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Vol. 5, No. 6 June 2014 ISSN 2079-8407
Journal of Emerging Trends in Computing and Information Sciences
©2009-2014 CIS Journal. All rights reserved.
http://www.cisjournal.org
447
Performance Evaluation of MPLS TE Signal Protocols with
Different Audio Codecs
1 Mahmoud M. Al-Quzwini, 2 Shaimaa A. Sharafali
1, 2 Computer Engineering Department, College of Engineering, Nahrain University, Baghdad, Iraq
ABSTRACT
This paper studies the performance of MPLS networks TE signal protocols with different voice codecs including PCM (64
Kbps), GSM FR (13 Kbps), G.723.1 (5.3 Kbps), G.726 (16 Kbps), G.728 (16 Kbps), G.729 (8 Kbps) and IS-641(7.4
Kbps). Simulation results show that the MPLS network with CR-LDP TE signal protocol outperforms the MPLS network
with RSVP TE signal protocol in terms of the total amount of received voice packets, voice packet delay variation, voice
jitter, and the number of maintained calls for all voice codecs. The results also show that G.723.1 codec type gives better
results in terms of the number of maintained calls, but with least voice quality compared with other voice codecs.
Keywords: MPLS, Traffic Engineering, VoIP, CODECS, CR-LDP, RSVP.
1. INTRODUCTION
The high increase in the number of internet users
made services such as telephone and television to reach
their customers via the internet and this has been forcing
Internet Service Providers (ISPs) to improve their quality
of service. With this increase as well as the advances
made in real-time applications (voice and video), the
traditional routers have the challenges of providing the
required high bandwidth, fast routing as well as quality of
service support. Due to the challenges of traditional
routers to provide these requirements especially for voice
and video, methods such as the use of Multiprotocol
Label Switching (MPLS) and so on are now used [1].
MPLS is not designed to replace IP; it is designed to add
a set of rules to IP so that traffic can be classified,
marked, and policed. MPLS as a traffic-engineering tool
has emerged as an elegant solution to meet the bandwidth
management and service requirements for next generation
Internet Protocol (IP) based backbone networks [2].
WAN bandwidth is probably the most expensive and
important component of an enterprise network, Network
administrators must know how to calculate the total
bandwidth that is required for Voice traffic and how to
reduce overall utilization, a description in detail for
coder-decoders (Codecs), codec complexity and the
bandwidth requirements for VoIP calls. A codec is a
device or program capable of performing encoding and
decoding on a signal or digital data stream. Many types of
codecs are used to encode-decode or
compress/decompress various types of data that would
otherwise use a large amount of bandwidth on WAN
links. Codecs are especially important on low-speed serial
links where every bit of bandwidth is needed and utilized
to ensure network reliability [3].
2. RELATED WORKS
Analyzing and optimizing voice traffic over data
networks have been a major challenge to researchers and
developers, many techniques have been proposed based
on analyses from real word and simulated traffic.
Mahesh Kr. Porwal [4] made a comparative
analysis of MPLS over Non-MPLS networks and showed
that MPLS have a better performance over IP networks,
through this paper a comparison study has been made on
MPLS signaling protocols (CR-LDP, RSVP and RSVP-
TE) with Traffic Engineering by explaining their
functionality and classification. The Simulation of MPLS
and Non-MPLS network is done; performance is
compared by with consideration of the constraints such as
packet loss, throughput and end-to-end delay on the
network traffic.
Ravi Shankar Ramakrishnan et al.[5] analyzed
three commonly used codecs using peer-to-peer network
scenario. The paper presents OPNET simulator and they
were considered only in Latency, Jitter and Packet loss.
They were able to present from the results that G.711 is
an ideal solution for PSTN networks with PCM scheme.
G.723 is used for voice and video conferencing however
provides lower voice quality. Music or tones such as
DTMF cannot be transmitted reliably with G.723 codec.
G.729 is mostly used in VoIP applications for its low
bandwidth requirement that’s why this type is mostly
common on the WAN connections and to transport voice
calls between multisite branches.
