower latency, and are
more efficient as compared to two-way reservation proto-
cols, they are mainly adopted in OBSNs.
3. Assumptions and notations
Before introducing our model, we highlight the assump-
tions and notations to be used hereafter in this paper.
In our model, the OBSN comprises of jingress and k
egress nodes, such that each egress node is reachable
from all ingress nodes. We define the set of ingress
nodes as I={I1, I2,...,Ij}and the set of egress
nodes as E={E1, E2,...,Ek}. Hence forward, the
terms ingress and egress are used interchangeably as
source and destination, respectively.
The Breadth First Search (BFS) algorithm is used to
determine the shortest path between every source and
destination. If more than one such path exists, one is
chosen at random.
Each ingress switch is connected to just one core
switch via a single link with a capacity of wwave-
lengths.
Ingress switch Iq(1 qj)generates traffic in ac-
cordance with a LRD process having mean input rate
of mq.
The destination of a burst generated by an ingress node
is uniformly distributed over the total number of desti-
nations, i.e. k.
Dphysical FDLs (each of length L) are assigned to
each optical link. Therefore, the total number of virtual
FDLs is Dw.
For any arbitrary link l, let λland δldenote, respec-
tively, the burst arrival and departure rates of l. Fur-
ther, let P bldenote the blocking probability of l, i.e.
the probability that a burst intending to pass the link
does not succeed and is dropped due to resource un-
availability (all wavelengths and FDLs are busy serv-
ing other bursts).
Each link connects one of the output interfaces of a
node to an input interface of another node. We define
head(l)as a function that returns the node having l
connected to one of its output interfaces and tail(l)as
a function that returns the node having lconnected to
one of its input interfaces. Further, let Pbe a path be-
tween some source and destination including las one
of its links. We define precP(l)as a function that re-
turns the preceding link of lon P, or null if lis the first
link on P. Also, last(P)is defined as a function that
returns the final link on Pconnected to an egress node.
Let Pl={P1, P2,...,Pj,...,PQ}be the set of all
paths, each containing las one of its links. Also, let
λPl
land δPl
lbe the burst arrival and departure rates of
lon path Pj, respectively.
The blocking probability of a link connecting an
ingress node to a core node is taken to be zero. In
other words, P bl= 0 if head(l)I.
Finally, we define P b as the network blocking prob-
ability, i.e. the probability that an arbitrary burst is
dropped somewhere on its path from source to desti-
nation.
4. The analytical model
In this section, we present our analytical model in three
steps. First, we introduce the model for a single ingress
node with self-similar traffic model. Then, we present a
model for a single core node followed by a model for the
entire OBSN.
4.1. The model of an ingress node
In this sub-section, we present the analytical model for
an ingress node under LRD input traffic.
As illustrated in Figure 2, an ingress node connects the
outside electronic world to the inner optical core network.
Packets arriving at such a node are aggregated into opti-
cal bursts before being sent into the core network. Due to
Optical
Network
Electronic
Network
Ingress node
A(t)
Figure 2. A single ingress node with self-
similar input traffic A(t).
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the LRD nature of self-similar traffic, we adapt the time-
continuous process reported in [8] to model the traffic in
our proposed model. That is,
A(t) = mt +am ·Z(t),(1)
where mis the mean input rate, ais a variance coefficient
(a > 0), and Z(t)is the standard fractional Brownian mo-
tion (FBM) with self-similarity parameter H(also known
as Hurst parameter). As given in [8], Z(t)is characterized
by the following properties:
P1:Z(t)has stationary increments.
P2:Z(t) = 0 and E[Z(t)] = 0 for all t.
P3:E[Z(t)]2=|t|2Hfor all t.
P4:Z(t)has continuous paths.
P5:Z(t)is Gaussian, i.e. its finite-dimensional distribu-
tions are multivariate Gaussian distributions.
