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A Mathematical Model for Evaluating the Performance of Multicast Systems

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The Internet is experiencing the demand of high-speed real-time applications, such as live streaming multimedia, videoconferencing, and multiparty games. IP multicast is an efficient transmission technique to support these applications. However, there are several architectural issues in this technique that hinder the development and the deployment of IP multicast such as a lack of an efficient multicast address allocation scheme. On the other hand, End System Multicasting (ESM) is a very promising application-layer scheme where all the multicast functionality is shifted to the end-users. Supporting high-speed real-time applications always demand a sound understanding of these schemes and the factors that might affect the end-user requirements. In this paper we attempt to propose both analytical and the mathematical models for characterizing the performance of IP multicast and ESM. Our proposed mathematical model can be used to design and implement a more efficient and robust ESM model for the future networks.
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Abstract—The Internet is experiencing the demand of high-
speed real-time applications, such as live streaming multimedia,
videoconferencing, and multiparty games. IP multicast is an
efficient transmission technique to support these applications.
However, there are several architectural issues in this technique
that hinder the development and the deployment of IP multicast
such as a lack of an efficient multicast address allocation scheme.
On the other hand, End System Multicasting (ESM) is a very
promising application-layer scheme where all the multicast
functionality is shifted to the end-users. Supporting high-speed
real-time applications always demand a sound understanding of
these schemes and the factors that might affect the end-user
requirements. In this paper we attempt to propose both analytical
and the mathematical models for characterizing the performance
of IP multicast and ESM. Our proposed mathematical model can
be used to design and implement a more efficient and robust ESM
model for the future networks.
Index Terms— End-system multicasting, IP multicast, real time
application, performance evaluation.
I. INTRODUCTION
There is an emerging class of Internet and Intranet multicast
applications that are designed to facilitate the simultaneous
delivery of information from a single or multiple senders to
multiple receivers. Different approaches of multicasting have
been suggested to improve the overall performance of
networks especially the Internet. These approaches are:
multiple unicast, IP multicast, and end-system multicast
(ESM). All of these methods have some advantages and
disadvantages but the last two approaches (IP multicast, and
ESM) mentioned above have had more research effort in terms
of performance evaluation of networks. Multiple unicast can
be described as a service where one source sends the same
copy of the message to multiple destinations. There is a one to
one connection all the way from the source to the destination.
In IP multicast, one source sends data to a specific group of
receivers. In this case, a unique and special IP address is used,
a class D address for the entire group. A tree rooted at the
source is constructed and only one copy of the message is sent
since the routers along the paths to the destinations performed
the necessary replication functionalities. Finally, in an ESM
approach, host participating in an application session have the
responsibility to forward information to other hosts depending
on the role assigned by a central data and control server. In
this case, the architecture adopted is similar to that of IP
multicast with the difference that only IP unicast service is
required. ESM uses an overlay structure, which is established
on top of the traditional unicast services. The overlay has its
meaning from the fact that the same link can have multiple
unicast connections for multiple pair of edges.
II. RELATED WORK
Previous works about ESM [1], [2], have proposed
experimental results and have been tested in very small group
size scenarios including the Internet. There is other end-hosts
multicast proposals like YOID [3], which is a set of protocols
designed to build a new architecture for general content
distribution. It considers three layers of protocols: an
identification protocol, a transport protocol, and a tree
formation protocol to construct optimal delivery trees. PBM
[4] uses end-to-end delay bounds to reduce the delivery delays
resulting from the well-known last mile bandwidth limitation
providing a more scalable alternative. Multicast Service Nodes
(MSN) [6] provides multicast services through a set of
distributed multicast service nodes, which communicate with
hosts and with each other using standard unicast mechanism.
The MSNs act as proxies which forward and replicate data
packets on behalf of the senders. Researchers usually refer to
this generic advanced multicast model as Amcast (Overlay
Multicast Network).
ALMI [5] approaches collaborative applications within a
reduced number of group members. A fundamental challenge
that ESM is facing is the fact of providing a method for nodes
to self-organize into an overlay network that efficiently
forwards multicast packets. These protocols primarily consist
of two components: (i) a group management component, and
(ii) an overlay optimization component. The first one ensures
that the overlay remains connected in the face of dynamic
group membership and failure of members. The second
component ensures that the quality of the overlay remains
good over time [1].
