PERFORMANCE ANALYSIS STUDY OF MULTICAST TRAFFIC

IN STAR-BASED LOCAL WDM LIGHTWAVE NETWORKS

Rabi W. Habash, Member, IEEE, Mohd Dani Baba, Mat Ikram Yusof, and Muhammad Ibrahim

Faculty of Electrical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

Borhanuddin Mohd Ali, Member, IEEE

Institute of Multimedia and Software, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Keywords: Multicasting, Broadcast-and-select, Star

coupler, WDM lightwave networks

Abstract: Multicasting refers to a one-to-many network connection. Man

y-to-one and many-to-many connections are

also categorized as multicasting. In a broadcast-and-select single-hop WDM network the only way to

transmit information successfully is to have both source's transmitter and destination's receiver tuned to the

same channel. The cost, scalability and efficiency issues of these approaches inspired researchers to study

different ways in which the physical medium can be shared efficiently. In this paper, we study multicast

traffic in single-hop local WDM optical networks based on a broadcast-and-select system. We use an

approximate analytical solution to show the influence of tuning delay on the system performance under

different network conditions. We also examine the effect of average packet delay on receiver throughput.

Finally, we demonstrate the channel blocking probability versus network offered load characteristics.

1 INTRODUCTION

The emergence of wavelength division multiplexing

(WDM) technology has been of particular

significance because of its high-speed long distance

transmission and vast transmission capacity, hence

supporting multiple simultaneous channels on a

single fiber. WDM optical networks are expected to

be the backbone network for a bulk transport of

traffic in the future broad-band networks. These

wavelengths channels can operate at peak electronic

speed, thus optically enabling an aggregate system

capacity of several terabits/second. WDM also

supports mechanisms such as multicasting at the

physical layer without buffering (Modiano, 1999.

Sue, 2002. Baldin, 2001).

WDM networks can be classified in two classes:

oadcast-and-select and wavelength routed. In

broadcast-and-select WDM network, a node sends

its transmission to the star on one available

wavelength, using a laser which produces an optical

information stream (Mukherjee, 2000).

Communication between sources and

estinations can be either single-hop or multihop. In

single-hop systems, WDM is achieved by using

lasers as tunable transmitters and optical filters as

tunable receivers in order to provide switching

between channels at high speeds. The hosts are

directly connected to each other via direct two-way

optical fibers to the passive star coupler (PSC). PSC

is a piece of glass which works as a multiplexer for

every incoming link by splitting the optical signal

into all of the outgoing links and, in essence,

broadcasting any input to all the outputs, hence the

name broadcast-and-select. Its minimal bandwidth

requirements make broadcast-and-select approach

especially appealing for transmitting multicast traffic

(Ramaswami 2002. Ramamurthy, 1998).

Multicast is the simultaneous transmission of

formation from one source to multiple destination

nodes. Multicast can be supported more efficiently

in optical domain by utilizing the inherent light

splitting capacity of optical switches than copying

data in electronic domain (Wang, 2002).

In single-hop WDM networks, the major issue is

he coordination (scheduling) of the transmissions,

because contentions may happen in such shared-

media and shared-channel networks. One source of

contention is so-called collision, when two or more

transmitters want to transmit to the same wavelength

channel at the same time. Another source of

contention occurs when, in a system with tunable

receivers, two or more transmitters want to transmit

243

W. Habash R., Ali B., Dani Baba M., Ikram Yusof M. and Ibrahim M. (2004).

PERFORMANCE ANALYSIS STUDY OF MULTICAST TRAFFIC IN STAR-BASED LOCAL WDM LIGHTWAVE NETWORKS.

In Proceedings of the First International Conference on E-Business and Telecommunication Networks, pages 243-249

DOI: 10.5220/0001395702430249

 SciTePress

to the same destination node on different channels

simultaneously. This situation is called a destination

conflict (He, 2002).

A number of multicast scheduling algorithms

(MSAs) for transmissions have been proposed.

These MSAs can generally be classified as random-

access-based MSAs, pre-allocation-based MSAs,

and reservation-based MSAs.

In (Kitamura, 2001), some random-access-based

MSAs are described. The system employs a

centralized scheduler that operates in a slotted mode,

maintains a request queue for each node, checks the

request queues, and makes appropriate scheduling in

each slot.

