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Effect of Limited Wavelength Conversion in All-Optical Networks
Based on de Bruijn Graphs
by
Hassan Zeineddine
A Thesis Submitted to the Faculty of Graduate Studies and Research
through the School of Computer Science in Partial Fulfillment of the Requirements for the Degree of
Master of Science at the University of Windsor
Windsor, Ontario, Canada I991
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Hassan Zeineddine 1997 O All Rights Reserved
In this thesis. we study the effect of employing limited-range wavelength
converters in all-optical networks. We study the performance of the network in
terms of blocking probability (the percentage of blocked calls). In the network
simulation. we adopt a regular topology based on a de Bruijn graph of degree 4 and
diameter 5. Most of the previous work has assumed that wavelength converters
translate a wavelength to any other wavelength. In this work. we employ realistic
all-optical converters to study the performance of the network according to the
following parameters: the number of converters per node, the conversion range
of converters. the total number of wavelengths in the network and the number of
local wavelengths that a node can use for transmission.
To my Morn and Dad.
Acknowledgments
I wish to thank my two advisors, Dr. Subir Bandyopadhyay and Dr. Arunita
Jaekel for their patience and intensive support throughout my graduate studies.
Without their interests and advice. this work wouldn't be achieved. Special
appreciation for Dr. Bandyopadhyay for guiding me with a keen scientific instinct
towards the right questions. and for his valuable comments to improve the quality
of the thesis. It has been a great privilege to be his student.
I am also grateful to Dr. Peter Tsin and Dr. Yash Aneja for their helpful
discussions. and appreciated suggestions. A special thanks to all my friends at
University of Windsor who made graduate school survivable.
Most of all. I want to express my gratitude to my parents for their love and
support throughout the years. This thesis is dedicated to them.
vii
TABLE OF CONTENTS
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
. . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .... vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
. . . . . . . . . . . . . . . . . . . . . . . . 2 REVIEW OF LITERATURE 3
Components of an optical network . . . . . . . . . . . . . . . . . . . 3
Single-hop networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Multihop networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Wavelength routed networks . . . . . . . . . . . . . . . . . . . . . . . 9
Static and dynamic schemes for allocating lightpaths . . . . . . . 12
Wavelength conversion in optical networks . . . . . . . . . . . . . 13
De Bruijn graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 PROBLEM SPECIFICATION . . . . . . . . . . . . . . . . . . . . . . 22
Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Our approach in a nutshell . . . . . . . . . . . . . . . . . . . . . . . 24
Illustrative examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 NETWORK SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . 33
Initialize parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
. . . . . . . Random select~on of a valid sourcedestination pair 35
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Establish lightpath 35
1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 RESULTS OF SIMULATION EXPERIMENTS . . . . . . . . . . . 44
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Topic 1 Experiments 1 and 6 . . . . . . . . . . . . . . . . . . 51
Topic 2 Experiments 2 and 7 . . . . . . . . . . . . . . . . . . 53
Topic 3 Experiments 3 and 8 . . . . . . . . . . . . . . . . . . 57
Topic 4 Experiments 4 and 9 . . . . . . . . . . . . . . . . . . 61
Topic 5 Experiments 5 and 10 . . . . . . . . . . . . . . . . . . 65
Critical Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6 FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 CONCLUSION 73
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX A 75
Set of results for alternative paths routmg . . . . . . . . . . . . . . 75
Set of results for shortest path routmg . . . . . . . . . . . . . . . . 76
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 VITA AUCTORIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 1 5
Figure 1 6
. . . . . . . . . . . . . . . . . . . . . Single hop network 6
. . . . . . . . . . . . . . . . . . . . . . Multihop network 8
. . . . . . . . . . . . . . . Wavelength routed network 11
. . . . . . . . . . . . Wavelength convertible network 14
. . . . . . . . . . . . . . . . . G(2. 3) de Bruijn graph 18
. . . . . . . . . . . . . . . . . . . Illustrative example 1 27
Illustrative example 2 . . . . . . . . . . . . . . . . . . . 29
Illustrative example 3 . . . . . . . . . . . . . . . . . . . 30
. . . . . . . . . . . . . . . . . . . Illustrative example 4 32
Simulation example . . . . . . . . . . . . . . . . . . . . 43
Charts of 10 Vs . 100 runs . . . . . . . . . . . . . . . 48
. . . . . . . . . . . . . Charts of experiments 1 and 6 52
Charts of experiments 2 and 7 . . . . . . . . . . . . . 56
Charts of experiments 3 and 8 . . . . . . . . . . . . . 60
Charts of experiments 4 and 9 . . . . . . . . . . . . . 64
Charts of experiments 5 and 10 . . . . . . . . . . . . 66
xii
List of Tables
Table 1 Comparison between experiments 1 and 3 . . . . . 58
Table 2 Comparison between experiments 2 and 4 . . . . . 62
Table 3 Converters - alternative paths routing . . . . . . . 69
Table 4 Converters - shortest path routing . . . . . . . . . . 69
Chapter 1 INTRODUCTION
Wavelength-division and multiplexing (WDM) is a technique allowing sevenl
communication channels to exist concurrently on a shared transmission medium.
Due to WDM's newly gained popularity in the telecommunication field. especially
with optical fibers. new perspectives emerged in the area of lightwave networks.
Wavelength routed all-optical networks started to receive attention and there are
sevenl studies dealing with wavelength allocation techniques. Some of the studies
concentrated on the number of wavelengths in the network. In other words, they
investigated techniques to maintain the best network performance with the fewest
possible number of wavelengths in the network. Recently. with the appearance
of limited-range wavelength converters, there have been studies on the effect of
applying wavelength conversion in wavelength routed networks. Prior to the
existence of technologically feasible limited-range wavelength converters, the
possibility of full range conversion has been investigated in the literature. Full
conversion is achievable by transforming the signal into the electrical domain. and
retransmitting the signal using some other wavelength. Thus. the network will
not be all-optical since the performance is bounded by the electrical interface.
However, limited-range wavelength converters are now available to convert a
wavelength to another nearby wavelength purely by operations in the optical
domain. In this case, the network still remains an all-optical network.
The effect of wavelength conversion on network performance has been studied
in [ 1,5.12.16]. In our work, we investigate the effect of employing limited range
wavelength converters in networks based on the de Bruijn graph topology G(4.
5). In the problem specification chapter, we give details about the parameters
adopted in the study.
We use network simulation in our studies and have written a program to model
the network components and the traffic. After running the simulation experi ments.
we derive the blocking probability (percentage of blocked call). We describe our
strategy in building the simulation in chapter 4 which gives details about the
steps adopted in the simulation process.
After collecting the simulation results, we show the most significant results
using charts. We have included. in chapter 5. discussions on the experiments
including a critical summary on the general observations summarizing the results
of all experiments. In chapter 6. we have suggested possible topics for future
studies in the field.
Chapter 2 REVIEW OF LITERATURE
2.1 Components of an optical network
After intensive research during the 1970's, optical fibers are now available
for commercial use in networking and data communication. Since optical net-
works provide higher bandwidth than networks based on electrical signals. an
optical fiber is able to carry hundreds of megabits per second over a distance of
a few kilorneters[3]. Its high bandwidth over long distances, immunity to elec-
tromagnetic interference and cross talk. and reliability against tapping. made the
optical fiber cable a very secure communication transmission medium[3]. In the
literature, several components for optical networks have been tested or discussed.
In an optical network. each optical signal is generated by a transmitter that
is typically a light-emitting diode (LED) or a laser diode (LD) and are connected
through fibers. A destination node receives optical signals by a receiver which is
either a photodiode or a photo transistor. The transmitter converts binary data to
a sequence of on-off light pulscs and transmits the light pulses through the fiber.
