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1. An ex ante forecast on economically engineered bit rates
for IPTV service via xDSL transports
of internodal access
Perambur S. Neelakanta & Angela S. Perez &
Daniel M. Baeza
Accepted: 14 February 2008 /Published online: 29 April 2008
# Springer Science + Business Media, LLC 2008
Abstract Concerning broadband IPTV service (of 12/24 MHz bandwidth) on a
digital subscriber line (xDSL), an algorithm (plus a numerical spreadsheet) that
computes the required, economically engineered bit rates (EEBRs) of associated
(aggregated) traffic is developed. The EEBR is decided by user (residential/business)
behavior at a wire center and is essential for economic design/implementation/
expansion of xDSL infrastructure. Using an available set of (ex post) data on xDSL
growth of services (collected over a period of semiannual terms) at a wire center, an
ex ante forecast on EEBR is elucidated. An EEBR-based economic utilization of
resources and connection admission control is indicated.
Keywords IPTV. xDSL economically engineered bit rates . Bit rate forecast
1 Introduction
The prospects of next-generation networking (NGN) in telecommunications (as overlay
efforts on existing infrastructure of circuit-switched network architectures) encompass
three technological components vis-à-vis their evolution and turf layout considerations.
The first one is the internodal access transport (otherwise, simply known as the “local-
Netnomics (2008) 9:21–46
DOI 10.1007/s11066-008-9009-y
P. S. Neelakanta (*)
Department of Electrical Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA
e-mail: Neelakan@fau.edu
A. S. Perez
IBM Global Engineering Services, STG, Bldg. 062-J1173039 Cornwallis Road,
Research Triangle Park, NC 27709, USA
e-mail: asperez@us.ibm.com
D. M. Baeza
AT & T Labs, 6451 North Federal Highway, RM # 619, Fort Lauderdale, FL 33308, USA
e-mail: db2058@att.com

2. loop”). It refers to the gamut of infrastructural facility of transport methods plus the
electronics stretching from the network interface device (NID) at the customer premises
to the serving central office (CO). The second one refers to the switching technology that
covers the CO-switch paraphernalia and the third is the internodal transport pertinent to
the whole plethora of interoffice facility (IOF).
The present study offers a method to design economically-engineered bit rates
(EEBRs) for upcoming and next-generation local-loop technology that may support
IPTV streaming to customer premises via xDSL (digital subscriber line) access
methods. The EEBR, in question, implies a prudent choice of bit rate requirements
of the network resources and the associated support systems consistent with
customer usage pattern. That is, the EEBR in essence, should economically provide
the unspecified bit rate (UBR) as well as the guaranteed bit rates (GBRs) negotiated
through service level agreements (SLAs) with the customers. In other words, the
EEBR represents an optimized bit rate that conforms to practical aspects of
bandwidth-provisioning and capacity management with respect to the physical layer
of xDSL transport. Proper adoption of EEBR would allow network resources to
adequately support the (non-deterministic) total bandwidth on demand from
customer side (including IPTV streaming in the present context) without prejudicing
the SLA. At the same time, the resources are not redundantly installed, lest it would
burden the capital and operational expenses (CAPEX and OPEX) involved.
In general, traditional xDSL networks support two classes of customers: (1)
Residential customers with a simple asymmetric DSL (ADSL) connectivity for
Internet access provisioned by an UBR-specific SLA; and, (2) business/enterprise
customers who may need xDSL connectivity but with an access that provides rather
a GBR class of service (with corresponding SLA).
In the upcoming as well as in the next-generation xDSL pursuits, the
telecommunication companies (telcos) would aggressively practice offering another
distinct class of service to residential customers who opt for IPTV (warranting large
BW/high bit-rate streaming via xDSL access). Multi-dwelling units (MDUs) and
hospitality premises are examples where such connectivity for down-streaming
cable-quality (or better) video access is needed [5]. In the competitive deregulated
environment, the telcos would tend to pursue such options so as to achieve return-
on-investment (RoI) benefits from the tons of buried copper lines of plain old
telephone service (POTS).