Preallocation-based MSAs are presented in

(Tseng, 1998). These algorithms simply coordinate

the transmissions according to some pre-determined

schedule. The slots are preallocated for unicast

purpose. In general, scheduling multicast

transmissions is much more challenging than

scheduling unicast transmissions, because the

transmitter of the source node and the receivers of

all the destination nodes in the multicast group need

to be tuned to a common wavelength

simultaneously. A multicast distance is used to

determine whether the arrived multicast packet

should be transmitted as a single multicast or

multiple unicast packets. This information along

with the multicast group of this packet is broadcast

to all other nodes via a control channel. When the

information for the multicast packet is received by

all of the nodes, all of the nodes run the same

scheduling algorithm to modify the preallocated

slots to accommodate the multicast packet.

Reservation-based MSAs can be found in (Jue,

1997), where some partition schemes are proposed

to address the problem of wasting the receiver

resources. In particular, when the multicast group

size is large, some receivers may have to wait for a

long time without receiving anything because some

other receivers in the same group are not available.

Specifically, these MSAs allow a multicast

transmission to be partitioned into multiple unicast

or multicast transmissions and separate transmission

is scheduled for each subgroup, in order to minimize

the large receiver waiting time. Every node in the

system model keeps track of the times beyond which

each of the transmitters, receivers, and channels will

be available.

For wide ranges of the traffic conditions and a

wide range of the number of data channels in the

network, a hybrid MSA has been proposed in (Lin,

2001). The proposed algorithm dynamically chooses

to employ a MSA which always tries to partition

multicast transmissions or a MSA which does not

partition multicast transmissions depending on the

average utilization factors of the data channels and

the receivers.

The paper is organized as follows. Section 2

describes the system and traffic model. In Section 3,

we use an approximate analytical approach to

analyze the system performance in terms of average

packet delay, receiver throughput and blocking

probability. Section 4 presents some analytical

results. Conclusion is given in Section 5.

2 SYSTEM DESCRIPTION

The system in study consists of a PSC with N nodes

as shown in Figure 1. There are W channels,

Figure 1: A broadcast-and-select star-based WDM system.

PSC

Station

Networks

Users

A pair of

Optical Fibers

Station

Networks

Users

Protocol

Processing

TT FT

FR TR

Control

Data

To/From

Users

-λ

λ(i)

Station

Networks

Users

PSC: passive star coupler

FT/R: fixed transmitter/receiver

TT/R: tunable transmitter/receiver

Multicast

Unicast

A station possible architecture

ICETE 2004 - WIRELESS COMMUNICATION SYSTEMS AND NETWORKS

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where W ≤ N. Each station is equipped with a

tunable transmitter and a tunable receiver. All

stations can communicate with one another. In

addition, a pair of fixed transceivers and control

receiver both are tuned to the control channel is

dedicated for pre-transmission co-ordination.

However, communication between two nodes is

possible only when the transmitter of the source

node and receiver of the destination node are tuned

to the same channel during the period of information

transfer. Each node is connected to the PSC by a

transmitting and receiving fiber, and each message is

addressed (multicast) to a number of receivers l

(destination set size), randomly chosen from the N

nodes and each receiver tunes to one of the

wavelength that has a message addressed to it.

Through multicasting, a source node is able to

send a multicast message to multiple destination

nodes in a single transmission, thus conserving the

source transmitter's usage and bandwidth. Messages

are transmitted repeatedly until received by all

intended receivers.

It is shown in (Jia, 1993) that the main problems

with MAC protocol for WDM optical networks are

contention and destination collision. Therefore, to

reduce the probability of destination collision a

MAC protocol is designed to incorporates

asynchronous transfer scheme to allow overlapping

of one node's tuning time with other node's packet

transmission time.

For example, a signal that originates on a

particular channel remains on it until it reaches its

destinations. Since, each node has a tunable

transmitter and a tunable receiver and each of them

can access any of the wavelength channels for

transmission or reception, therefore, each channel in

the network can be a copy of the network. These

copies of the network operate independently in

parallel with each other. The nodes on the other

hand can transmit a multicast packet or receive it on

as many copies of the network as the number of

transmitter or receivers available to them.