At the receiver side, the light pulscs are converted back to the electrical domain
so that computers may proccss rhc binary data in the form of electrical signals.
The Wavelength-Division Multiplexers and demultiplexers(2] operate on spa-
tially separated wavelengths. Tbc multiplexer combines individual signals from
the input pons and merges thcm into one signal which is sent through a single
output pon. The demultiplexer extracts the components from a composite light-
wave signal coming from a single input port and sends the component signals
through a number of output pons.
The Wavelength Router[lS] sends an input signal to an output port according
to the assigned wavelength. It is a generalization of the wavelength-division
demultiplexer where a network of demultiplexer forms a router. A router may
incorporate wavelength translator as well. In such a router. the wavelength of
the incoming signal may be converted to a new wavelength during the process
of selecting an output port.
The Acousto-optical Tunable Filter(l51 is used to select one or more wave-
length from a lightwave signal consisting of several multiplexed wavelengths.
To obtain the maximum benefit from the high bandwidth provided by the
optical technology. it must be possible to have concurrent transmission from
different users. One major limitation is the fact that user stations currently send
data through the fiber only at electronic speed (of the order of Mbps) which
is substantially lower than that of optical signals (of the order of Gbps). The
wavelength-division mu1 tiple access protocol (WDM) is used to allow concurrent
transmissions. In WDM systems. each user transmits at a bit rate equal to the
peak electronic speed on a specific wavelength channel. All user channels exist
simultaneously on the same fiber. Time division multiple access (TDMA) and
code division multiple access (CDMA) [2) are two other protocols investigated
in the lightwave networks but were less effective and attractive than WDMA. In
TDMA. nodes have to synchronize within one time slot. and one chip time for
(CDMA) which makes this technology difficult to use in the lightwave industry
Lightwave networks are classified according to three categories: single hop
networks, multihop networks. and wavelength routed networks. Each classifica-
tion will be explained in a subsequent section.
2.2 Single-hop networks
An optical network is called an all-optical network if there is no conversion
of the signal from the optical domain to the electrical domain during its entire trip
from the source to the destination (Fig. I) . In single hop networks(IO]. optical
signals are sent directly from any source to any destination without being routed
through intermediate nodes in the network.
Wavelength icl
k2
/ la- Transmitters Broadcast Star Tunable receivers
Figure l Single hop network.
One classification for WDM single hop systems is based on whether the
transmitters and receivers are tunable or fixed. There are 4 categories in this
classification; fixed transmitters-fixed receivers (FTs. FRs). fixed transrnitters-
tunable receivers (FTs. TRs). tunable transmitters-fixed receivers (TTs. FRs). and
tunable transmitters-tunable receivers (?Ts. TRs).
2.3 Multihop networks
In multihop networks11 I]. a signal travels from a source to a destination by
passing through zero or more intermediate nodes. When designing the network.
each node is assigned a set of channels for transmitters and. possibly, a different
set of channels for its receivers. Unlike single hop networks. in this approach, a
node cannot communicate directly with all other nodes in the network. A node S
can directly communicate with a node D, only if one of the transmitter channels for
S is a receiver channel for D. In other words, S communicates directly with D by
setting one of its transmitters to wavelength X and then starting the communication.
At the same time, D gets ready to receive the signal by tuning one of its receivers
to the same wavelength A. By this method of pre-assigning channels to the
nodes of the network. a logical topology (also called virtual topology) may be
defined. This logical topology determines which nodes can communicate directly
and hence defines the connectivity pattern of the network. The logical topology
can be represented by a graph where the nodes represent computers and an edge
from node x to node y represents the fact that node x has a transmitter which can
send at a wavelength X and node y has a receiver which can be tuned to the same
wavelength A. Depending on how the transmittedreceiver channels are assigned,
it is possible to define an irregular or a regular graph as the logical topology. In
a regular graph. all nodes have the same degree'. and the route from a source
node to a destination node. is achieved by means of some simple algorithm. The
actual network, consisting of computers linked by fibers, is called the physicoi
topology. For instance, the channels assignment for nodes connected in a star
physical topology may be represented in a logical topology that could be a toms
or a hypercube as shown in figure 2.
- -
' the degree of a node specifies the number of incoming edges and ourgoing edges a[ that M e .
7
An example 2 x 2 (4 node) multihop network: (a) physical topology; (b) logical topology.
Figure 2 Multihop network.
Designing a rnultihop network involves finding an efficient logical topology
8
for the network. The transmitter/receiver channels are assigned as links among
nodes following the logical topology. The goal for the designer is a topology
having a small average distance between nodes (the number of hops a packet will
make. on an average. from a source to a destination). and a simple routing scheme.
2.4 Wavelength routed networks
A wavelength routed network is usually an all-optical network. Each end-
node in the network is connected to an optical router using one or more fibers.
Each router is connected to one or more routers following the desired topology.
Every pair of end-nodes, representing a source and a destination, communicate
through an optically transparent channel and uses one wavelength division mul-
tiplexed (WDM) channel per fiber. Each WDM channel has an associated wave-
length. The end-to-end transparent channel for a communication is also called a
lightpath. Routing through intermediate nodes is relatively simple where simple
routing operations (e.g., optical wavelength deflection. wavelength conversion)
are performed on the signal. In such networks, the electronic bottleneck of mul-
tihop networks is avoided by using only a single lightpath from a source to a
destination for communication without any conversion to the electronic domain
at intermediate nodes in the route,
As an example, an all-optical wavelength routed network consisting of 4 nodes
is shown in figure 3. Here each link is capable of carrying two WDM channels
having wavelengths X I and A2. There are four end-nodes. W. X, Y and Z in
the network. connected to four routers 1. 2. 3 and 4 respectively. If W is the
source for a communication and Y is the destination. one possible lightpath uses
the following route
from end-node W to router 1
from router 1 to router 2
from router 2 to router 3
from router 3 to end-node Y
The end-to-end transparent channel for thc con~munication is shown in figure
3. From now on. to describe an optical route. \kc will specify only the nodes
connected to the routers in the path since tllc ;~ciu;ll route follows directly. The
route from W to Y using this notation is \\' - S - Y. In order to establish a
connection from W to Y. we need an cnd-lo-cnd innsparent channel such that
every WDM channel is currently nvailahlc c1.c.. ha\ not been allocated to any
other lightpath). I1 is clear that the connrcwn I \ not possible using wavelength
,\I since a channel with wavelength . \ I I \ ~lrcd! , used on the link X -- Y.
However. the connection can be done using ~ w c l c n ~ t h A?. since Ar has not been
used on links W -- X and X - Y. Th. 11 I \ p~\siblc to have an end-to-end
transparent channel from W to Y using \wclcnpth .\?.
Figure 3 Wavelength routed network.
Node
,,,,- Router
Due to restrictions of filtering and cross-talk. the available technology does
! Channel u :
: I , b
not allow us to have a large number of wavelengths on the same fiber[& 91.
Thus the number of wavelengths required to establish end-to-end transparent
! A 1 ' I
channels should be taken into consideration while measuring the efficiency of
. \ -. ' --- '-. ' Optical .' -----* Fiber
Cables
a particular topology. Thus. a system with better wavelength reuse capability is
: I t ' I , L I
more desirable. In addition. another metric is the power loss characteristics of a
topology. The power loss metric is calculated by the average number of nodes
i 1 t 3 1 4
traversed by a routed signal from any source to any destination. It is highly
+ ,,.--,,,,,- -- ---,,
desirable to have a low power loss in a system.
-..---.,.------
Due to the available photonic technology, low efficiency in performance is
the price for implementing all-optical networks[l] . However. the simple network
control mechanism and the spatial reuse of wavelengths in meshed topologies are
two important advantages over single hop and multihop systems.
