alexandria university faculty of engineering department of computer

114 Pages·2001·0.61 MB·English

ALEXANDRIA UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT OF COMPUTER SCIENCE AND AUTOMATIC
CONTROL

NEW ALGORITHMS FOR MULTICAST ROUTING
IN REAL TIME NETWORKS

A thesis submitted in partial fulfillment for the degree of
Master of Science

By

Mohamed Fathalla Hassan Mokbel
B.Sc., Faculty of Engineering, Alexandria University, 1996

Supervised by

Prof. Dr. Mohamed N. El-Derini
Department of Computer Science and Automatic Control
Faculty of Engineering, Alexandria University

Dr. Wafaa A. El-Haweet
Department of Computer Science and Automatic Control
Faculty of Engineering, Alexandria University

Alexandria
1999
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ACKNOWLEDGMENTS

My deepest admiration and thanks to my advisors, Prof. Dr. Nazih El-Derini
and Dr. Wafaa El-Haweet for their support and guidance. I was fortunate to have
them as my advisors. Dr.Nazih was never too busy to listen to me and offer his advice
whenever I need. Without his invaluable comments and suggestions, this work
wouldn’t have been accomplished. The effort, support and guidance that I got from
Dr.Wafaa was really inestimable and I appreciate it a lot.

My deepest gratitude to Dr. Hussein H. Aly for his support at the early stages of
my research.

I would like to thank all the staff in computer science department from whom I
learned a lot over five years of undergraduate and postgraduate courses.

I couldn’t ignore the role of my friends and the staff in Mubarak City for
Scientific Research and Technological Applications. The continuos help and
encouragement that I got from them over the last two years cheered me up at the most
difficult stages of my research.

Last, but not least, my deepest thanks to my family for their support,
understanding and encouragement without which this work wouldn’t have been
completed.
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ABSTRACT

Handling group communication is a key requirement for numerous applications
that have one source sends the same information concurrently to multiple destinations.
Finding a route from a source to a group of destinations is referred as multicast
routing. The objective of multicast routing is to find a tree that either has a minimum
total cost, which called the Steiner tree or has a minimum cost for every path from
source to each destination, which is called shortest path tree. With the rapid evolution
of real time and multimedia applications like audio/video conferencing, interactive
distributed games and real time remote control system, certain quality of services,
QoS, need to be guaranteed in underlying network. Multicast routing algorithms
should support the required QoS. In this thesis we consider two important QoS
parameters that need to be guaranteed in order to support the real time and multimedia
applications. Firstly, we consider the delay parameter where the data sent from source
need to reach destinations within a certain time limit. The problem is formulated as
delay constrained shortest path problem which is known to be NP-Complete. A new
heuristic algorithm, called DCSP, is proposed and discussed in depth with the
flowcharts and pseudo codes of its main subroutines. Large number of simulation
experiments have been done to analyze the performance of our new algorithm
compared to other previous algorithms. Secondly, in addition to the delay constraint,
we add the delay variation constraint. The delay variation constraint is a bound on the
delay difference between any two destinations. The problem is formulated as shortest
path routing under delay and delay variation constraints which is also know to be
NP-Complete. A new heuristic algorithm, called DVCSP, is proposed with in depth
discussion and analysis. The performance of the new algorithm is investigated by
simulating real time networks.

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Table of Contents

ACKNOWLEDGMENTS..….………………………………………….…………i
ABSTRACT…..……………………………………….………….……………… ii
Chapter 1 : Background……………………………………………..1
1.1. Multicast Group…..….………………………………………….…………..1
1.2. Multicast Routing…..……………………………………….………….……2
1.3. Multicast Routing in Real Time Applications………………………………3
1.4. Thesis Objective…………………………………………………………….4
1.5. The Thesis Organization………………………………………….…………4