3 SYSTEM ASSUMPTIONS AND

ANALYSIS

The behavior of the system is characterized by the

following assumptions:

• There are N nodes and W wavelength channels

in the system.

• Each message is multicast to a set of l receivers

where l < W ≤ N.

• Whenever the receivers of a multicast group are

ready to receive a data packet the source node's

transmitter is ready to transmit.

Data slot

Data part

Data channel

Tuning

part

1 2 W

… ………

Control channel

→

Control

←

slot minislot

Figure 2: Control and data channel structure.

• A packet that arrives at the start of a slot can be

transmitted during that slot to any one of the

other (N − 1) nodes with equal probability.

• Random selection of a destination node among

the (N − 1) nodes is renewed for each attempt of

transmitting a control packet.

The system operates in a slotted mode with a

time slot equals to the packet transmission time plus

the tuning part as shown in Figure 2. Time on a

control channel is divided into data slots. Each data

slot is divided further into W control slots. Time on

the data channel is synchronized with the time on the

control channel. A control packet contains only the

destination address and its transmission time is

defined as one mini-slot. The transmission time for

each control slot is equal to 1 unit.

3.1 System Performance

In this section, we analyze the system performance

in terms of average packet delay and throughput. We

first calculate the average delay a packet

experiences. This delay is due to the data packet

transmission delay, control channel delay, data

channel delay, and propagation delay.

The length of data packet is fixed and equals to L

control slots. Assume the receiver tuning time is T

control slots. Thus, the data packet transmission

delay equals to

TLD

. (1)

Assume the arrivals are Poisson of rate A per

control frame. The server process is deterministic

with rate

= 1 per control frame, and the offered

load

/Aa

. Therefore, the average delay a data

packet incurred before its corresponding control

packet is sent can be given by

)1(2/2/1

ccc

aaWD

−

. (2)

PERFORMANCE ANALYSIS STUDY OF MULTICAST TRAFFIC IN STAR-BASED LOCAL WDM LIGHTWAVE

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245

When the receivers of a multicast packet are

ready to receive a packet, a free channel is available

for transmission. If the number of free channels is

few, a free channel may not be available and the

packet may be delayed. Thus, the offered load can

be given as

. Therefore, the delay

due to the data channel can be calculated as

WDAa

dch

/)(=

)1(2/

chchch

aWaD −=

. (3)

The total propagation delay between any node in

the system and the passive star coupler is R and is

assumed to be the same for all the nodes. Thus, the

propagation delay for a data packet is

Note that the average packet delay is measured

from the time the packet is generated at the node

until it is completely received by the destination.

Therefore, the average packet delay can be given by

++=

(4)

where

is the average time the packet stays

waiting for generation (idle state),

is the

average waiting time the packet experiences from

the moment it enters the idle state to the moment it

returns to it, S is the system throughput, and T is the

transceiver tuning time.

SN /

At the maximum offered load, we obtain

pWTR

1221 ++++

(5)

where 1/p is the average time a node waits before it

transmits its control packet in a current control slot.

We now can obtain the achievable throughput of

the system as follows:

++=

211

(6)

WTaWaTWDa

NaW

/222/1)1(

/1/1

++++++

(7)

At the maximum offered load, we have

NTNWWNTWNNNWTWNR

+++++++

2/2/24

2/)(1

. (8)

3.2 Multicast Transmissions

The analysis that follows assumes that a new

message arrives at the beginning of a time slot only

when transmission of a previous message is

completed at the end of the previous slot. A new

message is destined to node i with probability

If we now let

be the number of messages

addressed to node i at the end of m

Nl /

time slots, and

since node i can only receive one message during

any time slot, we the have

)1,0max(

−+=

− m

(9)

where

is the number of new messages arriving

and destined to node i.

When the arrivals are Poisson of rate A, the

average number of messages destined to a receiver

can be expressed according to the M/D/1 queue

system by

)1(2

−

. (10)

Since there are N nodes, each node has lW/N

transmissions intended for it and it only receives one

transmission at a time

, the average number of

transmissions required by a message can be given as

lower bounded

> max (W/N, 1). When lW < N the

system is channel limited, i.e., there are not enough

channels to keep all the receivers busy, the receiver

cannot be fully utilized because messages will have

to be retransmitted many times. When lW > N the

system is receiver limited, i.e., number of receivers

is too small to keep all the channels busy with new

transmissions.