The ongoing efforts in telco business in implementing IPTV via xDSL is based on
using the so-called ADSL2/ADSL2+ services along with a strategy known as
“copper-bonding” that will facilitate the required upper limit on the bit rate for
(MPEG) quality picture transmissions [1].
To the best of authors’ knowledge, no efforts on explicit evaluation of EEBR
pertinent to intermodal access seem to exist or published in open literature. An US patent
[12] of 2002 describes a measurement system for post-estimation of the capacity of a
DSL local loop (on the physical lines already trenched in situ). This, however,
provides no a priori data on design requirements of bit rates needed for additional
services as such. Described in [4] details on preparing the infrastructure of legacy
networks for broadband services (such as IPTV). It includes relevant particulars on
data gathering, compilation of network information archive, access network check and
local loop qualifications, but does not offer any approach to estimate the bit rates to be
22 P.S. Neelakanta et al.

3. engineered. In a latest publication [5], the author queries that, in the existing copper
infrastructure of access loops, the “biggest unknown in the broadband services
equation is how much bandwidth will be needed to support video into the next
decade?” Today it is still a “wild card decision” in provisioning this queried
bandwidth/bit rate considerations due to the nonexistence of any tangible algorithm to
compute the bit rates to be engineered. This niche motivated the present study.
2 IPTV on xDSL infrastructure
For the implementation of broadband IPTV applications on DSL transports, the
aforesaid ADSL2/ADSL2+ schemes need ratings of the type and extent of bit rates
as listed in Table 1.
While resorting to ADSL2/ADSL2+ services (up to 18 kft reach), the underlying
large bandwidth (BW) is realized by what is known as multi-pair bonding [1]. This
strategy refers to bonding together multiple copper-pairs enabling a loop
aggregation. For example, four copper-pairs each serving at a xDSL rate of 2.3 Mbps
can be bonded (paralleled) to support a higher rate of 10 Mbps (at the cost of four
DSLs for a given reach-distance). Typically, 18 kft is considered (via line-
qualification field tests) as the allowable maximum distance to support typical
ADSL speed (or bandwidth). For IPTV transmissions (corresponding to MPEG
quality pictures), such a simple ADSL bandwidth will, however, be insufficient
(even for 18 kft access or less). Therefore, the aforesaid strategy of copper-bonding
is adopted towards total bandwidth requirements (such as for IPTV). That is, by
facilitating architecture of bonded copper-pairs in the physical layer, IPTV
transmissions can be enabled and provisioned on local-loops.
With reference to services rendered as per ADSL2/ADSL2+, though a guaranteed
bit rate is specified (as given in Table 1), the equipment in the turf that serves the
entire DSL customer base will not, however, be loaded at all times to the extent of
the sum total of GBR/UBR demands of the entire subscribers. The reason is that,
Table 1 Minimum-to-maximum ranges of bit rates on up- and down-links for different types of service of
interest: xDSL classifications of ADSL2/ADSL2+ [2]
Minimum-to-maximum ranges of bit rates:
(Rdmin − Rdmax)down-link/(Rumin − Rumax)up-link (kbps)
xDSL Service classification and bit rate type
(256–1,500)down/(128–256)up ADSL: Residential
High-speed Internet
Bit rate type: UBR/UBR
(12,000)down/(1,000)up: ADSL2: Residential/MDU
Entertainment/IPTV/high-speed-Internet:
18 kft Loop-length
Bit rate type: GBR
(24,000)down/(3,000)up ADSL2+: Residential/MDU
Entertainment/IPTV/high-speed Internet:
18 kft Loop-length
Bit rate type: GBR
MDU multi-dwelling unit
Ex ante forecast on economically engineered bit rates for IPTV 23

4. statistically it can be expected that at any given time, not all customers (of a service
area) will be availing the entire circuit (and the associated resources), nor that they
would avail simultaneously the maximum rate that the physical line of the loop can
support (per subscriber). Normally, it is conceivable that there exists a fraction of
customer population (in the service area) not using the line at all; and, some may be
using the xDSL sparingly for lean-traffic applications such as e-mail; and, active
IPTV transmissions being streamed through internodal access loop could only be a
fraction of the total traffic supported over that period of time.
