JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
INITIAL IP PBX TRUNK SIZING
Engineering the user base of an IP PBX,
PBX or key system to a number of telephone
network lines or VoIP capacity should
involve some form of predictive modeling.
Using a fixed extension to incoming line
ratio, such as 4:1, may be a tried-and-true
place to start, but competitive pressures
coupled with a new generation of Internetsavvy entrepreneurs means that many sales
professionals will only get one chance to
size it right and capture the business.
For an IP PBX, the complexity of predicting
the human behavior is compounded by the
technological
variables
involved
in
describing the operation of a VoIP telephony
system. When sizing a new installation,
much of the voice traffic information
required for proper capacity calculations
may not be available. Estimating busy hour
call attempts (BHCA) and other such key
parameters should be undertaken with care
and caution, especially when dealing with
small-medium businesses (SMBs) with user
populations of five to 50 extensions.
If we break down the design/sizing process,
we
propose
three
distinct
steps:
• Develop a rudimentary call model based
upon the total number of telephony users
and their calling patterns. The output of this
model will be quantified voice traffic
expressed as a high/low traffic range
representing different business models.
• Using the estimated voice traffic range,
calculate the PBX's required incoming
trunks (equivalent line appearances).
• Translate the required trunks into
corresponding VoIP network capacity in
terms of the codec and voice sample size
selected.
The best way to illustrate this is through an
example. A detailed discussion of the
concepts and methods follows the example.
SAMPLE CUSTOMER PROPOSAL
A cable operator is bidding on the
communication upgrade of an established
florist employing 10 people, and which is
currently serviced by four dedicated
telephone lines: one direct line for the office
manager, three lines shared among the
remaining staff, and a point of sale terminal.
These lines operate as a hunt group off the
main
directory
number.
Upon meeting with the customer, the sales
engineer captures the following user
telephony profile (see Figure 1):
1
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
FIGURE 1: Customer proposal, initial conditions
• One office manager: high telephone use
• Four customer-serving staff (counter); low
telephone
use
• Three noncustomer-serving staff accepting
and filling telephone orders (coordination of
deliveries):
high
telephone
use
• Two drivers; extremely low telephone use
at the business site, but high cellular use
• Existing cable modem-based data service,
with business grade 1 Mbps bidirectional
service. Data traffic includes access to
email, point of sale terminal, hosting
external Web site, B2B traffic (suppliers),
and
Web
surfing.
From this data, the sales engineer must now
attempt to size the IP PBX system for the
bid and confirm that the existing 1 Mbps
bidirectional cable modem service is
adequate.
Call
model
and
traffic
calculations:
• High-use user traffic = 4 * 0.15 = 0.6
Erlang
• Low-use user traffic = 4 * 0.10 = 0.4
Erlang
Total
traffic
=
1.0
Erlang
Required incoming telephony lines for 1.0
Erlang:
• One call blocked in every 100 - grade of
service
(GOS)
(0.01)
=
5
• 10 calls blocked in every 100 - GOS (0.1)
=
3
Recommendation: Start with computing the
network capacity for three and four trunks
(incoming lines) since some incoming call
blockage may be acceptable to the customer.
2
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
To find the required network VoIP capacity,
select a codec (G.729) and sampling rate (20
ms), and then compute or look up the
required capacity as shown in Table 1.
TABLE 1: Line rates
Recommendation:
• Provided that the network's end-to-end
latency characteristics are acceptable, G.729
with 20 ms @ 163.2 kbps would provides a
good balance between audio quality and
network
efficiency.
• It is up to the sales engineer, given his
understanding of this customer's calling
traffic patterns, to propose a three- or fourtrunk system. A competitive approach may
be to propose a three-trunk system at G.729
@ 20 msec sampling and a network capacity
of 122.4 kbps, upgrading to four trunks if
the customer encounters higher than existing
call blockage or customer complaints.
• The direct line to the manager is replaced
with a direct inward dial (DID) number that
is intercepted at the IP PBX and routed
directly to the manager's telephone.