A Mathematical Model for Evaluating the
Performance of Multicast Systems
Syed S. Rizvi and Khaled M. Elleithy
Computer Science and Engineering Department
University of Bridgeport
Bridgeport, CT 06601
{srizvi, elleithy}@bridgeport.edu
Aasia Riasat
Department of Computer Science
Institute of Business Management
Karachi, Pakistan 78100
aasia.riasat@iobm.edu.pk
In this paper we are mainly concerned about end-to-end
delay metrics for data-delivery process in Multiple unicast, IP
multicast and ESM. From the proposed mathematical model
and the simulation results, we can observe that there is no
significant difference when comparing ESM to IP multicast for
a small size of network. Besides, ESM represents a low-cost
solution to multicast service demand because there is no need
to pay for additional support from ISP or other network
service. However, it is still experiencing some limitations in
scalability, latency and bandwidth management.
III. THEORETICAL ANALYSIS
In this section, we will theoretically analyze the problems of
different level of multicasting, which hinder their performance
with respect to the bandwidth utilization and latency.
A. Multiple Unicast System
In the unicast IP network, the host acting as the source
transmits a copy of the message to each destination host as
shown in Fig. 1. No special configuration is needed either in
the source or in the core network. The intermediate routers will
have to carry all these messages to the proper destinations. The
chains of protocol entities that take care of the transmission
process also use processing capacity on the host for each
transmission. In addition, the transmission time is typically
increased with some magnitude and it will affect the global
end-to-end delay. These are the reasons to consider a multiple
unicast service an unpractical approach to implement on the
network.
B. IP Multicast
IP multicast is a service where one source sends data to a
group of receivers each of them containing a class D address
as membership identification. In IP multicast, a packet is sent
only once by the source. Routers along the route take care of
the duplication process. The IP-multicast capable version of
the network shown in Fig. 2 consists of network with native
multicast support. The traditional process includes the
construction of a source-rooted tree together with the members
of the multicast group. Since only one copy of the message is
required, we can say that a minimum bandwidth effort is being
used for the transmission of the message to all group members
connected in the network. The IP-multicast transmission takes
the same bandwidth on source host's network as a single copy,
regardless of how many clients are members of the destination
host group in the Internet.
However, the main disadvantage of IP multicast is the need
of commercial routers supporting multicast protocol. In theory,
almost all routers support multicast but in practice this is not
the case. Investors still think that there is not enough multicast
application demand and that multicast traffic could take their
routers down due to congestion problems.
Several approaches to multicast delivery in the network have
been proposed which make some improvements or
simplifications in some aspects, but they do not improve upon
traditional IP multicast in terms of deployment hurdles. A
major obstacle for deployment of multicast is the necessity to
bridge from/to the closest multicast router to/from the end-
systems. Existing IP multicast proposals [1, 7] embed an
assumption of universal deployment, as all routers are assumed
to be multicast capable. The lack of ubiquitous multicast
support limits the deployment of multicast applications, which
in turn reduces the incentive for network operators to enable
multicast. Therefore, from the above discussion one can expect
that we need another multicast alternative in which network
routers have not to do all of the work; instead each of the host
will equally contribute in the overall multicast process of the
messages.
C. End-system Multicast (ESM)
ESM is a very promising application layer solution where
all the multicast functionality is shifted to the end users as
shown in Fig. 3. There is one central control server and one
central data server residing in the same root source as shown in
Fig. 3. In ESM, host participating in an application session can
Source 1
R 1
Source 2
Router 2
Source 3
Source 4
1
2
3
4
5
1
1 2
Source 1 wants to
send to 3 different
destinations
Source 3 wants to
send to 4 different
destinations
Source 2 wants to
send to 2 different
destinations
Source 4 wants to
send to only one-
destinations
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
R-4
R-3
D10
D9
D7
D6
D5
D4
D3
D2
D1
D8
Fig. 1 Example of multiple unicast
have the responsibility to forward information to other hosts.