Several options exists in designing lightwave systems by the trade off between
space diversity and wavelength diversity. In [8. 91, several topologies for
wavelength routing systems have been studied and compared.
2.5 Static and dynamic schemes for allocating lig htpaths
For all-optical wavelength routed networks. the proposed schemes for wave-
length allocation to allow a number of source-destination pairs to communicate
simultaneously can be classified as static or dynamic.
Static lightpath allocation in networks is a technique of assigning a static
end-to-end transparent channel to every source-destination pair in the network.
For any communication between two nodes. the path and the wavelength are
predefined. A. Marshan et ai, [8]. reported the number of wavelength needed in a
number of topologies using a static allocation technique. For example, in the de
Bruijn graph topology G(A, d) - see section 2.7. the total number of wavelengths
needed to establish connections between all possible source-destination pairs is
dAd- l , assuming that a single fiber connects each pair of adjacent nodes. The
problem with static methods such as [8]. is that it assumes that each node can
communicate with every other node simultaneously and, as a result, the number
of wavelengths required is large compared to the actual number needed at any
given period of time under realistic conditions.
Dynamic wavelength allocation is a technique of assigning WDM channels to
create a lightpath to a source-destination pair as needed and then reclaiming the
WDM channels once the communication is over. R. Ramaswami described[l4]
a wavelength allocation scheme where he proved that the number of required
wavelengths in the network is considerably less than what is needed in the static
method described in [8 1. This may be used in a dynamic strategy with little
modifications. For example. in a de Bruijn topology G(4, 5) where each node
can initiate 5 simultnneous connections. 14 wavclcnpth are enough to keep the
blocking probability equal to 1 o - ~ while thc s ~ i c allocation technique given by
Marshan et a1 requires 1280 wavelengths. On t l~c other hand, the price for such
improvement in the required number of w u cicnpthh. is the time delay and the
processing overhead causcd by searching l'or an dlc wavelength on all the links
that make the path betwcen the source-dc\t ~n;rllon pair.
2.6 Wavelength conversion in optical networks
Wavelength conversion in all-optical n c r ~ o r k s i s a scheme that allows the
wavelength of a lightpath. connecting s sour^-c-dcstination pair using route R, to
vary from one fiber in the roure R to the ncu t i k r in the route. In general, an
I.?
incoming signal reaching a node using wavelength A, may be translated to some
other wavelength Xb before routing it to some outgoing link.
Figure 4 shows the same optical network described in figure 3. where a
connection is required between node W and Y on the following route: W -- X - Y. Node W starts transmitting through X I which is the only available wavelength
on the link W - X. Since X I is occupied on the link X -- Y. the router at X
converts A , to the available wavelength X2 before routing the signal through the
link X Y. In this particular example. wavelength X I and X 2 on the route W - X -- Y form the lightpath carrying the connection between W and Y.
Figure 4 Wavelength convertible network.
14
Before the appearance of the all-optical wavelength converters with their
limited wavelength conversion capability. full wavelength conversion could be
achieved only by
transforming the signals in the optical domain to the electrical domain
reconvert it into optical domain using some other carrier frequency.
The bottleneck caused by the electronic interface at each step of wavelength
conversion means the major benefit of optical communication - transmission
speed. is lost [6].
Another approach is to use optical wavelength converters with limited wave-
length conversion capability[l2. 161. In this case, the price of taking advantage
of the full speed provided by the optical fiber was to live with the limitations of
the optical converters. where each wavelength can be convened only to a set of
nearby wavelengths and not to the complete range of the available wavelengths.
The conversion range defines what the nearby wavelengths are. If the set of
wavelengths in themetwork is Xo, XI, ... AN-, and if the conversion range is K. a
converter can convert a wavelength Xi to one of the wavelengths in the following
set : (Xi + 1 , . . . . Xi + K), where the addition is performed modulo N.
The first study about the effectiveness of limited-range wavelength conversion
was reported by J. Yates et al. in [16]. They analyzed simulation results for the
ring and the mesh torus topologies. "In many cases. limited-range wavelength
translators can provide almost d l of the improvement in blocking probability
by full-range translators."[ 161 Other studies assuming full wavelength conversion
were to derive the blocking probabilities in paths with and without wavelength
converters [ 1 . 51.
Sometimes, an all-optical wavelength routed network is said to be a wave-
length convertible network when wavelength conveners are used(61. In such
networks. each node has a router and a set of wavelength converters. Each con-
vener will serve to translate one wavelength at a time. Once a converter has
been allotted to a lightpath. it cannot be used to serve another connection until
it is free again.
2.7 De Bruijn graph
The de Bru ijn graph is a well known regular topology for data communication
and has been investigated for multihop lightwave networks and for wavelength
routed networks[ 1 1. 141. A (A. D) de Bruijn graph is a directed graph having
lD nodes where the degree of each node is A. Any node S in a (A, D) de Bmijn
graph may be represented by a suing of D digits sl sz ... SD where each digit
is between 0 and A - 1 . A network with - z3 nodes may be represented
as follows :
Node number
0
String representation of the node I
000
A node A = a1 a2 ... aD is connected to a node B = bl bz ... bo (A -- B) iff
A link between adjacent nodes may be represented by @ + I ) A-ary digits. For
instance, the edge from node 0 10 to 10 1 may be represented by 010 1 . In general.
the first D digits of the edge from il node A to an adjacent node B is the address
of node A, and the last D digits is the address of node B. Figure 5 shows the
connectivity pattern of n G ( 2 . 3) de Bruijn graph.
Figure 5 G(2. 3) de Bruijn graph.
In [14]. the procedure to find the shortest path between any source node A =
a , a2 ... a~ and any destination node B = bl bz ... bD is described as follows:
1 . Find the smallest value k such that (bl b2 ... bD,k) = (ak+l ak+Z ... a ~ )
2. The shortest path between A and B is given by the following path :
Example
a) In a G(4, 5) de Bruijn graph the shortest path between node 10220 and
node 2201 1 is as follows :
The number of hops is equal to 2.
b) In a G(4. 5). the shortest path between 1002 1 and 20200 is as follows:
The number of hops in this case is equal to the maximum distance 5 between
any two nodes in G(4. 5).
The diameter, or the maximum hop distance. in a de Bruijn graph G(A. D)
is equal to D. Considering N as the total number of nodes ( A ~ ) in G. the mean
hop distance between any two arbitrary nodes is given by h. [14], where
One of the attractive features of the de Bruijn graph is the fact that the
connectivity of such graphs is high so that a number of alternative paths exist
between any source-destination pair. In addition to the shonest path routing.
another routing strategy has been investigated in the literature which is called the
altemative routing strategy [13]. The main idea behind this strategy is to explore
several alternative paths rather than the shortest path only. In general. between
any source node A = a1 a2 ... aD and any destination node B = bl b2 ... bD. in a
de Bruijn graph G(1. D). there exist il paths of maximum length equal to D + 1.
The ith path. for all i. 0 5 i c D consists of
the edge a1 a2 ... a~ -- a? a3 ... a~ i followed by the
shortest path from a? a3 ... a~ i to B.
The 1 alternative paths existing between A and B are :
1. Path 1: a , a2 ... aD -- a? a3 ... aDO -- ... shortest path ... --bl bz ... b~
2. Path 2: a1 a? ... aD - a? a3 ... a~ 1 -- ... shortest path ... --bl b, ... b~
4. Path 1: a1 a2 ... aD - a2 a3 ... a ~ ( h - 1 ) - ... shortest path ... --bl
b2 .-. b~
One of these altemative paths is
Example
In a G(4. 5) de Bmijn graph
node 2201 1 are the following :
the shortest path from A to B.
the 4 alternative paths between node 10220 and
De Bruijn topology supports larger number of nodes compared to the Shuffle
net Topology for the same degree and avenge number of hops[9, I I 1. It retains
the simple addressing and routing properties of ShuffleNets. However. the shuffle
net performs better than de Bruijn graph when the network diameter is small[9].