• The final proposal would look like that
shown
in
Figure
2.
3
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
FIGURE 2: Customer proposal, final design
Conclusions:
predictive
• The existing 1 Mbps bidirectional data
service is adequate to carry the existing data
and
the
new
VoIP
traffic.
• Additional attention may be required to the
cable modem at the premises to ensure that
the VoIP packets and their QoS markings
are provided the correct service levels.
In 1909, while employed by the Copenhagen
Telephone Co., A.K. Erlang published his
first work on the "Theory and Probabilities
of Telephone Conversations." His legacy is
a body of works that provide both a proof
and working models to engineer telephony
networks based upon Poisson's law of
random distribution. His mathematical
insights linked the quantity of network
resources (trunks) to the demand (user
traffic) by the number of call failures
stemming from lack of resources (grade of
service,
or
GoS).
TELEPHONY TRAFFIC BASICS
The best way to engineer a PBX is to record
the voice traffic levels over multiple days
and to design a system accordingly. But
when actual data is not available, estimating
is the only option, and to do so is akin to
predicting how often and for how long the
subscribers use their telephones. The type of
business and the total number of possible
telephone connections were identified as
predictors of telephony traffic nearly 100
years ago during the development of
statistical
models.
Today, different traffic models and their
derivatives are the standard used to engineer
the number of public switched telephone
network (PSTN) trunks that are required to
support a given number of PBX extensions.
The models have multiple variants
specifically designed to emulate different
call treatment behaviors as seen in the
4
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
current feature-rich environment of PBX.
The Erlang B and Extended Erlang B
models are used for noncall center PBX
modeling - that is, for installations where
call blockage rates are very low and call
overflow is to an automated facility such as
voicemail. Conversely, the Erlang C model
was developed to describe systems where
calls are directed or queued for treatment by
attendants or call center agents. In fact, the
model and its associated tables are used to
engineer such parameters as the number of
call agents and the behaviors of autoattendants.
Typical SMB deployments of the five to 50
user ranges are at the periphery of the
descriptive capabilities of statistical models.
It is recommended that sales engineers
utilize a bracketing technique coupled with
their judgment when designing systems.
Intuitively, given the same number of
extensions, an auto-parts distributor will
probably receive more calls per hour than a
gas station and should have more incoming
trunks from the PSTN. Thus, developing a
high-low range of options will provide for a
better overall design. As stated earlier, triedand-true methods, such as a fixed 1:4 ratio
of incoming lines to extensions, are perhaps
a good starting point, but having greater
design options can only increase the overall
value
to
the
end
customer.
in these small user base installations in a
way that reflects the business model and
generates the high-low traffic options. In the
absence of actual traffic data for an
installation, a good place to start is with the
end users and their telephone use patterns.
Busy hour
The most precise way of determining the
number of network trunks needed to support
a specific group of users is to observe their
calling patterns over a period of time to
determine when they are at their busiest. The
voice traffic during this busy hour, in
combination with the acceptable percentage
of call failures (blocking), is the point for
which
the
system
is
engineered.
The problem faced by my colleague, and
cable operators in general, is that for new
installations and customers there is little or
no busy hour data available. Thus, an
approximation must be developed that
provides enough realism that a system can
be sized for bidding and initial installation.
The specific challenge lies in finding a
simple way to characterize the traffic flows
Two key pieces of information are needed to
use an Erlang table: the maximum traffic
load generated by the PBX and the
acceptable quantity of failed calls (GoS). A
way of estimating the former is to build a
call model that describes the behavior of the
PBX users at busy hour. For example, if we
average out the calling rates of all of the
users of a PBX and inject best field practices
to create a sample busiest hour, we can
propose the traffic rates shown in Table 2.
TABLE 2: Sample user traffic (This
information is provided as non-definitive
values, which should be used with caution;
users are encouraged to follow best practices
5
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
and to refine their traffic estimation methods
within the context of their market forces and
customers' values.)
