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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 ≤q≤j)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 (i−1)∆Tand i∆T. Therefore, we have:

Li=A(i∆T)−A((i−1)∆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

=m∆T+√am ·Z(t).(4)

Because of the self-similar and Gaussian nature of Z(t),P3,

P4, and P5yield:

Li

iid

=m∆T+√am ·∆THZ(1)

∼N(m∆T, am∆T2H).(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 ≤

i≤x)and out of link l0

j(1 ≤j≤y)is denoted

by Bi(t)and Cj(t), respectively.

core switch such that every wavelength λi(1 ≤i≤w)can

be converted into any of the other w−1wavelengths.

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

Pre-print

model reported in [8]. Thus, the volume of trafﬁc being

served and held in the optical buffers can be written as:

V=sup

s≤t

(A(t)−A(s)−Cw(t−s)),(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

1−H1−H!,

(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 (C−m)2

2σ2

mσ√2πZ∞

C

(y−C)exp −(y−m)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 m∆Tand each burst is served at a constant

rate, the average amount of trafﬁc to be served by each of

the wwavelengths is m∆T/2. Hence, every core node can

be modeled as a storage with limited capacity of:

L+m∆T

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 +mj∆T

2·w

=αj·¯

φ 1

√amjwC−m

HHL+mj∆T

2·w

1−H1−H!.

(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

Pre-print

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.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 20 30 40 50 60 70 80 90 100

Service Rate (C)

Blocking Probability (Pb)

Analysis

Simulation

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-

Pre-print

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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