It has been reported that simulation experiments on 1024 nodes connected in a
shuffle net topology and later in a de Bruijn graph topology indicate that de Bruijn
graph topology has a higher throughput and lower average delay than the shuffle
net [14].
Chapter 3 PROBLEM SPECIFICATION
3.1 Problem definition
A previous study [ i j j by A. Sengupra. S. Bandyopildhyay, and A. Jaekei
showed that. if we explore a limited number of alternative routes in a de Bruijn
graph instead of the shortest route alone, the blocking probability can be reduced
significantly. In this investigation. no wavelength conversion was allowed. This
leads to the following question:
I f we use a wavelength convertible all-optical nenvorks. and explore alternarive
routes, can we achieve a better result?
In this thesis. we have studied this problem. Our objective was to measure
and analyze the effect of applying limited wavelength conversion to an all-optical
network based on a regular topology. Due to the attractive features of the de
Bruijn graph mentioned above, we decided to study the de Bruijn graph as a
physical topology for our network.
If the conditions for establishing a communication from a source S to a
destination D is satisfied. then an end-to-end optical lightpath can be defined
from S to D. When designing a network. a very important consideration is the
expected number of attempted communications which were not successful. The
blocking probability is the ratio of the number of calls which are not successfuI to
22
the total number of attempted calls. This blocking probability depends critically
on a number of factors. One of our primary tasks was to identify which factors
are critical. The factors we considered are
The total number of wavelengths in the network.
The number of wavelengths a transmitter in a node can tune to.
The number of wavelength conveners per node.
The convertibility limit of a wavelength convener.
Routing strategy.
In brief. our major concern is to reduce the blocking probability (ratio of
blocked call to the total number of calls). Dr. Ramaswarni [I41 has studied
the blocking probability of applying dynamic wavelength allocation technique
in wavelength routed all-optical networks without wavelength conversion. Dr.
Bandyopadhyay et al. [I61 have carried out a similar study by allowing the traffic
to be routed on the alternative routes. Some previous studies considered the effect
of applying full wavelength conversion in all-optical networks [ I . 51. One study
[I61 considered the effect of limited wavelength conversion in torus networks.
We believe that our study is the first to consider the problem of applying limited
wavelength conversion to networks based on the de Bruijn graph. taking into
consideration the above mentioned list of parameters.
3.2 Our approach in a nutshell
As mentioned earlier, we are interested in the ratio of b
total number of attempted calls. In order to generate the req
implemented a network simulator that runs' as follows:
locked calls to the
pired statistics. we
Initialize network parameters (a list of parimeters is given in the previous
section).
Run steps 3 to 6 ten times accumulilting the number of misses and hits
resulting from each run.
Repeat steps 4 to 6 until no source with on available transmitter or no
destination with an available receiver c ~ s t s .
We randomly pick a source with an av31l;lhlc trmsmitter and a destination
with an available rccciver.
a. If we arc considering the shonc\t pat11 routing alone. we establish. if
possible. a lightpath involving thc lour\t number of conversions using
the shonest path.
b. If we are considering the altcmcltnc path\ routing. we establish. if
possible. a 1 ightpath involving the low c\t number of conversions on
the shonest path. If the shonc\~ rwtc i \ blocked. we try to establish
a connection on the alternative route that provides a lightpath using a
minimum number of conversions.
6. If we are successful in establishing a lightpath. we increment the number of
hits; otherwise, we increment the number of misses.
7. We calculate the ratio of blocked calls to the total number of attempted calls.
3.3 Illustrative examples
We now give some examples to illustrate the problem and our approach to
the problem.
Example 1 In this example we have an all-optical network based on a de Bruijn
graph G(2. 3) where each node in the graph represents a computer in the network
connected to an optical router and each edge represents a communication link.
We assume that each edge in our network is realized by a single optical fiber and
can carry a total of two wavelengths A 1 and X2. In this particular example (Fig.
6), let there be two existing connections :
a connection from node 000 to node 101 using wavelength A2
a connection from 100 to 00 1 using h l
Both connections use the shortest path from the source to the destination. We
now attempt to establish a connection from 100 to 010. If no optical wavelength
converter is used in this network. the connection from 100 to 0 10 is impossible
using the shortest path because we need a channel that must be free on all links
on the path from the source to the destination. In this case, the shortest path
connecting 100 to 010 is 100 - 00 1 - 01 0 where h 1 is already used on the
edge 100 - 00 1 and X2 is already used on the edge 00 1 - 0 10. Thus. there is
no wavelength available for both the edges 100 - 00 1 - 0 10 and 00 1 - 0 10
and the connection is blocked.
If we wish to use the shortest route and communicate from node 100 to 0 10,
we have to use a wavelength converter at 001. In this case, node 100 transmits
the signal at X2. 001 will route the signal to 0 10 after converting the wavelength
carrier A2 to X I . Finally, 010 will receive the signal coming from 100 at X2.
Figure 6 Illustr~tivc cwnplc 1.
Example 2 Now we consider a situilrion u l w c cach node in a network based
on G(3. 4) has a number of limited w\-clength crmcners and each link can
carry four concurrent wnvelengths. Each arnuner can convert one wavelength
hi to the next adjacent wavelength + I I nltd I]. The current situation in one
selected path is shown in figure 7 so that on cdpc 20 12 -- OIZO. for instance,
wavelengths A. and 8\? are currently in uw. At any time. we are free to use
wavelengths A I and X3 on this edge.
We now examine one scenario (lightpath 1) in detail.
Node 2012 can use wavelength X I to send a message to node 0120 using
the edge 2012 -- 0120.
Sincc X 1 is not available on the ncx: link 9 120 - ! 202. we need tc tcnven
the wavelength from X 1 to X 2 for communication on the edge 0 120 -- 1202.
Since A2 is not available on the next link 1202 - 2022. we need to convert
the wavelength from A2 to X 3 for communication on the edge 1202 -- 2022.
However. all the conveners at 1202 are already allocated and this particular
attempt is blocked (Fig. 7).
Similarly our next attempt (light path 2 in figure 7) is also blocked since
neither A3 nor Xo exists on the link 1202 -- 2022 to carry the incoming signal
originally carried by A 3 . Our final attempt (light path 3 in figure 7) is successful
since all the required wavelengths and the needed converters are available. In this
case, two wavelength trimslations are needed for this communication process.
Conversion Table
All converters
Light path 1
k Blocked Y
P v 0
Light path 2 Light path 3
2 conversions are needed.
Figure 7 Illustrative example 2.
Example 3 As an extension of example 2. if we allow each wavelength to
be converted to two adjacent wavelengths as shown in the conversion table of
figure 8. and taking into consideration the available wavelengths on each link,
the communication can use any one of six possible lightpaths (lightpaths 1 -
6 of figure 8). According to the lightpaths table shown in figure 8. lightpaths
number 1 and 4 involve the lowest number of wavelength conversions. Since we
are interested in selecting a lightpath having a minimum number of conversions,
we may randomly pick either lightpath 1 or 4.
Conversion Table
-1 13
p, p, pa pi3 pn yi3
?.nP,?,?,?,,P, All converters
C W + i + 4 i are busy
p o A0 P m pi0 pa f a
pi0 0 0 0 p i 1 [* p k o p,1 p 0 0 0 L
wavelength Conversions
Figure 8 illustrative example 3.
Example 4 This example shows how the availability of alternative routes helps
us in establishing communicarion. As we mentioned in section 2.7. a de Bruijn
graph G(A, D). has. in general, 4 or 3-1 alternative paths of length almost D
+ 1 , from any source to any destination. Three altemative paths from node 20 12
to 0222 are shown in figure 9.