Here, end users who participate in the multicast group
communicate through an overlay structure. However, doing
multicasting at end-hosts incurs in some performance
penalties. Generally, end-hosts do not handle routing
information as routers do. In addition, the limitation in
bandwidth and the fact that the message needs to be forwarded
from host-to-host using unicast connection, and consequently
incrementing the end-to-end delay of the transmission process,
contribute to the price to pay for this new approach. These
reasons make ESM less efficient than IP multicast. The
structure of the ESM is an overlay in a sense that each of the
paths between the end systems corresponds to a unicast path.
The end receivers could play the role of parent or children
nodes. The parent nodes perform the membership and
replication process. The children nodes are receivers who are
getting data directly from the parent nodes. Any receiver can
play the role of parent to forward data to its children. Each
client has two connections: a control connection and a data
connection.
IV. PROPOSED MATHEMATICAL MODEL FOR MULTICASTING
Let G is an irregular graph that represents a network with a
set of N vertices and M edges such as:
{
}
,
G N M
= . Let L is a
direct communication link between a single pair of source (s)
and destination (d) where both source and destination belong
to N such as:
{
}
,
s d N
. In addition, each packet transmitted
between source (s) and destination (d) must traverse one or
more communication links in order to reach the final
destination. Let the value of D(L) denotes packet-delay that is
associated with each direct communication link. Therefore,
each transmitted packet will typically experience a delay of
D(L) on a particular link. In connection less communication
such as IP network, there might be multiple routes exist
between a pair of source and destination. As a result, each
packet might follow a different route in order to reach the final
destination where each route requires traversing of one or
more communication links (L). A single route between a pair
of source and destination can be defined as:
{
}
{
}
, ,
R s d where s d N
A. Mathematical Model for a Unicast System
In unicast, a packet is sent from one point (source) to
another point (destination). As mentioned earlier, when packet
transmit from one source (s) to a specified destination (d),
there exist multiple routes where each route can have multiple
links. This implies that the packet-delay for unicast is entirely
dependent on the number of links a packet needs to traverse in
order to reach the final destination system. Based on the above
argument, one can define the packet delay such as:
1 2
( ) ( ) ( ) ......... ( )
n
D R D L D L D L
= + + + where n is the
maximum number of links that need to be traversed on route R
between s and d. The delay can be generalized for one
particular route (R) that exist between source (s) and
destination (d) such as:
R-3
R-4
Source 3
Sender 4
1
2
3
4
5
1
2
3
4
5
6
7
8
9
10
D10
D9
Source 1
Router 1
Source 2
Router 2
1
2
3
1 2
1 2
1 2 3 4
1
2
3
4
5
6
7
8
9
1
2
3
1
D8
D7
D6
D5
D4
D3
D2
D1
Fig. 2 Example of IP multicast
Parent node
Client A
Child Node
Client D
Client B
Parent node
Data
Server
Control
Server
Client C
Fig. 3 Example of End-System Multicast
1
1 2
1
( ) ( )
( ) ......
n
i
i
n
i n
i
D R D L
where L L L L M
=
=
=
= + + +
(1)
Equation (1) can be further expressed as:
( )
( )
( )
s d
L R s d
Delay D D L
= =
(2)
where
(
)
L R s d
represents the value of the total delay
associated with the route R between source s and destination d.
Based on (1) and (2), one can also simply derive a
mathematical expression for estimating an average-delay
(denoted by AD) which each packet may typically experience
if it traverses one of the available routes. The mathematical
expression for an estimated AD is as follows:
( )
( )
1
y
i
s d
i
AD D R y
=
(3)
where y represents the maximum number of possible routes
between source s and destination d.
In addition to the average delay, one can also chose the
optimal route with respect to the minimum delay that each
packet may experience when traverse from one particular
source to a destination such as:
( )
( )
1
y
i
s d
i
OD Min D R
=
=
(4)
The above derivations can be further extended for the
multiple unicast system where a single source (s) can transfer a
packet simultaneously to multiple destinations. This hypothesis
leads us to the following argument: multiple routes can be
established between the source (s) and each destination
system. The following mathematical expression can be used to
estimate the total delay that the entire packet transmission will
experience in a multiple unicast system:
( )
( )
1 2
, ,......,
1
multiple
y
y
i
s d d d
i
D D R

=
=
(5)
where y in (5) is the maximum available unicast routes
between a particular source (s) and multiple destinations.