The present study uses this statistically anticipated, limited use of resources to
design economically, the bit rates engineered for the transport of aggregated traffic
(including IPTV) of internodal loop access. Hence a forecast scheme is devised to
ascertain the EEBRs on ex ante basis using the available (ex post) details on
infrastructure growth versus services rendered in the customer base.
3 DSL infrastructure
In order to understand the underlying considerations, briefly reviewed in the
following section are details on the working aspects of xDSL architectures.
Typically, xDSL is provisioned in a service area via two methods. The first one
involves direct copper-connectivity from customer premises to the serving CO. This
is feasible when the distance between the CO and customer serving area is within the
permissible (distance × bandwidth) criterion set for that service (such as, 18 kft for
normal ADSL service as limited by the distributed inductance and capacitance of the
physical copper-lines). This system is illustrated in Fig. 1.
A second type of xDSL refers to accommodating the service via a remote terminal
(RT) as illustrated in Fig. 2. That is, when the serving area is beyond the reach-
distance required for the DSL in question, a remote terminal can be established in the
vicinity of the serving area and all the copper-lines from the customer premises are
brought to this RT as shown in Fig. 2. Hence, an RT-DSLAM multiplexer (RT-
MUX) and a digital loop carrier (DLC) arrangement enable aggregating the data
from copper-pairs and forwarding them to the CO via DS3 transport (or on an OC-3
fiber/passive optical network, PON). Regardless of the aforesaid different versions of
xDSL infrastructure-based service, the capacity provisioning should conform to
EEBRs for network economy.
LP
filter
ADSL
modem
ATU-R
Copper
pair
DSLAM
ATU-C
PSTN
Voice
network
Data
network
NSP
Interoffice
facility (IOF)
ATM
switch
CO
(Class-5)
Local
switch
Fig. 1 Direct ADSL access to-and-from the central office. LP filter low-pass baseband audio filter, ATU-R
access terminal unit-remote, DSLAM/ATU-C DSL access module/access terminal unit-CO, PSTN public
switched telephone network, ATM asynchronous transfer mode, NSP network service provider
24 P.S. Neelakanta et al.

5. 4 Description of a customer base in a traditional local-loop
Typically, the services rendered in a local-loop consist of: (1) POTS providing
simple land-line telephony wherein, the line from a customer premises is either
directly terminated at the CO or alternatively, taken to a curb-side DLC (digital loop
carrier) box where, the lines from several customers are multiplexed as per T/E-
hierarchy. The multiplexed signals are then hauled to the CO via a large bandwidth
physical layer such as an optical fiber. (2) Some of the POTS subscribers may also
be using dial-up modems for their computer usage; (3) For fast access, such dial-up
modem connectivity can be substituted with xDSL transports, either directly to the
CO or via a remote terminal (RT); and, (4) service for IPTV can be provisioned
through xDSLs with the technique of copper-bonding mentioned earlier.
5 Computation of infrastructure EEBR for IPTV customer base
With reference to various xDSL service provisioning in a local-loop mentioned above,
the associated design of capacity management relevant to such xDSL deployment
refers to first addressing the underlying traffic engineering (TE) considerations, which
are mostly inventory details that could be found in the following database of any telco.