Md. Arifur Rahman [6] calculated the minimum
number of VoIP calls that can be created in an enterprise
IP network. The paper presents OPNET simulator
designing of the real-world network model. The model is
designed with respect to the engineering factors needed to
be reflected when implementing VoIP application in the
IP network. Simulation is done based on IP network
model to calculate the number of calls that can be
conserved
Sarmad K. Ibrahimet al. [7] studied the
performance of MPLS networks with TE signal protocols
in relation with voice codecs. Simulation were performed
and compared for a multisite network with PCM and
GSM based VoIP. Simulation results show that the MPLS
network with CR-LDP TE signal protocol outperforms
Vol. 5, No. 6 June 2014 ISSN 2079-8407
Journal of Emerging Trends in Computing and Information Sciences
©2009-2014 CIS Journal. All rights reserved.
http://www.cisjournal.org
448
the MPLS network with RSVP TE signal protocol in
terms of both the total amount of received voice packets
and the number of maintained calls for both voice codecs.
The main goal of our research is to study the performance
of traffic engineering signal protocols (CR LDP and
RSVP)with voice codecs for voice over MPLS network.
3. TRAFFIC ENGINEERING IN MPLS
NETWORKS
Traffic Engineering (TE) is a mechanism put in
place to control the flow of traffic in networks and it
provides the performance optimization of the network
resources. The main characteristics of TE are fault-
tolerance, optimum resource 448utilization and resource
reservation [8]. The basic objective of the consideration
of TE is to improve quality of service of some
applications and use the available network resources
efficiently. There are some important factors, which are
needed for TE. These factors are; Path Selection, Traffic
Management, Direction of Traffic along Computed Paths
and Distribution of Topology Information. The LSPs in
the MPLS network are established and the labels are
distributed on each of the hops along the LSPs before
packets could be forwarded. The LSPs can be established
either by explicitly routed LSP or control driven LSP.
Control driven LSPs can also be referred to as hop-by-
hop LSP and are set by the use of LDP protocol.
Explicitly routed LSPs can also be referred to as
constraint based LSPS (CR-LSPs), which are specified in
the setup message. At each hop, a label request is sent to
the next hop along the LSP [9].There are basically two
protocols used to set CR-LSPs in MPLS. These protocols
are; Resource Reservation Protocol (RSVP) and
Constraint based routed LDP (CR-LDP).
3.1 Constraint Based Routed LDP (CR-LDP)
CR-LDP is an extension of LDP to support
constraint based routed LSPs. The term constraint implies
that in a network and for each set of nodes there exists a
set of constraint that must be satisfied for the link or links
between two nodes to be chosen for an LSP [10]. CR-
LDP is capable of establishing both strict and loose path
setups with setup and holding priority, path Preemption,
and path re-optimization [11]. CR-LDP and LDP
protocols are hard state protocols that means the signaling
message are sent only once, and don’t require periodic
refreshing of information. In CR-LDP approach, UDP is
used for peer discovery and TCP is used for session
advertisement, notification and LDP messages. CR-LSPs
in the CR-LDP based MPLS network are set by using
Label Request message. The Label Request message is
the signaling message which contains the information of
the list of nodes that are along the constraint-based route.
In the process of establishing the CR-LSP the Label
Request message is sent along the constraint-based route
towards the destination. If the route meet the
requirements given by network operator or network
administrator, all the nodes present in route distribute the
labels by means of Label Mapping message.
3.2 Resource Reservation Protocol (RSVP-TE)
RSVP-TE is an extension of RSVP that utilizes
the RSVP mechanisms to establish LSPs, distribute labels
and perform other label-related duties that satisfies the
requirements of TE [12]. The revised RSVP protocol has
been proposed to support both strict and loose explicit
routed LSPs (ERLSP). For the loose segment in the ER-
LSP, the hop-by hop routing can be employed to
determine where to send the PATH message [10]. RSVP
is a soft state protocol. It uses Path and RSVPcommands
to establish path. The CR-LSPs established by RSVP
signaling protocol in MPLS network is described by the
following steps:
a. The Ingress router in the MPLS network selects
a LSP and sends the Path message to every LSR
along that LSP, describing that this is the desired
LSP used to establish as CR-LSP.
b. In this process the Path and RSVP messages are
send periodically to refresh the state maintained
in all LSRs along the CR-LSP [13].
c. The LSRs along the selected LSP reserve the
resources and that information is send to Ingress
router using the RSVP message.