Although, in multiple unicast system, a single packet can be
transmitted from one source to multiple destinations, the
transmitted packet may follow a different route in order to
reach the appropriate destination. Consequently, each packet
transmission may yield a different delay depending on the
number of links the packet needs to traverse on the chosen
unicast route. This leads us to the following mathematical
expression for an average delay:
( )
(
)
( ) ( )
1 1
y
n
i
i i
s d
i i
D R
AD where D R D L
y
= =
=
(6)
where y represents the maximum number of unicast routes
between a source (s) and multiple destinations and n represents
the maximum number of links a unicast route has.
B. Mathematical Model for Multicast System
In IP multicast system, a single source (s) sends a packet to
a group that consists of multiple destination systems. In
addition, a packet is sent only once by the source system where
as the intermediate routers along the route perform replications
with respect to the number of destinations a group has. Let M
G
denotes a multicast group that consists of one or more
destination systems whereas Z represents the size of the group
such as Z = | M
G
|. In an IP multicast system, all multicast
groups (M
G
) can be typically organized in a spanning tree. We
consider a spanning tree rooted at the multicast source (s)
consisting of one of the multicast groups (M
G
) that has a size
of Z. The spanning tree can then be expressed as: T = (N
T
, M
T
)
where the numbers of destinations in one multicast group (M
G
)
belong to the total number of nodes present in the network
such as: M
G
M. Also, Based on the above discussion, we
can give the following hypothesis: The total delay (D)
experienced by multicast packets when transmitted from a root
node (s) to a multicast group (M
G
) can be defined as a sum of
total delay experienced by each link of a spanning tree from
the root nodes (s) to all destinations (d
M
G
) and the delay
experienced by each link of an intermediate routers. Thus, this
leads us to the following expression for total delay (D)
experienced by multicast packets transmitted from root node
(s) to a destination node (d):
( )
( ) ( )
1 1
G
Z n
i i
s M
i i
D D L D L
= =
= +
(7)
where Z is the number of destination systems in one
multicast group of a spanning tree (T) where n represents the
total number of links a route has.
The first term of (7) yields the total delay associated with
the number of links with in a spanning tree when a packet is
transmitted from a root node (source) to all the leaf and non-
leaf nodes. The second term of (7) provides a total delay that a
packet may experience when transmitted along a certain route.
Equation (7) can be further generalized for one of the specific
destinations (d) within a multicast group such as d
M
G
, if
we assume that we have a route within a spanning tree (T)
from multicast source (s) to a specific destination (d) such as
R
T
(s, d), then the multicast packets transmitted from a source
node to a destination experience a total delay of:
( )
(
)
( )
,
,
,
n Z T
G
n Z
L R s d
s d M
D D L
=
(8)
where L
n,Z
represents the total number of links (i.e., Z
R
T
)
that a packet needs to traverse in order to reach the specific
destination d along a path of R
T
with in the tree T as well as the
number of links from source s to a multicast group M
G
.
C. Mathematical Model for an End- System Multicast
Because of the limitations in IP multicast, researchers have
explored an alternative architecture named ESM, which is built
on top of the unicast services with multicast functionalities. In
ESM, one of the end-system nodes (s) participating in an
application session can have the responsibility to forward
information to other hosts. Here, end users that participate in
the ESM group communicate through an overlay structure. An
ESM group can have at most N end-system nodes where we
focus on one of the end-system nodes (s) that multicast
information to the other participating nodes of a multicast end-
system group. From the source host point of view, this ESM
group can be considered a group of destination systems. For
the sake of mathematical model, lets ESM
G
denotes an ESM
group that consists of one or more end-system destination
where as X represents the size of the group such as X = | ESM
G
|. Based on the derived expression of unicast in the previous
sections, these unicast links can not exceed to M such as
1 2
, ,.........,
y
m m m M
where one of the edges provides a
unicast connection between two end-system nodes such as:
{
}
{
}
{
}
1 2
, ,
unicast link
m M n n s N
 (9)
An overlay network consists of a set of N end-system nodes
connecting though M number of edges where one of the end-
system is designated as source host (s) such as:
{
}
, ,
G s N M
= .