Chapter 2 : Previous Work in Multicast Routing Problems………5
2.1 Introduction………………………………………………………………….5
2.2 Shortest Path Tree Problem………………………………………………….5
2.2.1 Unconstrained Shortest Path Problem………………………………….5
2.2.2 Constrained Shortest Path Problem…………………………………….6
2.3 Steiner Tree Problem………………………………………………………...7
2.3.1 Unconstrained Steiner Tree Problem………………………..………….7
2.3.2 Constrained Steiner Tree Problem…………………………..………….7
2.3.2.1 Centralized Constrained Steiner Tree Problem……………………7
2.3.2.2 Distributed Constrained Steiner Tree Problem……………………9
2.4 Other Constrained in Multicast Routing Problems…………………………10
2.4.1 Multicast Routing with Bandwidth and Delay Constraints……………10
2.4.2 Multicast Routing with Delay and Delay Variation constraints……….10
2.4.3 Multicast Routing with Degree Constraints……………………………11
2.5 Other Multicasting and Real Time Problems……………………………….11
2.5.1 Multicast Routing in ATM Networks………………………………….11
2.5.2 Dynamic Multicast Routing……………………………………………12
2.5.2.1 Unconstrained Dynamic Multicast Routing………………………12
2.5.2.2 Constrained Dynamic Multicast Routing…………………………13
2.5.3 Constrained Unicasting and Broadcasting…………………………….13
2.6 Other Survey Work…………………………………………………………14
2.7 Conclusion………………………………………………………………….14
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Chapter 3 : Proposed Delay-Constrained Shortest Path Algorithm
(DCSP).……………………………………………………………….15
3.1 Introduction…………………………………………………………………15
3.2 Definitions…………………………………………………………………..15
3.3 Problem Formulation………………………………………………………..18
3.4 The Delay Constrained Shortest Path Algorithm……………………………20
3.4.1 Main Idea of the Algorithm…………………………………………….20
3.4.2 DCSP Heuristic Algorithm………………………………………….….21
3.4.3 Getting the Optimal Solution form the Heuristic Algorithm…..………24
3.4.4 Main Subroutines of the Algorithm…………………………………….24
3.5 Correctness and Complexity Analysis of the algorithm…………………….28
3.5.1 Algorithm Correctness and Termination………………………………28
3.5.2 Algorithm Complexity…………………………………………………29
3.6 Conclusion………………………………………………………………….30

Chapter 4 : Performance Analysis of the Proposed DCSP
Algorithm.…………………………………………………………….31
4.1 Introduction…………………………………………………………………31
4.2 Random Graph Generator…………………………………………………..31
4.3 Simulated Algorithms………………………………………………………32
4.4 The Effect of Changing Network Size on DCSP Algorithm………………..34
4.5 The Effect of Changing Multicast Group Size on DCSP Algorithm……….38
4.6 The Effect of Changing Average Node Degree on DCSP Algorithm………41
4.7 The Effect of Changing Delay Constraint on DCSP Algorithm……………44
4.8 The Effect of Changing Parameter K on DCSP Algorithm…………………48
4.9 Conclusion..…………………………………………………………………52
Chapter 5 : Proposed Shortest Path Algorithm with Delay and
Delay Variation Constraints (DVCSP)……………………... ……..53
5.1 Introduction…………………………………………………………………53
5.2 Problem Formulation……………………………………………………….54
5.3 The Delay and Delay Variation Constrained Shortest Path Algorithm
(DVCSP)…………………………………………………………………...55
5.3.1 Phase I: The Delay Constraint Phase………………………………….55
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5.3.2 Phase II: The Delay Variation Constraint Phase………….…………...61
5.4 Analysis and Complexity of DVCSP Algorithm……………………………67
5.5 Conclusion…………………………………………………………………..70

Chapter 6 : Performance Analysis of the Proposed DVCSP
Algorithm……………………………………. ……………………….71
6.1 Introduction…………………………………………………………………..71
6.2 Simulated Algorithms..………………………………………………………71
6.3 Performance Factors…………………………………………………………72
6.3.1 Failure Rate…………………………………………………………….72
6.3.2 Average Cost per Path………………………………………………….72
6.4 The Effect of Changing Delay Variation on DVCSP Algorithm……………73
6.4.1 Failure Rate…………………………………………………………….73
6.4.2 Average Cost per Path………………………………………………….75
6.5 The Effect of Changing Multicast Group Size on DVCSP Algorithm……...78
6.5.1 Failure Rate…………………………………………………………….78
6.5.2 Average Cost per Path………………………………………………….81
6.6 The Effect of Changing Network Size on DVCSP Algorithm………………83
6.6.1 Failure Rate…………………………………………………………….83
6.6.2 Average Cost per Path………………………………………………….85
6.7 Conclusion…………………………………………………………………..86

Chapter 7 : Conclusion and suggestions for Future Work………..87
7.1 Conclusion………………………………………………………………….87
7.2 Suggestions for Future Work………………………………………………88

References…………….……………………………………………...90

Appendix A : Pseudo Code of DCSP Algorithm…………………..94

Appendix B : Pseudo Code of DVCSP Algorithm…………………98

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Chapter 1

Background

1.1 Multicast Group

Multipoint communication is one of the oldest forms of communication among
humans. It has been long recognized that communicating a message to multiple
recipients simultaneously is a very efficient method of getting the message across.
Whether the message is delivered in the form of a smoke signal, political speech,
religious sermon, town-hall meeting or a classroom lecture, the scalability of
multipoint communication is apparent. In the early days of communication, both one-
to-one and multipoint communication were possible. Telephone and telegram
technologies allowed point-to-point communication while radio and television
technologies allowed multipoint communication. At this time, multipoint
communication was analogous to broadcasting. Nowadays, with the recent advance in
communication and the new applications like distributed database systems, remote
control and distributed computing, a need for multicasting is apparent. Multicasting is
a special case of broadcasting, where instead of sending data to all the recipients, data
is sent to a selected multicast group. Multicast group always changed dynamically
where new member can enter the group at any time and also any old member can exit
from the group. When data is sent by any node, member or non-member of multicast
group, all the members of the multicast group should receive it.