When node 20 12 needs to establish a communication with 0222. we consider
three possible connection requests - one for each of these alternative routes as
foilows :
We first consider the shortest route ( 20 12 -+ 0120 - 1202 - 2022 - 0222). This attempt did not work since the call was blocked at 0120.
We now consider the first alternative route ( 2012 -- 0121 - 1210 - 2102 -- 1022 -- 0222). This was successful and needed 2 wavelength
conversions
We now consider the second alternative route ( 2012 - 0 122 - 1220 - 2202 -- 2022 - 0222). This was successful and needed 1 wavelength
conversions.
Since the lightpath on the second altemative route number involved fewer
wavelength conversions. than that for the first altemative, we will use the second
altemative for our lighrpath. If all these routes are blocked. the request for
connection is considered to bc blocked.
Conversion Table
I AO. i2. W 7
Table of lightpaths that involve the minimum number of converters on each route
Shortest route
0120 NO matching 1 lighpa th has
1 202 ; been found 2022 I on this mute
I
Alternative route 1
7 9 ! Destination
f 2 wavelength conversions
Alternative 2 I
Figure 9 Illustrative example 4.
: wavelength - -*,e- - , - - - - - - - -, 2012 1 A0
I
0122 1 A0
1220 j 10 2202 1 11
I
2022
The lightpath that involves the minimum number of wavelength conversions on the alternative route # 2 is to be considered.
+ t wavelength conversion
Chapter 4 NETWORK SIMULATION
Since it is difficult to apply analytical tools to study the run time behavior
of the investigated network. we will study our approach using simulation. We
first describe the steps of the simulation process and then describe how we have
implemented the simulator.
In this study, we start with an initial condition where the network has no
communications at all. In such a situation all attempts to establish connections
are guaranteed to succeed. Then we generate arbitrary source destination pairs and
attempt to establish a lightpath between each pair. Some of these attempts will
succeed and the rest will fail. As the process continues starting from the initial
condition. more and more attempts will fail. The network is "saturated" when
all transmitters and all receivers in the network are used up. We have chosen to
generate source destination pairs until the network is "almost saturated" where we
need a very large number of attempts to establish a communication. At this point.
we stop the simulation program and collect summary information regarding the
number of successful connections and the number of failed ones.
The number of successful connections depends critically on the number of
wavelengths used in the network. Since we wish to design a network using as
few wavelengths as possible. we vary the total number of wavelengths in the
network in different simulation runs. We assume a G(4. 5) de Bmijn topology,
where each node has
El a router
4 incoming and 4 outgoing fiber links
5 transmitters and 5 receivers. The set of wavelengths that each transmitter
can tune to is either the entire set of wavelengths in the network or a
selected subset.
a fixed number of wavelength conveners.
We now elaborate the steps of the simulation process described in section 3.2.
4.1 Initialize parameters
before running the simulation. we initialized the following list of parameters:
Node degree A, and network diameter D.
Number of transmitters and receivers per node.
Number of wavelengths in the network.
Number of wavelengths per node.
Number of wavelength converters per node.
Conversion range for each wavelength converters.
Routing strategy.
4.2 Random selection of a valid source-destination pair
During the simulation run. we pick a source and a destination randomly using
the following algorithm:
at the source node Q:
a. Repeat
Pick a random source node S
Until S has an available transmitter.
b. Repeat
Pick a random destination node D
If D has no available receiver, it is not usable.
If D and S are the same node, it is not usable.
If a previous communication from S to D has failed. it is not usable.
Until 3 usable D is found.
4.3. Establish lightpath
After choosing a random source-destination pair. we attempt to establish the
lightpath using the protocol given below. In our description. when we talk about
a path P from the source node S to the destination node D. we mean either the
shortest path or any one of the alternative paths as discussed in section 2.7. This
path P has k edges and has the form xo = S - x 1 - ... - xk- = D so that the first
node is the source S, the last node is the destination D and x i -- ... - xk-2 are
the intermediate nodes. In our algorithm. we will assume that each wavelength
X i on a particular edge p - q. has an index given by p -- q) which
shows the number of conversions needed to reach /Ii at the edge p -- q from the
source S. All wavelength indices are originally initialized to lnfini$. We will
use the array W having the path as index. to store the wavelengths making the
lightpath. We will use As to denote the set of wavelengths that a transmitter in
node S can tune to. Let N be the total number of wavelengths in the network.
We will denote a wavelength by X i , O i < N.
We summarize the algorithm for establishing a lightpath in two points:
Update all the indices of all wavelengths which are not used on the path
from S to D.
Choose the lightpath that involves the lowest number of conversions by
checking the indices.
We give the details of the algorithm below.
At the source node. we derive the path P from S to D according to the
algorithm described in section 2.7 (de Bruijn graph). In addition. for every
wavelength not used on the outgoing edge belonging to P. we set its index to
-
By Infinity we mean a very large number that is greater than my number uxJ in our ofxntlons.
36
zero. If all the wavelengths are occupied, we consider the connection to be
blocked. The following algorithm describes the procedure at the source node: Processing at the source node xo (=S):
a. Find the required path P from S to D.
b. For every .!; not used o ~ ? he ourgoing edge xc - x : . If A , E As . Set xo - x,) to 0.
c. If every xo -- X I ) = Infiniv.
Repon that the connection is blocked on the path.
At each intermediate node, we update the index of each wavelength A on the
outgoing edge. The index could be the index of the same wavelength X on the
incoming edge. or the index of another wavelength. convertible to X. incremented
by 1. The value of the index should be the lowest possible value.
The following algorithm describes the process at intermediate nodes:
37
Processing at intermediate nodes x,, 0 I r < k-1:
a. For every X i not used on the outgoing edge x, - x,~.
al. If Index(Xi. x,- -- x,) c lnfinip.
Set Index(&. X, - x,,) to index(,+. x,- 1 -- x,).
aZ. For every Aj not used on the incoming edge x,+ -- x,.
If A, is convertible to Xi, and
If x,- 1 -- x,) + I < Index(Xi, X, - xr+l ). and
If there exists a free convener at x,,
Set Index(Xi. x, - n,,! ) to Index(,\,. x,- -- x,) + I .
b. If every x, -- X,I ) f t ? / h i h .
Repon that the connection is hltx.Ld on the path.
At the destination node. we derive tho 11ghrp;blh which involves the minimum
number of conveners according to the tidloump algorithm:
38
Processing a t destination node X ~ - I (=D):
Derive lightpath:
a. At the edge xk-2 -- xk- ,. al. Get the minimum Index(Xi, xk-2 - ~ k . l ) .
a2. Set W[k-21 to ,ii.
b. For every edge x,-I -- x, on the path P,
bl. If Index(W[r], x,-I - x,) = Index(W[r+l], x, -- xWl) .
Set W[r] to W[r+l].
b2, Else
b2'. Get the minimum 1ndex(Xj, x,-~ -- x,), where
Aj is convertible to Xi.
b2". Set W[r] to Xj.
Choose lightpath:
a. If we are using shortest routing, Choose P and W.
b. If we are using alternative routing,
bl. If the shortest path is not blocked, Choose P and W.
b2. Else Choose P ' and W' that involves the minimum
number of conversions.
After choosing the lightpath, we establish the lightpath by locking the desig-
39
nated wavelengths and the needed converters. The following algorithm describes
the process of establishing a lightpath:
Establishing Lightpath:
For every node x, != D on the path P.
a. Reserve W[rj.
b. If a wavelength conversion is needed,
Decrement the number of converters at x,.