Based on the above definition, we assume that the traffic
entering an ingress node is of the form A(t). Packets enter-
ing the ingress node are aggregated into bursts and sent into
the optical core after constant time intervals, say T. Thus,
the length of the ith burst (Li) generated in the ingress node
depends on the amount of traffic entering that node between
time intervals (i1)∆Tand iT. Therefore, we have:
Li=A(iT)A((i1)∆T).(2)
According to P1and P2, equation (2) can be written as:
Li
iid
=A(∆T)A(0) iid
=A(∆T),(3)
where iid
=denotes i.i.d or “independently and identically
distributed”. Substituting equation (1) in (3) results in the
following:
Li
iid
=mT+am ·Z(t).(4)
Because of the self-similar and Gaussian nature of Z(t),P3,
P4, and P5yield:
Li
iid
=mT+am ·THZ(1)
N(mT, amT2H).(5)
4.2. The model of a core node
We now introduce an analytical model for an optical core
node. As shown in Figure 3, consider a core switch with
xinput interfaces and youtput interfaces. Each interface
is connected to an optical link with a capacity of wwave-
lengths. Also, we assume the presence of full WCs in the
w wavelengths
l
1
l
2
l
y
Core
l1
l2
lx
B1(t)
B2(t)
Bx(t)
C1(t)
C2(t)
Cy(t)
Figure 3. A single core node with xinput links
and youtput links. Each link has a capacity
of wwavelengths. The traffic into link li(1
ix)and out of link l0
j(1 jy)is denoted
by Bi(t)and Cj(t), respectively.
core switch such that every wavelength λi(1 iw)can
be converted into any of the other w1wavelengths.
A burst entering an input link of a core switch is routed
to the appropriate output link according to its destination
address. On arriving at the output interface, the burst is al-
located one of the free wwavelengths to be forwarded to the
next node. If at the instant of arrival, no wavelength is found
idle at the output interface, the burst is delayed in the optical
buffer. On leaving the optical buffer, if any wavelength is
made free, it is allocated to the burst for transmission. In the
case when all resources (optical buffers and wavelengths)
are busy, the burst is lost and is said to be dropped. In this
subsection, we present an apposite model to calculate the
burst loss probability for the traffic model mentioned in the
preceding subsection.
Let qij denote the routing probability of a burst from in-
put link lito the output link l0
jof a single core switch. Thus,
the traffic contribution of lito the total outgoing traffic from
l0
jis equal to qij Bi(t). Therefore, the total outgoing traffic
on l0
j, denoted by Cj(t), is the sum of the bursts routed to
l0
jfrom each of the xinput links. Thus, Cj(t)can be calcu-
lated as:
Cj(t) =
x
X
i=1
qij Bi(t).(6)
As in equation (4), the incoming traffic on link li, which we
denote by Bi(t), can be written as:
Bi(t) = mit+ami·Z(t).(7)
A similar equality can be obtained for Cj(t)as follows:
Cj(t) = ˆmjt+paˆmj·Z(t),(8)
where ˆmj=Pk
i=1 qij mi. In order to model the burst trans-
mission and optical buffer, we adapt the stationary storage
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model reported in [8]. Thus, the volume of traffic being
served and held in the optical buffers can be written as:
V=sup
st
(A(t)A(s)Cw(ts)),(9)
where Cis the service rate of each wavelength, wis the
number of wavelengths and t(−∞,). According
to [8], we have:
P(V > x)¯
φ 1
am wC m
HHx
1H1H!,
(10)
where ¯
φ(y) = P(Z(1) > y)is the residual distribution
function of the standard Gaussian distribution. For an opti-
cal buffer of length x, the burst loss probability, PLoss, can
be calculated as follows:
PLoss =α·P(V > x),(11)
with αgiven as:
α=
exp (Cm)2
2σ2
2πZ
C
(yC)exp (ym)2
2σ2dy.
(12)
In the case of Gaussian traffic, with mean mand variance
σ2=am, equation (12) is simplified as follows:
α=a
2π(wC m+am).(13)
Now, consider a core node with an optical buffer of
length Lfor which the “busy queue” assumption made in
the storage model of [8] holds. Since the average length of
each burst is mTand each burst is served at a constant
rate, the average amount of traffic to be served by each of
the wwavelengths is mT/2. Hence, every core node can
be modeled as a storage with limited capacity of:
L+mT
2·w. (14)
Therefore, the probability of losing a burst on the jth link
of a core node can be obtained as:
P bj=αj·PV > L +mjT
2·w
=αj·¯
φ 1
amjwCm
HHL+mjT
2·w
1H1H!.