4. VOIP CODECS
There are many codecs available for audio,
video and text. We used in our evaluations some of G.7xx
of ITU-T standards for audio compression and
decompression. Table.1 shows number of compression
schemes. Table 1: Common Audio Codecs
Algorithm Bandwidth /Kbps Codecs types PCM64 G.711 RPE LTP 13 GSM FR ACELP 5.3/6.4 G.723.1 ADPCM 16/24/32/40 G.726 LD-CELP 16 G.728 CS-ACELP 8 G.729A ACELP7.4 IS-641
The popular voice codecs used in the
telecommunication industry are G.711 which is widely
used in the PSTN environment [14, 15].G.711 represents
logarithmic pulse-code modulation (PCM) with 8 bits
samples for signals of voice frequencies, sampled at the
rate of 8000 samples/second, on 64 kbps channel. Using
G.711 audio codec for VoIP will give the best voice
quality; as it uses no compression and it is the same codec
used by all Public Switched network and ISDN lines. It
sounds just like using a regular phone or ISDN phone.
But this codec takes more bandwidth then other codecs,
up to 84 Kbps including all TCP/IP overhead. However,
with increasing broadband bandwidth, this should not be
a problem [16].
G.723.1 is the ITU-T standard that specifies the
coded representation for speech in PSTN using Algebraic
Code-Excited Linear Prediction (CELP) coding rates at
Vol. 5, No. 6 June 2014 ISSN 2079-8407
Journal of Emerging Trends in Computing and Information Sciences
©2009-2014 CIS Journal. All rights reserved.
http://www.cisjournal.org
449
5.3Kbit/s and Multiples Maximum Likelihood
Quantization (MP-MLQ) at 6.3 Kbit/s. The 6.3 Kbit/s
provides very good voice quality whereas the lower bit
rate provides good quality with some more functionality
[17].
G.726 is the Recommendation for speech coding
at 40, 32, 24, and 16 Kbit/s (variable bit rates) using
Adaptive Differential Pulse Code Modulation (ADPCM)
transcoding technique [18].
G.278 is the ITU-T Recommendation for speech
coding at 16 Kbit/s utilizing Low-Delay Code-Excited
Linear Prediction Coding (LD-CELP) [19].
G.729a this annex provides the high level
description of a reduced complexity version of the G.729
speech codec. This version is bit stream interoperable
with the full version, i.e. a reduced complexity encoder
may be used with a full implementation of the decoder,
and vice versa [20]. Offers toll quality speech at a low bit
rate of 8Kbps using CS-ACELP (Conjugate Structure –
Algebraic Code Excited Linear Prediction). However, it is
a rather "costly" codec in terms of CPU processing time;
therefore some VoIP phones and adapters can only handle
one G.729 call (channel) at a time. This codec provides
robust performance but at the price of its complexity.
This can cause calls to fail if the user attempts to use
three-way calling, or place simultaneous calls on both
lines of a two-line device, and G.729 is the only allowed
codec [16].
Another standard used in our evaluations is ETSI
GSM. The GSM system uses Linear Predictive Coding
with Regular Pulse Excitation (LPC-RPE codec). It is a
full rate speech codec and operates at 13 Kbits/sec. As a
comparison, the old public telephone networks use speech
coding with bit rate of 64 Kbit/s [16].
And IS-641 speech coding is based on the
ACELP (Algebraic-code-excited linear prediction) [21].
The bit rate of the speech codec is 7.4 Kbit/s. The
standard has been superseded by TIA/EIA-136-410.
5. SIMULATION
The simulation environment employed in this
paper is based on OPNET 14.5 simulator which is
extensive and powerful simulation software. Figures1
and 2 show two different MPLS networks, each one is
simulated with CR-LDP and RSVP TE signal protocols.
To simulate real network environments voice, video,
HTTP, FTP, DB, Telnet and Email applications are used
in each network. The VoIP traffic is sent from source
(voice 1) to destination (voice 2), the video traffic is sent
from source (video 1) to destination (video 2), DB and
HTTP traffic is sent from source (DB, HTTP) to
destination (DB, HTTP server), remote traffic is sent
from source (remote) and FTP traffic is sent from source
(FTP) to destination (FTP, remote server). The network
in figure.1 consists of six routers and four switches and in
figure.2 consists of eight routers and four switches. These
routers in each network are connected with DS3 cable
with data rate of 44.736
Fig 1: first MPLS network topology
Fig 2: Second MPLS network topology
Mbit/s. The end nodes are connected to the
network via switches. Links of each switch are 100BaseT.