Let M

max

be the number of messages waiting in

the transmitter queue and let Q

max

is the maximum

number of messages waiting in the queue, then the

number of new arrival messages can be obtained as

max

= M

max

− Q

max

. (11)

In a slotted system, if there are new arrivals to

the queue during a slot, half of these new arrivals

will be placed ahead of the given message in the

queue and half behind it. Hence, if

is the average

number of new arrivals to the queue, the average

waiting time in the queue can be given by

max

QTT +++=

. (12)

However, if the arrival rate is greater than unity,

will be infinite and S will be zero. Since the

transmission takes place on W wavelength channels,

the average number of completed multicast

transmissions per time slot is

/W and the average

arrival rate can be given by

TNWl

. (13)

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246

It is shown in (Laxman, 1997. Modiano, 1999)

that when the number of nodes with receiver busy

time is equal to the multicast size, the behavior of

the system could be described using an approximate

Markov chain model shown in Figure 3, where

represents the probability that the receiver is busy,

and

is the arrival rate of data packets per control

slots. The maximum receiver busy time over all the

nodes is assumed to be B

Rmax

. If a node has receiver

busy time less than B

Rmax

, the receiver busy time

equals to B

Rmax

– (L + T

) = L’. The probability that

the value of B

max

increases is given by

and the

probability that a multicast packet is transmitted in a

current slot is given by

. If B

Rmax

= 0 or 1, the value

of B

Rmax

approaches L'. Therefore, there is only one

forward transition from state 0 and from state 1 to

state L'. For B

Rmax

< L', the receiver busy times of the

nodes will either equals to B

Rmax

or zero.

Therefore, there are two possible probabilities.

The first is (

γσ

) if at least one node participating in

the multicast has receiver busy time equals to B

Rmax

and in this case the next state is B

Rmax

+ L' − 1. The

second is

(1−

) if all the nodes in the multicast

have receiver busy time equals to zero, and in this

case the next state is L'.

3.3 Channel Blocking Probability

Channel blocking probability is defined as the

probability that there is no sufficient capacity for a

channel in a finite link. For a finite buffer case, the

system throughput equals the arrival rate multiplied

by (1 - blocking probability) (Vastola, 1997).

In the following we make the assumption that

the multicast size has a uniform distribution. The

throughput is then limited by a form of blocking

results from a channel being efficiently used while

the message being transmitted on that channel is

waiting for receivers to become available.

Now consider a single channel

using W

i,on

and

i,off

to denote the mean on and off periods in a

finite system, respectively. Hence, the blocking

probability of channel i can be given by

offiionii

offii

λλ

−

(14)

where the numerator denotes the mean number of

failed attempts to subscribe to W

during a time slot

and the denominator represents the mean total

number of attempts during a time slot. When the

channel is off, we have

γ γ

γ (1

−σ

)

. . . . . .

−

γ 1

−

γ 1

−

γ 1

−

γ 1

−σ

γ 1

−σ

0 1 2

L'+1 L'+2

1)/1(

−=

offiiB

. (15)

Figure 3: Markov chain transition probabilities.

The request for connection between any two

users will be blocked if there is no wavelength

which is available on every link between them. We

assume that a node will select one message

randomly when there are many transmissions to

choose from. This means during each slot, W

messages are chosen for transmission from among N

nodes.

Let C be the average duration of a connection,

and

is the arrival rate on the i

link of the path.

The average offered load on the

link of the path

is then C

. Thus, the probability that all the W

channels are busy on that link connecting source and

destination which represents the probability of

blocking is finally obtained as

∑

⎟

⎠

⎞

⎜

⎝

⎛

)(

. (16)

4 RESULTS

The effect of tuning time on average packet delay is

shown in Figure 4. Note that when T increases the

packet delay gets larger but the system throughput

does not change because there is enough bandwidth

available to accommodate all of the traffic demand.

With larger T, the maximum throughput of system

stops at a lower value when

= 1 since more states

in the system are waiting for transmitting or

receiving packets.