(15)
4.3. The model of an entire OBSN
In this subsection, we aim at calculating the blocking
probability of an entire OBSN. As mentioned in the model
for an ingress node (subsection 4.1), the input traffic has
been modeled as an FBM process. Similarly, in the model
proposed for a core node (subsection 4.2), the input traffic
is taken to be an FBM process. The traffic leaving the core
node is also an FBM process having the same variance coef-
ficient (a) and Hurst value (H) as that of the incoming traffic
into the core node. The traffic entering and leaving a core
node only differ in their mean service rates (m). Therefore,
the traffic model adapted to calculate the burst loss proba-
bility at each output link of a core node holds for the other
links as well.
Based on the notations defined in the earlier section, λlis
the sum of the arrival rates of individual paths in Pl. Thus,
we have:
λl=
Q
X
j=1
λPj
l,(16)
where Qis the cardinality of Pl. Further, λPl
lcan be de-
scribed recursively as follows:
λPj
l=
δPj
precPj(l)precPj(l)6=null
λhead(l)
|I|otherwise
,(17)
where |I|is the total number of ingress nodes in the network
and the burst departure rate δPl
lis given as:
δPj
l=λPj
l(1 P bl).(18)
Before proceeding into the next section, we provide a
more detailed explanation for the second case given in equa-
tion (17), i.e., when precPl(l) = null. Occurrence of this
condition implies the fact that lis connected to an ingress
switch and thus, λl=λhead(l)(as mentioned in the assump-
tions). Also, since we assumed that there exists a specified
shortest path between each source and destination, and that
the destination of a burst is uniformly distributed, the sec-
ond case in equation (17) holds.
The network blocking probability can be defined as the
ratio of the total number of bursts not reaching the egress
switches to the total number of bursts injected from ingress
switches into the optical core at a long-run. Thus, P b can
be defined in terms of δland λlas:
P b = 1 X
tail(l)E
δl
X
head(l)I
λl
,(19)
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where the departure rate of link lis computed as δl=
λl(1 P bl).
5. Simulation and numerical results
The performance of the analytical model has been val-
idated in terms of blocking probability for the network
shown in Figure 4 in the Ptolemy environment. Each sim-
ulation was run until the network converged to steady state
which is often very slow under self-similar traffic. Through-
out this section, the dark lines in the figures denote the re-
sults obtained through analysis while the dotted lines repre-
sent the simulation results. Also, FBM has been modeled
using the rmd33 method reported in [8].
Figure 5 illustrates the influence of the Hurst parameter
(H) on the network blocking probability (P b). In this sce-
nario, L= 10,C·w= 200 and a= 1. As shown in the fig-
ure, P b increases with increase in H. Such a behavior is not
out of expectation as self-similar traffic is featured with in-
herent burstiness extended over a wide range of time scales.
The peaks observed in the traffic trace are the result of such
burstiness. Since the servers are unable to provide service
to the incoming traffic at such peaky periods, a large frac-
tion of bursts is lost during this period. With increase in the
degree of self-similarity (H), the amount of traffic bursti-
ness also increases. Such an event, in turn, adds to traffic
burstiness, thus increasing the burst loss probability.
From Figure 6, we observe that with increase in opti-
cal buffer length (L), the network blocking probability de-
creases. Over here, H= 0.8,C= 10000 and w= 10.
This implies that by increasing the length of the buffers in
the core nodes, more number of bursts can be delayed in the
buffers and thus, prevented from being dropped in absence
of any idle wavelength. In terms of the storage model, the
storage capacity increases, resulting in lower burst overflow.
This justifies the storage model adapted in the core node as
an appropriate model for optical buffers in an OBSN.
In Figure 7, the effect of the Hurst parameter on P b for
different optical buffer lengths is depicted. As shown, net-
works with lower Hvalue experience lesser burst loss than
those with higher Hvalues. The traces shown in Figure 7
summarize the results obtained in the previous two figures.
Figure 8 represents the blocking probability for different
values of C·w, which is the product of the service rate and
the number of wavelengths. For this scenario, H= 0.8
and a= 50. As can be seen, for small values of C·w,
the burst blocking probability is high. But as the value of
C·wincreases, this probability falls. For C·w= 400,
the burst loss probability becomes almost negligible. This
figure implies that P b can be reduced by either increasing
the service rate or number of wavelengths, or even both.