The voice workstations use different types of codecs,
namely, PCM (64 kbps), GSM FR (13 kbps), G.723.1
(5.3 kbps), G.726 (16 kbps), G.728 (16 kbps), G.729a (8
kbps), and IS-641 (7.4 kbps) each type of codecs
simulated individually and their results shown in figures 3
through 16, for the sent and received voice packet.
Figures 17 through 30 show results of packet delay
variation and end to end delay. Voice jitter and main
opinion score results are depicted in figures 31 through
44.
6. PERFORMANCE METRICS
In our simulations, we use the following metrics
to evaluate the performance of MPLS network.
6.1 Mean Opinion Score (MOS)
MOS provides a numerical measure of the
quality of human speech in voice telecommunications,
with value ranging from 1 to 5 where 1 is the worst
quality and 5 is the best quality. In our simulation, we
compute MOS through a non-linear mapping from R-
factor as in [22]:
Where; R : the
effect of impairments that occur with the voice signal, :
the impairments caused by different types of losses
occurred due to codec's and network, and : represents
the impairment caused by delay particularly mouth-to-ear
delay. Using the default setting for and A Eq. (1) can
be reduced to:
Vol. 5, No. 6 June 2014 ISSN 2079-8407
Journal of Emerging Trends in Computing and Information Sciences
©2009-2014 CIS Journal. All rights reserved.
http://www.cisjournal.org
450
6.2 Packet end-to-end delay (De2e)
The total voice packet delay; De2e represent in
this formula:
(2)
Where , , , and represent the
network, encoding, decoding, compression and
decompression delay, respectively [23].
6.3 Jitter
The jitter is defined as the signed maximum
difference in one-way delay of the packets over a
particular time interval.
Let t(i) and t’(i) be the time transmitted at the
transmitter and the time received at the receiver,
respectively. Jitter is then, calculated as in [24]:
(3)
According to equation (3), the jitter value can be
negative which means that the time difference between
the packets at the destination is less than that at the
source.
6.4 Packet delay variation (PDV)
Packet delay variation plays a crucial role in the
network performance degradation and affects the user-
perceptual quality. Higher packet delay variation results
in congestion of the packets, which can results in the
network overhead.
PDV is defined as the variance of the packet
delay, which can be, calculated from the following
Equation [24].
(4)
Where is the average delay of the n selected packets.
7. RESULTS AND DISCUSSION
7.1 MOS
The MOS values shown in table.2 and figures 31
through 44 indicate that the voice calls with G.723.1
codec have the less quality than calls with other types of
codecs.
7.2 Number of Maintained Calls
The voice delay can be divided into three
contributing components which are described as follows
[3, 25]:
• The delay introduced by the G.711 codec for
encoding and packetization are 1 ms and 20 ms
respectively. The delay at the sender considering
above two delays along with compression is
approximated to a fixed delay of 25 ms;
• At the receiver the delay introduced is from
buffering, decompression, depacketization and
playback delay. The total delay due to the above
factors is approximated to a fixed delay of 45
ms.
• The overall network delay can be calculated
from the above sender and receiver delays to be
80 ms approximately (150-25-45).
The 150 ms represents the maximum acceptable
end-to-end delay so that the quality of the established
VoIP call is acceptable [25].
In this paper the traffic drop time is used to
calculate the number of maintained calls. In all
simulations, the values of the packet end-to-end delay
when the traffic drops were all less than the maximum
acceptable end to end delay. This will show the difference
among different codecs.
Then the number of maintained calls = (drop time – start
time) /2 (5)
The voice call start at 10 sec, and the drop time
for each scenario is shown in table.5, and the number of
calls maintained are shown in table.6. The results show
that the number of maintained calls when using CR LDP
TE signaling protocol is greater than those with using
RSVP TE signaling protocol with all codecs.
7.3 Jitter
Table.3 and figures 31 through 44shows the
results of maximum jitter values for different scenarios.