0 10203040

Tuning time

Average packet dela

W = N = 10 0

W = 20, N = 10 0

Figure 4: Average packet delay vs. tuning time.

PERFORMANCE ANALYSIS STUDY OF MULTICAST TRAFFIC IN STAR-BASED LOCAL WDM LIGHTWAVE

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247

0 5 7.510 1520 2530 3540 4550

Receiver throughput

Average packet dela

l = 5

l = 15

l = 50

10 0

15 0

200

250

300

0 0.2 0.4 0.6 0.8 0.85 0.9 0.95 1

Offered load

Average packet dela

Tr = 0

Tr = 5

Tr = 10

Figure 5 examines the average packet delay

versus offered load characteristics of a system with

N = 100, W = 20, propagation delay is 10, receiver

tuning time is 0, 5, and 10, transmitter tuning time is

zero, and the offered load varies from 0 to 1. When

the offered load is high (1 >

> 0.8) the average

packet delay increases significantly since the

available channels will not be enough to

accommodate large number of packets that are

transmitted by the users.

In Figure 6, we demonstrate the average packet

delay versus number of wavelengths characteristics.

We can observe that for a same number of

wavelengths and average waiting time for a node,

the average packet delay is very small for a system

with zero tuning time and zero propagation delay

compared to a system with T = R = 10 control slots.

The maximum packet delay occurs when number of

wavelengths is small.

Figure 7 examines the effect of the average

packet delay on receiver throughput. Note that when

the destination group size is small the receiver

throughput is large since the mean number of nodes

with receivers busy is relatively small as the mean

number of receivers required by the new messages

that enter the system. The probability that a new

message can find the particular receiver it requires

for its particular multicast connection is high.

Figure 7: Average packet delay vs. receiver throughput.

Figure 5: Average packet delay vs. offered load.

Figure 8 demonstrates the receiver throughput

versus receiver tuning delay characteristics for a

system with 50 nodes and 10 channels. The

probability that the number of nodes with busy

receivers is assumed to be 0.5 and 0.8 and the

system has a constant multicast size equal to 5 and

15 respectively with packet length equal to 10.

0 10203040 5060708090100

Receiver tuning time

Receiver throughput

l = 5

l = 15

Figure 8: Receiver throughput vs. tuning time.

In Figure 9, we evaluate the system performance

in terms of channel blocking probability against

offered load for a system with 100 nodes and a

different number of channels. Note that for a same

load, the maximum blocking probability decreases

10 20 30 40 50 60 70 80 90 100

Number of channels

Average packet dela

T = R = 0, p = 0.05

T = R = 10, p = 0.05

T = 50, R = 10, p = 0.05

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 10 2030405060708090100

Offered load

Channel blockin

probability

W = 4

W = 10

W = 20

Figure 9: Channel blocking probability

vs. offered load.

Figure 6: Average packet delay vs. number of channels.

ICETE 2004 - WIRELESS COMMUNICATION SYSTEMS AND NETWORKS

248

as the number of channels increases. This is because

when the number of channels in a system increases,

the probability that every user in the system will find

an available channel also increases.

5 CONCLUSION

The system can accommodate large tuning delays

and keeps with suitable throughput when the number

of wavelength is equal to the number of nodes.

When the number of wavelengths is comparable to

the number of users the tuning time influence on the

packet delay increases. The multicast performance

may be improved by allowing the new messages to

be transmitted while the old messages are waiting to

be retransmitted. Alternatively, nodes select the

message they receive which transmits multiple times

to the same destination simultaneously. When the

system is examined under uniform distribution of

multicast set size, the throughput efficiency is higher

for a system with a small number of wavelengths

compared to a system with a large number of

wavelengths. When the system has many receivers

per message, it requires all those receivers to be

available as the transmission takes place and hence,

with a small multicast size the probability that this

requirement can be satisfied is bigger.

ACKNOWLEDGEMENT

The Authors would like to thank the Ministry of

Science, Technology and Innovation (MOSTI),

Malaysia, and the Institute of Research,

Development and Commercialization (IRDC),

Universiti Teknologi MARA (UiTM), Shah Alam,

Malaysia, for funding this research.

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