This also shows that an ESM is built on top of the unicast
services using a multicast overlay network that can be
organized in a spanning tree such as T = (N
T
, M
T
) rooted as an
ESM source (s) where the numbers of destinations in one
multicast group (ESM
G
) belong to the total number of nodes
present in the network such as: ESM
G
M. The end receivers
in a multicast tree could be a parent or a child node depending
on the location of the node. In a multicast spanning tree (T), all
the non-lead nodes can be both parent and child at the same
time where as all the leaf nodes are considered to be the child
nodes. Based on the above argument, one can say that a
multicast packet originated from the root (s) of a spanning tree
(T) need to traverse typically two links; source to non-leaf
node (P
n
, C
n
) and a non-leaf node to a leaf node (C
n
). Lets R
T
(s, non-leaf node) represents a route between a source node (s)
and non-leaf nodes that could be parent or child nodes such as:
{
}
T n n G
R P C ESM= where
{
}
,
n n
P C s N
(10)
where, R
T
(P
n
, C
n
) represents a route from a parent node to a
child node such as:
{
}
,
T n n G
R P C ESM
= .
Equations (9) and (10) lead us to the following expression
for computing the total delay involve in transmitting a
multicast packet from a source node to one or more parent
nodes (i.e., the delay associated with the first link of
transmission):
( )
{ }
( )
( )
( )
,
1
,
1
multiple unicast
n n n n
n n
y
s P C s N
i s P C
i
n
i
ii s P C
i
D D R
where D R D L

=
=
=
(11)
In (11), y is the maximum unicast routes between a source
(s) and one or more non-leaf nodes and n represents the
maximum number of links a unicast route can have. Similarly,
the total delay experience by a multicast packet transmitted
from a parent node to a child node can be approximated as
follows:
( )
( )
( )
( )
( )
( )
,
1
,
1
multiple unicast
n n
n n
n n
y
i P C
P C
i
n
i
i P C
i
D D R
where D R D L

=
=
=
(12)
By combining (11) and (12), the total delay experience by a
multicast packet that transmitted from a source node (s) to a
child node (C
n
) can be approximated as:
( ) { }
( )
( )
( )
, ,
1
,
1
+
multiple unicast
n n n n
n n
n
s C s P N i s P C
i
n
i P C
i
D D L
D L

=
=
=
(13)
V. PERFORMANCE ANALYSIS
A. System Model
Simulations are performed using OPNET to examine the
performance of Multiple unicast, IP multicast, and ESM
schemes. Figure 4 shows an OPNET model for the Multiple
unicast, IP multicast and ESM simulations. The OPNET
simulation has run for a period of 900 seconds for all three
scenarios where we collect the simulated data typically after
each 300 seconds. For all scenarios, we have setup one sender
node that transmits video conferencing data at the rate of 10
frames/s using 2,500-stream packet size to one or more
potential receivers via a link that operates at 100 Mbps. In
addition to these 100 Mbps licks, we use separate DS3 links
for the core network (Internet). The same traffic pattern is
assumed for all scenarios.
It should be noted in Fig. 4 that we use four backbone
routers that connect multiple subnets to represent Bay
Networks concentrator topology using ATM Ethernet FDDI
technology. In order to generate consistent simulation results,
we use the same topology for the first two scenarios with some
minor exceptions. For Multiple unicast, we disable the
multicast capabilities of backbone routers where as for the IP
multicast this restriction does not impose. Finally, in order to
examine the behavior of the ESM, we use an OPNET Custom
Application tool that generates the overlay links and the source
root.