Except the GSM FR and G.726 codecs in the first
network, it is observed that CRLDP TE signal protocol
has lower values than RSVP TE.
7.4 Packet Delay Variation (PDV)
Table.4 and figures 17 through 30show the
results of packet delay variation for different scenarios.
Except the GSM FR codec, it is observed that CRLDP TE
signal protocol has lower values than RSVP TE.
Table 2: Summary statistics of MOS values experienced
Codecs
Types Network
number MOS value
CR LDP RSVP
PCM 1 3.595 3.595
2 3.674 3.674
GSM 1 3.467 3.467
2 3.548 3.548
G.723.1 1 2.559 2.559
2 2.546 2.546
G.726 1 3.595 3.595
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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©2009-2014 CIS Journal. All rights reserved.
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451
2 3.674 3.674
G.728 1 3.562 3.562
2 3.675 3.675
G.729A 1 3.000 3.000
2 3.059 3.059
IS-641 1 3.468 3.468
2 3.550 3.550
Table 3: Summary of maximum jitter values experienced
Jitter value (sec) Max. Network
number
Codecs Types RSVP CR LDP 0.0000947 0.0000020 1 PCM 0.0002061 0.0000461 2 0.0016100 0.0017600 1 GSM FR 0.0019630 0.0002930 2 0.0041170 0.0002120 1 G.723.1 0.0026980 0.0000410 2 0.0001278 0.0001930 1 G.726 0.0003929 0.0000340 2 0.0002050 0.0001730 1 G.728 0.0003496 0.0000180 2 0.00039900.0000370 1 G.729A 0.0003462 0.0000230 2 0.0003830 0.0000050 1 IS-641 0.0011320 0.0001330 2
Table 4: summary of voice packet delay variations
Table 5: summary of traffic drop time
Table 6: summary of number of maintained calls
Table 7: summary of End-to-End delay values
Packet Delay Variations
(sec)
Network
number
Codecs types
RSVP CR LDP 0.0000660 0.0000030 1 PCM 0.0000493 0.0000200 2 0.0000670 0.0004080 1 GSM FR 0.0002900 0.0005940 2 0.0004600 0.0000370 1 G.723.1 0.0002220 0.0000030 2 0.0018100 0.0001900 1 G.726 0.0001870 0.0000060 2 0.0009330 0.0001710 1 G.728 0.0005940 0.0000020 2 0.0003190 0.0000023 1 G.729A 0.0001700 0.0001100 2 0.0002300 0.0000200 1 IS-641 0.0001410 0.0000070 2
Number of calls/sec Network
number
Codecs types RSVP CR LDP 14 45 1 PCM 15 57 2 15 46 1 GSM FR 15 154 2 46 225 1 G.723.1 15 225 2 18 78 1 G.726 16 76 2 17 78 1 G.728 15 75 2 15 75 1 G.729A 15 78 2 10 150 1 IS-641 15 153 2
Codecs
types Network
number End-to-End delay (sec)
CRLDP RSVP
PCM 1 0.079467 0.076834
2 0.078400 0.087500
GSM FR 1 0.126400 0.114500
2 0.142964 0.124584
G.723.1 1 0.148105 0.137048
2 0.111531 0.123505
G.726 1 0.111500 0.112300
2 0.070800 0.128800
G.728 1 0.113900 0.141138
2 0.070900 0.081100
G.729A 1 0.081200 0.098600
2 0.127800 0.106300
IS-641 1 0.109300 0.103700
2 0.104046 0.116862
Traffic drop time(sec) Network
number
Codecs types RSVP CR LDP 38 100 1 PCM 40 125 2 40102 1GSM FR 40318 2102 460 1 G.723.1 40 460 2 46 166 1 G.726 42 162 2 45166 1G.728 40160 240 160 1 G.729A 40 166 2 30 310 1 IS-641 40 316 2
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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452
Fig 3: 1st network PCM send and received voice traffic
Fig 4: 1st network G.723.1send and received voice traffic
Fig 5: 1st network G.726 send and received voice traffic
Fig 6: 1st network G.728 send and received voice traffic
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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453
Fig 7: 1st network G.729 send and received voice traffic
Fig 8: 1st network GSM FR send and received voice
traffic
Fig 9: 1st network IS-641 send and received voice traffic
Fig 10: 2nd network PCM send and received voice traffic
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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454
Fig 11: 2ndnetwork G.723.1 send and received voice
traffic
Fig 12: 2nd network G.726 send and received voice traffic
Fig 13: 2ndnetwork G.728 send and received voice traffic
Fig 14: 2ndnetwork G.729 send and received voice traffic
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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455
Fig 15: 2nd network GSM FR send and received voice
traffic