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1.2 Multicast Routing

Sending data from source node to destination node in point-to-point
communication requires that the source setups a route to the destination and then
sends the data along that route. The route could be a direct one or it could use some
intermediate nodes, this process is called routing. Sending data from one sender to
multiple destinations either for broadcasting or multicasting can be achieved by using
multiple point-to-point communication, i.e. sending data to each destination
individually by setting a route to each destination. But this would be very inefficient
and the utilization of the links between source and destinations will be very low since
the same packet could be sent over the same link more than one time which gives
inappropriate overhead of the network links. Multicast routing refers to the
construction of a tree rooted at the source and spanning all destinations. Sending data
on such a tree will be performed such that exactly one copy of a certain packet will
traverse any link in the multicast tree. For any source and any group of destinations
there may be a large number of such a tree. Choosing the best tree that can perform
routing is a requirement for any application that needs multicasting. The best tree can
be considered to be the tree that the sum of its path’s cost is minimum, this is called
Steiner tree. However, for some applications the best tree may be considered as the
one with the lowest possible cost for each destination individually, this is called
shortest path tree. In Fig. 1.1, the difference between two kinds of multicast tree is
apparent while Steiner Tree has less total cost, it has higher average cost per
destination.
B 4 D B 4 D
6 6
A A
2 4

5 5

C 3 E C 3 E

(a) Shortest Path Tree. Total Cost=18, (b) Minimum Steiner Tree. Total Cost=12,
Average Path Length = 9 Average Path Length=11
Fig. 1.1. Comparison of a shortest path tree and minimum Steiner tree for the same
mult icast group and the same multicast source. The number assigned to each link
repre sents the link cost. The multicast group G = { D, E} node A is the multicast source
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1.3 Multicast Routing in Real-Time Applications

With the rapid growth of the network and computer technologies and the
appearance of new applications like multimedia applications, audio/video
conferencing and real-time applications, the concept of finding the best route is
changed. Certain quality of services, QoS, should be guaranteed on the selected
multicast tree. An example of QoS is the delay, the data should be sent from a source
to each destination within a certain delay limit. So, the best multicast tree should be
either delay constrained Steiner tree or delay constrained shortest path tree. Delay
constrained Steiner tree is the tree that has the minimum total cost of its links given
that each path from source to any destination does not violate the delay constraint.
Delay constrained shortest path tree is the tree that has minimum cost path from the
source to each destination given that each path from source to any destination does
not violate the delay constraint. It is apparent that delay constrained trees have higher
costs than unconstrained trees, the difference on the cost is considered to be paid for
the QoS. Other QoS is also required and may affect the resulted tree such as the delay
variation where the resulted tree should be constructed given that the difference in the
delay between any two destination should be less than a certain delay variation limit.

Although researchers have been studied variations of the multicast routing
problem in communication networks for many years, multicasting was not deployed
over wide area networks until March 1992 [1]. At this date, meeting of the Internet
Engineering Task Force (IETF) in San Diego, live audio from several sessions of the
meeting was audiocast using multicast packet transmission from the IETF site over
the internet to participants at 20 sites on three continents spanning 16 time zones. This
experiment was not only the first sizeable audio multicast over a packet network, but
also significant for the size of IP network topology itself.

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1.4 Thesis Objective

The work in this thesis is motivated by the need for new algorithms for
multicast routing that can guarantee certain QoS parameters. Two main QoS are
considered in the thesis, the delay and delay variation between all participants. Two
new heuristic algorithms are proposed. The first one for the problem of delay
constrained shortest path tree. The other for the shortest path tree under delay and
delay variation constraints.

1.5 The Thesis Organization

This thesis is organized as follows:
Chapter 1 presents a general introduction and the background of multicast group
and multicast routing.
Chapter 2 contains an exhaustive survey of the problems related to multicast
routing under constraints and its proposed solutions so far.
Chapter 3 contains the proposed algorithm for solving the problem of delay
constrained shortest path tree associated with the proof of its complexity and
correctness.
Chapter 4 presents the performance analysis of the proposed algorithm in chapter 3
by comparing it with other algorithms via large number of simulation experiments.
Chapter 5 contains the proposed algorithm for solving the shortest path problem
under delay and delay variation constraints associated with the proof of its
complexity.
Chapter 6 presents the performance analysis of the proposed algorithm in chapter 5
by comparing it with other algorithms via large number of simulation experiments.
Chapter 7 contains the thesis conclusion and suggestions for future work in the
area of multicast routing.
Appendix A contains the pseudo code of the proposed algorithm for delay
constrained shortest path tree presented in chapter 3.
Appendix B contains the pseudo code of the proposed algorithm for delay and
delay variation constrained shortest path tree presented in chapter 5.
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