In Figures 9 and 10, we study the effect of burst aggre-
gation time (T) on the burst loss probability. We know
E1
E2
E3
E
B
D
A
C
I2
I3
I1
I4
Figure 4. The simulated OBSN.
0.003
0.005
0.007
0.009
0.011
0.013
0.015
0.5 0.6 0.7 0.8 0.9
Hurst parameter value (H)
Blocking Probability (Pb)
Analysis
Simulation
Figure 5. Network blocking probability (P b) in
terms of the Hurst parameter (H) (L= 10,
a= 1).
H = 0.8
0.0015
0.002
0.0025
0.003
510 15 20 25 30 35 40 45 50
Buffer Length (L)
Blocking Probability (Pb)
Analysis
Simulation
Figure 6. Network blocking probability (P b) in
terms of optical buffer length (L) (H= 0.8,
a= 50,Cw = 100000).
that with increase in aggregation time, the average burst size
also increases. Since each control packet reserves the re-
quired resources for the corresponding burst regardless of
its length, with increase in the average burst length, the av-
erage amount of traffic served by the wavelengths also in-
creases. Thus, as shown in Figure 9, the loss probability
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H = 0.8
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0.0022
0.0024
0.0026
0.0028
5 10 15 20 25 30 35 40 45 50
Buffer Length (L)
Blocking Probability (Pb)
Analysis
Simulation
H = 0.6
Figure 7. Comparison of network blocking
probability (P b) in terms of optical buffer
length (L) for two different values of H.
Figure 8. Network blocking probability (P b) in
terms of service rate (C) (H= 0.8,a= 50).
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
0 1 2 3 4 5 6 7 8 9 10
Aggregation Time (ǻT) (10E-5)
Packet Loss Probability
(10E-05)
Analysis
Simulation
Figure 9. Impact of aggregation time (T) on
the packet loss probability (H= 0.8,a= 50).
experienced by every single burst is reduced with increase
in T(according to equation (15)).
On the other hand, with increase in the average burst
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8 10 12
Aggregation Time (ǻT) (10E-5)
Byte Loss Probability (10E-5)
Analysis
Simulation
Figure 10. Impact of aggregation time (T) on
byte loss probability (H= 0.8,a= 50).
length, more amount of information is packed in each burst.
Thus, if such a burst is dropped, a large amount of infor-
mation is lost. Since the decrease in burst loss probability
due to increase in aggregation time is not as much as that
due to increase in average burst length (which increases lin-
early), the average number of bytes lost due to burst loss is
directly proportional to T(Figure 10). Thus, keeping this
in mind along with other factors such as header overhead,
the aggregation time period should be selected with great
care.
6. Conclusions
Based upon several surveys conducted on the contempo-
rary communication networks, traffic prevailing in such net-
works is reported to exhibit fractal nature with long-range
dependence. This causes the traffic to look alike irrespec-
tive of time scales over a long range interval. Such be-
havior makes the traffic very bursty. Thus, adapting tradi-
tional models based on Poisson-related processes can there-
fore lead to erroneous conclusions in network performance
evaluation. The search for an appropriate high-speed par-
adigm to support this burstiness as well as to fulfill the
ever-growing bandwidth demand has gained great impor-
tance. As one of the main supporting technologies for next-
generation optical Internet, optical burst switching (OBS)
has been widely accepted as a suitable alternative to optical
packet switching. In this paper, we presented an analyti-
cal model with QoS provisioning for an OBS network un-
der the influence of multimedia traffic. The proposed mode
has been studied at three abstract levels: ingress node, op-
tical core node and the entire OBS network. Based upon
the proposed model, we also have investigated the influence
of burst aggregation time on the total burst loss probabil-
ity. We have studied the performance of the model in terms
of burst blocking probability and have evaluated its correct-
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ness through simulation experiments conducted at the net-
work level.
In future work, we tend to study the network perfor-
mance of an OBS network in terms of latency and provide
an improved mathematical model for the optical buffer so
as to further reduce the blocking probability of the bursts in
the core network.
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