Fig 16: 2nd network IS-641 send and received voice
traffic
Fig 17: 1st network PCM PDV and E2E Delay
Fig 18: 1st network G.723.1 PDV and E2E Delay
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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Fig 19: 1st network G.726 PDV and E2E Delay
Fig 20: 1st network G.728 PDV and E2E Delay
Fig 21: 1st network G.729 PDV and E2E Delay
Fig 22: 1st network GSM FR PDV and E2E Delay
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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Fig 23: 1st network IS-641 PDV and E2E Delay
Fig 24: 2nd network PCM PDV and E2E Delay
Fig 25: 2nd network G.723.1 PDV and E2E Delay
Fig 26: 2nd network G.726 PDV and E2E Delay
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458
Fig 27: 2nd network G.728 PDV and E2E Delay
Fig 28: 2ndnetwork G.729 PDV and E2E Delay
Fig 29: 2nd network GSM FR PDV and E2E Delay
Fig 30: 2nd network IS-641 PDV and E2E Delay
Vol. 5, No. 6 June 2014 ISSN 2079-8407
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Fig 31: 1st network PCM jitter and MOS values
Fig 32: 1st network G.723.1 jitter and MOS values
Fig 33: 1st network G.726 jitter and MOS values
Fig 34: 1st network G.728 jitter and MOS values
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Fig 35: 1st network PG.729 jitter and MOS values
Fig 36: 1st network GSM FR jitter and MOS values
Fig 37: 1st network IS-641 jitter and MOS values
Fig 38: 2nd network PCM jitter and MOS values
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Fig 39: 2nd network G.723.1 jitter and MOS values
Fig 40: 2nd network G.726 jitter and MOS values
Fig 41: 2nd network G.728 jitter and MOS values
Fig 42: 2nd network G.729 jitter and MOS values
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©2009-2014 CIS Journal. All rights reserved.
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462
Fig 43: 2nd network GSM FR jitter and MOS values
Fig 44: 2nd network IS-641 jitter and MOS values
8. CONCLUSIONS
In this paper, the performance of MPLS traffic
engineering signaling protocols CRLDP and RSVP have
been investigated with seven types of codecs PCM, GSM
FR, G.723.1, G.726, G.728, G.729a, and IS-641. The
performances of these codecs have been presented and
compared.
Performance analysis focused on voice metrics
included voice MOS values, voice end-to-end delay,
voice jitter, voice packet delay variation, and voice
sent/received packets. The number of calls is calculated
and compared for each codec.
Results have showed that the MPLS network
with CR-LDP TE signal protocol has a noticeable
performance advantage compared to the MPLS network
with RSVP TE signal protocol. It is five times more than
RSVP in terms of number of maintained calls in the 1st
network, this performance difference increases as the
network becomes larger as it becomes seven times in the
second network. CRLDP has 1.12% less end to end delay
of that of RSVP 9 in the 1st network and by 8.09% in the
2nd network. For voice jitter, CRLDP is 34.34% of that of
RSVP in the 1st network and 8.3% in the 2nd network. The
voice packet delay variation of CRLDP is 21.4% of that
of RSVP in the 1st network and 44.88% in the 2nd one.
The performance of the G.723.1 codec has the
highest number of calls than other codecs but with poor
voice quality. The IS-641 codec has higher number of
calls 66.667% of that of G.723.1 codec with fair voice
quality. Other codecs have less number of calls
approximately 33.333% of that of G.723.1 codec but with
fair voice quality. These results are for the respective
codecs when applied with CRLDP protocol, however a
similar performance difference between the codecs is
obtained with RSVP protocols.
Increasing the number of paths in the 2ndnetwork
increases the performance advantage of the CRLDP over
the RSVP. This is due to the RSVP scalability issue when
there are a large number of paths passing through a node
due to the periodical refreshing of the state for each path.
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