Example As an illusuation. we will apply the previous algorithm to the example
number 3 given in section 3.3. Beside each edge, we show the wavelengths that
are currently available. In this example (Fig. 10). S is 20 12 and D is 0222. We
assume that transmitters in S are tunable to the whole set of wavelengths in the
network. Considering the shortest path routing. we apply the previous algorithm
as follows:
a. For the edge 20 12 -- 0 120. since A I. A?, and h3 are not in use, we update
the indices for these wavelengths to 0.
b. For the edge 0120 -- 1202.
we set the index of A. to 1, because
Xo is not available on the incoming edge 20 12 -- 01 20, and
the index of X r on 20 12 -- 0 120 after being incremented by I is less
than the index of A. on 0 120 -- 1 202. We considered A z because
it is convertible to A*.
we set the index of ,\r to the index of A 2 on the incoming edge 2012
-- 0120. because
Xz is ava~lable on 2012 - 0120. and
the indices of Xo and XI on 201 2 -- 0 120. after being incremented
by 1 . are not less than the indcr of A? on 0120 -- 1202. We
considered Xo and XI becausc hoth of them are convertible to X z .
c. for the edge 1202- 2022.
we set the indca of Xo to the indrk (II on the incoming edge 0120
-- 1202. bccausc
Xo is avtlilablc on 0120 - 1202.
The indices of other wavclcng~h\. trn 0 1 20 -- 1202. that are convert-
ible to are not considered kCclu\c rherc is no available convener
at the node 1202.
we keep index of A3 set to intinlt! ~C'WU\C.
A3 is not available on the inwni~ng edge 01 20 -- 1202.
St
The other wavelengths that are convertible to X o are not considered
because there is no available converter at the node 1202.
d. For the edge 2022 -- 0222.
we set the index of X o to the index of X o on the incoming edge 1202
-- 2022, because
Xo is available on the incoming edge 1202 -- 2022. and
the indices of h2 and X 3 on 1 202 -- 2022 after being incrernented by
1 are not less than the index of Xo on 2022 -- 0222. We considered
Xo and X I because both of them are convertible to X2.
we set the indices of A , and X 2 to the index of Xo on che edge 1202 - 2022 incremented by I . because
X and X z are not available on the incoming edge 1202 - 2022, and
Xo is the only available wavelength on 1202 - 2022 that we can
use to convcn to XI or A2 on 2022 -- 0222.
Going backward through the edges of the path. we choose the wavelengths
that will form the lightputh. First. we pick A. one the edge 2022 -- 0222, since
the index of Xo is the minimum among all the wavelength indices on that edge.
Then, since the index of Acl on 1202 -- 2022 is equal to the index of Xo on 2022
-- 0222, we also pick A. Same case applies for Xo on edge 0120 -- 1202. At
2012 -- 0120, the index of A,, on 20 12 - 0 120 is not equal to the index of Xo on
01 20 - 1202. Thus, we need to reach X o from a wavelength that is convertible
to Xo. We have two possibilities, either X 2 or X3. where we will choose the
wavelength with the lower index. In this case, since A? and X3 have the same
index, we choose the first one. A?.
Conversion S Table of Indices
A3 -+ LO, A1
All converters
The Lightpath
Figure 10 Simulation example.
Chapter 5 RESULTS OF SIMULATION EXPERIMENTS
In order to study the eff'ect of limited wavelength conversion in all-optical
networks based on !he de h i j n egaph, we need to vary relevant parameters and
determine how they affect the network performance. Due to the fact that each
run was quite time consuming, we decided to concentrate on networks based on
de Bruijn graph G(4.5) since the number of nodes involved in such a network is
representative of networks of medium size. Furthermore. we assume that each
node has 5 transmitters and 5 receivers so that each node allows 5 concurrent
lightpaths starting from or ending at that node.
The parameters expected to affect the performance of the network are
number of conveners in each node,
conversion range for each of the conveners,
the total number of wavelengths in the network.
the number of wavelengths a particular station transmitter can tune to.
the routing strategy
We now discuss why we felt that these parameters should be significant.
a) The number of converters at each node determines the number of connec-
tions that can be converted from one wavelength to another at that node.
Due to cost considerations, we are interested to find the minimum number
of converters that a network should have.
b) The conversion range determines the number of wavelengths to which a
wavelength can be converted. If we have a wider range, it is more likely
that we will be able to find an unused wavelength if the original wavelength
is blocked.
c) If the number of wavelengths available at each node increases, it is more
likely that we will be successful in finding a wavelength not used on any
of the edges so that we expect that the number of successful connections
will increase.
d) The number of wavelengths in a particular station determines the number
of wavelengths assigned to a transmitter in that station. If the number of
wavelengths is lower. the cost of the transmitter is also lower.
e) The routing strategy dictates the time and the overhead needed to establish
a connection. In our case. the alternative routing strategy needs more set-up
time and cost overhcad compared to the shortest path routing. However,
the alternative routing strategy explores a number of routes and therefore is
more likely to succeed.
In general, by studying the results of combinations of the above parameters, we
want to determine how wc may reach the best network performance at the least
cost.
Since we are trying to maximize the number of successful connections, we
need to find out how many attempts to establish connections are successful and
how many are not. We therefore collect. for each combination of pararneters.
statistics on T. the total number of attempted calls and F. the total number of calls
which did not succeed. The ratio FIT gives us the blocking probability caused
by a particular set of parameters.
In our experiments. we chose the parameters from the following sets of data
number of converters to be selected from the set (0, 1, 3, 5. 10)
conversion range to be selected from the set (2. 5, 10)
number of wavelengths in the network to be selected from the set ( 1 0. 1 1.
... , 30).
number of wavelengths for a particular station to be 40%. 60% or 100% of
the whole number of wavelength in the network.
the routing strategies are either the shortest path. or alternative path strategy.
For each combination of parameters, we will run the simulation ten times. We
intended to run the simulation 100 times for each case; however, we discovered
that it was time consuming with respect to the wide number of combinations. For
example. running the simulation for one combination of panmeters took two days
of execution. Thus, we decided to reduce the number of runs to 10 times. In
the experiment number 0. we show that running the simulation 10 times or 100
times will lead to the same conclusion, although 100 times of running produce
more precise charts. See figure number I 1.
10 Runs
- 3 conveners - nnge 2 - local wavelengths I00 5
lli 5 conveners - nnge 2 - local wavelengths 100 %
10 I I 12 13 I4
Number of wavelengths in the network
100 Runs
- 3 conveners - nngc 2 - local wavelengths 100 9
& 5 conveners - nngc 2 - local wavelengths 100 C/c
10 I I ! 2 13 14 Number of wavelengths in the network
Figure 1 1 - Charts of 10 Vs. 100 runs.
5.1 Experiments
During our investigations, we carried out a comprehensive series of exper-
iments'. In this section. we will focus on 10 sets of experiments since they
represent the most significant results. In experiments 1 to 5 ( 6 to 10). we con-
sidered the alternative ( shortest) path routing strategy. The objectives of our
experiments are listed below.
Experiment # I and 6 :
a) Establish a base case where there i s no wavelength conversion. This
makes it possible to study the extent of improvements when we have
wavelength conversion.
0 b) Study whether the performance is affected if we decrease the number
of wavelengths per node. If there is no significant degradation in
performance. the number of wavelengths/node can be safely decreased.
Experiment # 2 and 7:
0 Study whether the performance is affected if we increase the number
of converters per node. What is the trade-off between the number of
wavelengths in the network and the number of converters/node?
. We have given the complete set of mults in Appendix #A.
49
Experiment # 3 and 8:
Study whether the performance is affected if we decrease the number of
wavelengths per node by employing converters at intermediate nodes.
If there is no significant degradation in the performance. the number of
wavelengthshode can be safely decreased.