The intent of Table 2 is to develop an easily
customizable call model that provides a
high/low traffic range needed to guide the
final system design. The values contained
are for demonstrative purposes and should
not be mistaken for actual field data. With
use, this model can be refined to reflect
specific user behaviors and market trends
and will ultimately provide sales engineers
with
design
options.
If we look at an example, a non-call center
PBX with 15 users and an acceptable
It should be noted that in this example, the
fixed 1:4 ratio would have prescribed four
trunks (10% blocking), which may have
been acceptable for the customer. However,
with the range of options presented by this
bracketing technique, the sales engineer can
better tailor the design to the individual
customer's business model.
Traffic and capacity
The great innovation of our time, the
Internet, has begun to revolutionize the total
connection experience, and the underlying
technologies of Ethernet and IP are making
a fundamental change to the way
communications are transported and
processed. VoIP brings with it the promise
of economic benefits as users converge their
blockage of rate of between 1 and 10 calls in
very 100 would give:
GoS:
0.01
(1%
blocking)
Table:
Erlang
B
(noncall
center)
Busy hour high = 15 * 0.15 E = 2.25 Erlang
Busy hour low = 15 * 0.1 E = 1.5 Erlang
Required
trunks
high
=
7
Required
trunks
low
=
5
GoS:
0.1
(10%
blocking)
Table:
Erlang
B
(noncall
center)
Busy hour high = 15 * 0.15 E = 2.25 Erlang
Busy hour low = 15 * 0.1 E = 1.5 Erlang
Required
trunks
high
=
5
Required
trunks
low
=
4
traffic onto one infrastructure. For the
purposes of engineering an IP PBX's
network connection needs, both the
Ethernet-based VoIP packet and the
digitized voice sample need to be quantified.
Starting from the basics, the VoIP IP packet
is a multi-protocol sandwich in which the
voice payload is encapsulated in layers of
real-time transport protocol (RTP), user
datagram protocol (UDP), IP and QoSenabled Ethernet (802.1q). Each protocol is
defined with fixed and variable length
components, which in combination with the
voice payload become a packet stream that
we will refer to as the line rate. (See Figure
3.)
6
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
FIGURE 3: 802.1q VoIP Packet Structure
If we complete the math on the VoIP packet
stream, by adding up all of the protocol and
framing related bytes, we see that each voice
sample will have minimum of 82 bytes of
packet overhead for this protocol
combination. (See Table 3.)
7
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
TABLE 3: Packet overhead
The next step involves calculating the exact
size of the voice payload for the specific
combination of codec and sampling rate
utilized. Once calculated, the encapsulating
packet overhead is added to produce the
total packet size; from this the effective line
rate is calculated. A summary of the most
common codecs and sample sizes is
provided in Table 4.
8
JFM-RTU
COMMUNICATIONS SYSTEM DESIGN/VoIP SUPPLEMENT
TABLE 4: Line rates
(Calculated line rates are a product of the
assumptions used in the calculation of the
packet overhead. By including or omitting
optional parameters and physical attributes
such as inter-frame gaps, your line rate
calculations may vary from these.)
The line rates from Table 4 provide an
equivalent bit stream for each half of the
voice conversation. Thus, if your customer
is transporting G.711 @ 30 mSec sampling
VoIP calls over an 802.1q bidirectional
Ethernet facility, each session will be
transmitting a packet stream of 98.9 kbps. If
this is done over a 2 Mbps facility reserved
for VoIP traffic, then a maximum of 20
simultaneous calls can be supported. Note:
This discussion pertains to the capacity from
the cable modem to the IP PBX. When the
term "2 Meg pipe" is used, it refers to what
is available to the end user. Additional
DOCSIS overhead would apply if we were
discussing the capacity needed within the
cable plant.
CONCLUSION
The question can only be answered if we
understand the IP PBX's voice traffic use
patterns and the choice of codec and
sampling rates. The simplified method
presented in this article can help newcomers
to commercial services develop their own
practices for initial IP PBX trunk sizing.
This is a lucrative market where cable
operators can effectively leverage their QoSenabled DOCSIS infrastructure, provided
they master the concepts of enterprise voice
engineering.
9