B. Experimental Verifications
For the Multiple unicast scenario, video conferencing data is
being sent by the root sender at the rate of 25 K-bytes per
second. This implies that a total of three copies traveling
which result in 75 K-bytes per second of total traffic. The last
mile bandwidth limitation typically provides the most
important delay impact. OPNET collected all the delays for all
the receivers and calculated the average. The packet end-to-
end delay for Multiple unicast was 0.0202 seconds. For the IP
multicast approach only one copy of the packet is generated at
the root source. For this reason, the total video-conferencing
traffic sent and received is only 25,000 bytes/s. Thus, a better
performance in the average packet end-to-end delay can be
observed. This is approximately 0.0171 seconds. Finally, after
performing ESM simulations, we obtain an average end-to-end
delay packet of 0.0177 seconds.
It can be seen in Fig. 5 that ESM packets transmission
provides comparatively good performance than the Unicast but
not as good as the IP multicast. The reasons are the RDP
(Relative Delay Penalty or the ratio of the delay between the
sender and the receiver) [2] and the LS (Link Stress or the
number of identical copies of a packet carried by a physical
link) experienced by each network schemes. Even though, a
Unicast scheme provides comparatively low RDP, the value of
LS is not optimal. On the other hand, IP multicast performs
with a little bit higher RDP but it gets a better LS. ESM has the
inconvenience of RDP higher than IP multicast due to the fact
that for a second receiver, there is an increasing delivery–delay
because of the end-user replication (the second user has to wait
for the data sent by its father node or sub-server). This is the
penalty that ESM has to pay. One possible solution would be
the design of a robust multicast protocol to optimize the
delivery of data for the final users. Note that the additional
delay could be reduced if we optimize the bandwidth
utilization in the potential parent nodes. This is not a simple
task because it requires a smart protocol to recognize
bandwidth limitations in potential parent nodes and to
establish an algorithm to limit the number of children nodes
for these parent nodes.
VI. CONCLUSION
In this paper, we presented a complete mathematical model
that can be used to evaluate the performance of multicast
systems. Specifically, the proposed mathematical model can be
used to compare the performance of the ESM, the IP multicast
and the multiple unicast topologies. We concluded that ESM is
a promising alternative for the next generation networks. For
the future work, it will be interesting to extend and implement
the proposed mathematical model to measure the bandwidth
consumption and the overall data throughput per system.
ACKNOWLEDGEMENT
The authors would like to thank Mr. Guillermo Loaisiga for
his initial research on ESM
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Fig. 4 OPNET model for Multiple unicast, IP multicast and End-System
Multicast videoconferencing transmissions.
Fig. 5 Average end-to-end packet delays for Multiple unicast, IP multicast and
ESM simulations.
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Conference Paper
The IP multicast model allows scalable and efficient multi-party communication, particularly for groups of large size. However, deployment of IP multicast requires substantial infrastructure modifications and is hampered by a host of unresolved open problems. To circum- vent this situation, we have designed and implemented ALMI, an application level group communication mid- dleware, which allows accelerated application deploy- ment and simplified network configuration, without the need of network infrastructure support. ALMI is tailored toward support of multicast groups of relatively small size (several 10s of members) with many to many se- mantics. Session participants are connected via a vir- tual multicast tree, which consists of unicast connections between end hosts and is formed as a minimum span- ning tree (MST) using application-specific performance metric. Using simulation, we show that the performance penalties, introduced by this shift of multicast to end sys- tems, is a relatively small increase in traffic load and that ALMI multicast trees approach the efficienc y of IP mul- ticast trees. We have also implemented ALMI as a Java based middleware package and performed experiments over the Internet. Experimental results show that ALMI is able to cope with network dynamics and keep the mul- ticast tree efficient.
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Thesis (D. Sc.)--Washington University, 2002. Dept. of Computer Science. Vita. Includes bibliographical references.
5 Average end-to-end packet delays for Multiple unicast, IP multicast and ESM simulations
  • Fig
Fig. 5 Average end-to-end packet delays for Multiple unicast, IP multicast and ESM simulations.
A Case for End System Multicast
  • Y Chu
  • S Rao
  • H Zhang
Y. Chu, S. Rao, and H. Zhang. "A Case for End System Multicast," Proceedings of ACM Sigmetrics, June 2000.