Experiment # 4 and 9:
CI Study the network performance by increasing the number of conveners.
where the number of local wavelength is 40% of the total number of
wavelengths.
Experiment # 5 and 10:
U Study what is the effect of changing the conversion range of conveners.
We now give the details of ex~eriments 1 - 10.
Experiments 1 and 6
Set of parameters : We chose the following set of parameters to build a base case:
Zero conveners.
The percentage ratio of the number of local wavelengths to the total number
of wavelengths is one of the following :
The results of the experiment are shown in figure 12.
Observations for Exp 1: As we decrease the number of wavelengths per node
as a percentage of the total number of wavelengths. we need larger number
of wavelengths in the network to get an acceptable blocking probability. This
observation is what we expected and hold both for shortest path routing and
alternative path routing.
Exp 1
0 conveners - local wavelcngths I00 5
+ 0 convcners - local wrtvrtlcnglhs 60 5
- 0 conveners - local wavelenglhs 40 9
10 1 1 12 13 I4 15 I 6 17 I X Number of wavelengths in the network
Exp 6
0 rtmwnrrs - local w;lvclc.ngths 100 9
0 c r a u . . r r s - I w a l wavclcngths 60 8
0 ~tn\mrn - local wavelcngths 40 '7c
-6 - -- - 10 I I I ? 13 I 4 I F 16 17 I S 19 2 0 2 1 2: , '; 24 2." 26 27 28 29 30
Number of wavelengtns rn tne nerwork
Figure 12 Chans of ckpnrncnts 1 and 6.
Experiments 2 and 7
Set of parameters : We selected
a conversion range to be 2.
the number of ioclti waveiengrhs ic, be 100% sf tihe iota1 iiunbci of xavc-
lengths.
the number of conveners per node to be one of the following :
The results of the experiment are shown in figure 13.
Observations: As we increased the number of conveners per node in the network.
when we use alternative path routing, we noticed a slight improvement in the
blocking probability. In other words. if we wish to have a given blocking
probability, the total number of wavelengths we need in the network decreases
slightly if we allow the number of conveners per node to increase. However. we
noticed that we are limited to a threshold in the number of converters. Going
beyond this threshold will gave us little improvement. For example. in the case
of alternative routing strategy, if we used more than 3 converters, we got similar
results as using 3 converters.
In the case of shortest path routing, there was some improvement if we allowed
I converter in each node. However, if we allowed more than 1 converter per
node there was negligible improvement.
1 Number ol wavelengths In me netwoh -6
10 I I 12 13 I J I S
Exp 7
! Number al wavelengths In tne *(Y* -6 '
10 I1 12 I? 14 15 lh I -
Figure 13 Cham of c.\pcnmcnt\ 2 and 7.
Experiments 3 and 8
Set of parameters : We selected
the conversion range to be 2.
The percentage ratio of the number of local wavelengths to the total number
of wavelengths is one of the following :
The results of the experiment u c shown in figure 14.
Observations: This experiment was similar to experiment 1 and 6. The only
difference was that we allou~d each node to have a fixed number of converters.
As we decreased the totill number of wavelengths per node as a percentage of the
total number of wavelengths in the network, we needed a very small increase in
the total number of wavelengths in the network to preserve an acceptable blocking
probability. This increase was significantly less compared to the case where we
did not use any convener in thc network. The following table illustrates this
situation:
Experiment Number of Total number of
wavelengths (TW)
Number of local
wavelengths as a
percentage of TW
Table 1 Comparison between experiments I and 3.
In the case where we did not use converters, we needed 6 additional wave-
lengths. However. we needed only 1 wavelength if we employ conveners.
The same observation applies to the shortest path routing experiment. but
the range of increase in the number of wavelengths was wider than the case of
shortest routing experiment.
Exp 3
5 conveners - rmge 2 - local wsvclmgrhs 100 F
-'\. 5 convcncn - range 2 - local wave lengths 60 3
5 canvcnes - range 2 - local wavelengths 40 Pc
- 10 I I I ?. If t 4 15
Number of wavelengths in the network
Exp 8
. . 5 convenen - nnge 2 - local wavclcngthc 100 F
* 5 convenen - range Z - lcml w;lvclcngth.\ 60 9
- 5 convenes - m g c 2 - local w;~velcnpths 40 4
-6 10 1 1 I? If I 4 15 16 17 I S 19 20 21 22 3 24
Number of wavelengths In the network
Figure 14 Charts of experiments 3 and 8.
Experiments 4 and 9
Set of parameters : We selected
the conversion range to be 2.
the number of !ma! wwelengths to be 40% of the total number of wave-
lengths in the network.
the number of conveners per node to be one of the following :
The results of the experiment are shown in figure 15.
Observations: These experiments were similar to experiment 2 and 7. The only
difference was that the number of wavelengths available to each node is 40 % of
the total number of wavelengths in the network. As in the cases of experiments 2
and 7, as we increased the number of converters. we needed fewer wavelengths
to maintain an acceptable blocking probability. However. in experiment 4, the
decrease in the number of wavelengths was significantly more compared to the
experiment 2. The following table illustrates this situation:
Experiment
number
Number of
converters
Total number of
wavelengths (TW)
Number of local
wavelengths as a
percentage of TW
Table 2 Comparison between experiments 2 and 4.
In these experiments. as in the cases of experiments 2 and 7, we observed the
threshold values for the number of converters. If the number of converters was
above the threshold value, there was little difference to the blocking probability.
Exp 4 I i - 0 convsncn - range 2 - local wsvelcngth\ JO 5
A ! i 91 I convcnen - range 1 - locd wavekngths 40
i 0 1 3 convrnen - mngr 2 - local w;rvelcngrh JOG
-- 5 convene3 - ringc 2 - local w;rvelcn$tk\ 40
+ 10 convene3 - range Z - local wavclengtt.L* 40 Flr z rn -
\ e -3
'-\
a
Exp 9 I
- 0 converten - range 2 - local wwelng~ha 40 Q
- 1P I convench - range 2 - local wavelength.* JO 5 'D 0 !-=, 3 convcnm - rmgc 1 - local wavclcnpths SO EG'
.Y
-. - .* - 5 convcna - rmgc 1 - local wwclngth 40 Ci 5 - I - .- + 10 convene - range 2 - local w;rvcltngthh 40 B
z m . =8, \ - 2 -2 --
Figure 15 Charts of experiments 4 and 9.
Experiments 5 and 10
Set of parameters : We selected
the number of converters to be 1.
the conversion range to be one of the following :
the number of local wavelengths is 100% of the total number of wavelengths.
The results of the experiment are shown in figure 16.
Observations: In the case of the alternative path routing strategy, as we in-
creased the conversion range of converters. we needed somewhat lower number
of wavelengths to maintain an acceptable blocking probability. However. the
improvement in the number of wavelengths was extremely small. There was no
improvement at all for the shortest routing experiment.
Exp 5
- I convener - nnge t - locat wavclcngths 100 "r
8 I converrcr - nnge 5 - local wavelengths 100 Q
I convener - nnge I 0 - local wavelengths 100 Ti-
-6 10 I I I 2 13 I 4 15
Number of wavelengths in the network
Exp 10
- I convener - range Z - local wavelengths 100 Ci
I convencr - m g r 5 - local wavelengths 100 %
I convener - nngc I 0 - local wavclenglhs 100 %
10 1 1 I Z 13 I4 I 5 I 6 17 I S
Number of wavelengths in the network
Figure 16 Charts of experiments 5 and 10.
5.2 Critical Summary
In the above experiments. we have described the most significant results of our
simulation experiments on a network based on the de Bruijn graph G(4. 5). One
general observation is that employing wavelength converters doesn't result in a
dramatic decrease in the total number of wavelengths. In other words. the resulting
decrease in the total number of wavelengths doesn't justify the additional expense
for wavelength converters. In addition. the use of wavelength converters requires
additional network overhead. since more search is involved when establishing a
new lightpath and we have to keep track of the wavelength of each WDM channel
constituting a lightpath. For example. considering shortest path routing in G(4.
5) network with 5 possible connections per node. we needed 18 wavelengths to
maintain a blocking probability of l(r5. Meanwhile. if we use 3 converters per
node. we needed 17 wavelengths to get a similar blocking probability. On the
other hand, employing alternatives routing strategy. and considering the previously
stated parameters. we needed 14 wavelengths with 0 converters per node. versus
12 wavelengths with 3 conveners per node.
Another general observation is that increasing the conversion range per con-
verters has a minimal effect on the over-all performance of the network. Using
conveners of wider range does not significantly reduce the number of wavelengths
needed in the network to preserve a good blocking probability. This conclusion
is in agreement with the statement "In many cases. limited-range wavelength
translators can provide almost all of the improvement in blocking probability by
full-range translators."[ 161
We observed the best improvement in the situation where the transmitter in
each node can be tuned to only 40% of the total number of wavelengths in the
network. Reducing the number of wavelengths per node is useful since the cost
of such transmitters is lower and it allows us to reduce the tuning range of each
transmitter and hence reduce the set-up time. In such networks. we found that the
use of converters per node gave us a significant decrease in both the total number
of wavelengths and the number of local wavelengths that a station can tune to.
For example by applying the alternative routing strategy. with 6 wavelengths per
node, 17 wavelengths in the network. and 1 convener per node. we can maintain
a blocking probability of lrS (Table 4) . If we use 5 conveners per node we
reduced the number of wavelengths to IS and the local number of wavelengths
per node to 5. However. the improvement is not as dramatic as the case of I
converter.
Table 3 Conveners - alternative paths routing.
Number of conveners
0 1
I
5
In the case of the shortest path routing. by employing 1 converter. we needed
9 wavelengthshode. and a total of 25 wavelengths in the network in order to
maintain a similar blocking probability. Whercss. without conveners. the number
of local wavelengths and the total number of uavclengths were respectively 29
and 1 1 (Table 5).
Total number of
wavelengths
22
I7
IS
Tdbie 4 Conveners - shmcsi p;lth routing.
Number of local
wavelengths I
8
6
5
Number of conveners
I
0
1 I
5
In general. the number of local wavelength\ pcr node in the case of alternative
routing strategy was lower than the case of h ~ n c . ; ~ path routing. We believe that
since we explore a number of alternate path\ In thc former strategy. we have a
Total number ot'
wavelengths
29
25
24
Number of local
wavelengths
1 1
9
9
higher chance to find a path as compared to the later strategy where we only
look at one path. In other words, when a node is assigned a wavelength A. this
node will be able to use X on delta alternative outgoing edges. according to the
alternative routing. However, the node can use X only on one outgoing edge in
the case of &he shonest routing. For example. in a C(4. 5) network whcic ihc
local number of wavelengths per node is 5. a node can access the 5 assigned
wavelengths on its 4 outgoing edges. In this case, we notice that each node can
access 20 different wavelength x edge combinations. The cost of this advantage
over the shortest path routing is the additional network overhead, represented by
the extm routes.
We believe that the minimal improvement in the total number of wavelengths
in a network where we have N wavelengths is due to the fact that some edges might
be carrying a total of N lightpaths and hence cannot carry any more lightpaths. In
this case, the existence of converters at those edges will have no effect in solving
the bottleneck at such edges.
Chapter 6 FUTURE WORK
As a result of our study, we recommend that some additional work be done in
this area. In this thesis, we investigated the possibility that each node can transmit
using 3 subset of the wavelengths used in the network. However, we assumed
that all receivers are tunable to any frequency in the network. If we use receivers
that are tunable to a subset of the total number of wavelengths. it is possible that
wavelength converters in the network might be more useful.
In a network with N nodes. E edges and a given set of W wavelengths. we
have a total of E x W channels5. Clearly, no communication is possible when all E
x W channels are already used for existing lightpaths. In an informal experiment.
we found that when existing lightpaths in the network uses approximately E x
W 1 3 channels. no further communication is possible using either shortest path
or alternative path strategy. It is quite possible that an intelligent search using
somewhat longer paths may help in finding paths even in such situations. We
suggest that methods such as the genetic algorithms may help tinding routes
especial 1 y when using converters.
In this thesis. we have only looked at de Bruijn graph of a specified size G(4,
5). We believe that our conclusions will hold for de h i j n graphs of other sizes
as well. However, this remains to be investigated. It is possible that in other
-Z A channel is a wavclcngth .\ on a porticuliu rdgr .
68
topologies. wavelength conversion may be more useful. We suggest that this be
studied in the future.
Chapter 7 CONCLUSION
In the course of the thesis, we investigated the possibility of employing
limited-range wavelength conveners in wavelength-routed dl-optical networks.
In our approach, we assumed a G(4. 5) de Bruijn topology where each node
has a number of conveners. The conveners had limited wavelength conversion
capability. Each wavelength can be converted to a subset of nearby wavelengths.
In an all-optical network. the tuning time for the transmitter has an imponant
effect on the set-up time. This tuning time may be reduced if we allow the
transmitters at each node in the network use a selected subset of the wavelengths
in the network rather than the whole range of wavelengths. We have explored
the effect of allowing each node to range from 40% to 100 % of the wavelengths
used in the network to study this effect. We considered two routing strategies:
shortest. and alternative path routing.
We implemented a network simulator to model the network operations and
performance. The cornponcnts of the simulation include algorithms for routing
techniques and for establishing a lightpath. For each set of parameters that we
studied, we varied the total number of wavelengths in the network. After a
simulation run, we collected thc number of successful connections and the number
of failed connections in ordcr to derive the blocking probability.
After investigating the most significant results of our simulation. we noticed
some improvements in the blocking probability if we used wavelength converters.
We believe that this small improvement is not worth the price of using wavelength
converters and adding more overhead to the process of establishing a connection.
We base this observation on a G(4. 5) de Bruijn graph. However, we may get
better result with other topologies. The same observation applies for the case
of varying the conversion range. We get some decrease in the total number of
wavelengths, but it is minimal compared to the overhead caused by increasing
the convertibility range of converters. This leads to the conclusion, reached by
previous works. that employing limited wavelength conversions is as efficient as
employing full wavelength conveners.
The most significant result of the study is that, with wavelength conveners, we
can reduce the number of wavelengths that a node can tune to while transmitting.
without severely increasing the total number of wavelengths in the network.
Hence, we can employ transmitters with lower tunability range. In this case, the
trade off between the number of converters and tunability range of transmitters
depends on the device cost.
APPENDIX A
A.l Set of results for alternative paths routing
We used the following shorthand notations:
\Ar = Tstal umber sf wavelengths in the network.
LW = Number of local wavelength per node.
C = Number of conveners per node.
CR = Conversion range per converter.
Hits = number of successful connections.
Misses = number of failed connections.
W LW C C R Hits Misses
A.2 Set of results for shortest path routing
We used the following shorthand notations:
W = Total umber of wavelengths in the network.
LW = Number of local wavelength per node.
C = Number of conveners per node.
CR = Conversion range per convener.
Hits = number of successful connections.
Misses = number of failed connections.
Wv LW C CR Hits Misses
51086 51145 5 1 1 8 1 51195 5 1 1 4 9 5 1 ZOO
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Hassan Zeineddine was born in 1970 in Beirut - Lebanon. He graduated
From high school in 1988. From there he went on to the American University of
Beirut where he obtained a B. Sc. in Computer Science in !993. He is cumnrly
a candidate for the Master's degree in Computer Science at the University of
Windsor.