The TE database normally include details concerning: (1) On-line tracking of xDSL;
(2) tracking system for capacity outlay; (3) automatic updates on loop-electronics/
equipment inventory; (4) loop-test database on the service area; (5) trunks inventory
record keeping system (TIRKS) [11]; (6) planning and forecasting on network
Voice
network
Data
network
NSP
ATM
switch
CO Mux
N × T1
OC 3
DS 3
DS 3
OC 3 DSLAM
hub-shelf
switch
DS 1
DLC
RT
Mux
DS 1
or
DS 3
RT-DSLAM
LP
filter
ADSL
modem
ATU-R
Copper
pair
Fig. 2 ADSL access to-and-from a remote terminal (RT). Mux multiplexer, DLC digital line carrier, DS1/
DS3 digital signal 1 and 3 corresponding to T-1/T-3 hierarchy
Ex ante forecast on economically engineered bit rates for IPTV 25

6. facility; (7) operating the network management system; and, (8) details on record-
keeping in CO operations and maintenance.
For the purpose of developing an algorithm that computes the infrastructure
EEBR when IPTV deployment is provisioned on xDSL in a given service area, a set
of inventory details can be gathered from the aforesaid database of a telco pertinent
to a wire center in question connected to the access loops of the service area.
Considering an internodal loop access system, relevant details (with appropriate
notations) can be listed as follows:
(a) Subscriber demography
Total number of subscribers (including POTS subscribers) N
POTS-only subscribers (with basic telephone lines only) NP
Dial-up modem subscribers (featuring dial-up modem access lines) ND
xDSL subscribers/xDSL access lines (including copper-bond pairing for IPTV provisioning) NxDSL
(N = NP + ND + NxDSL)
(b) Bandwidth (BW) capacity per line
POTS (voice) line capacity BWv=4 kHz/64 kbps
Dial-up modem line capacity BWD=56 kbps (maximum)
ADSL (uplink) from customer-end BWul-ADSL=64 kbps (up to 18 kft)
ADSL (downlink) to customer-end BWdl-ADSL=1.5–2.0 Mbps (up to 18 kft)
Further, with reference to Table 1, it follows that,
ADSL2 (uplink) BWul2=1 Mbps (up to 18 kft)
ADSL2 (downlink) BWdl2=12 Mbps (up to 12 kft)
ADSL2+ (uplink) BWul2+=1 Mbps (up to 18 kft)
ADSL2+ (downlink) BWdl2+=24 Mbps (up to 12 kft)
(c) Service rate versus service classifications
When xDSL serves as the backhaul to asynchronous transfer mode (ATM) trunk
transmissions at the edge/core network, service classifications (expressed as above in
terms of their bit rates) would decide subsequent ATM transport adaptations in the core
network. The service rate versus service classifications expressed in terms of minimum-
maximum/up- and down-link rates and type of classifications can be denoted (for
example, with reference to a residential service) by the following notation:
R Min Max
ð Þdown link
.
R Min Max
ð Þup link:
Service classification $ Rdmin Rdmax
ð Þdown
.
Rumin Rumax
ð Þup: Residential
ð1Þ
Further, the types of bit rate along up and down streams are denoted by constant
bit rate (CBR), UBR, GBR, etc. on ad hoc basis. With reference to xDSL under
26 P.S. Neelakanta et al.

7. consideration, relevant details are as given in Table 1. In addition, in order to
develop algorithms toward EEBR computation under consideration, the following
explicit details are required:
– Number and types of customers connected to a given DSLAM version
– Maximum number of active customers supported on this DSLAM during peak-
hours [9]
– Total bandwidth in demand specified by the statistics of the bit rate profile
prevailing on the customer side
– DSLAM type (CO-based or RT-based) and physical line (DS-3/OC-3) feed
adapted at the DSLAM for directing the aggregated DSL traffic to the CO
– xDSL physical port capacity to be provisioned/engineered
(d) Suppose, the total number of ADSL customers connected to the DSLAM at
a CO is specified as, NADSL-CO, then more explicit parameters can be defined
(specific to the types of subscribers and versions of services) as follows:
5.1 Residential customers not opting for IPTV, (identified by the subscript index, R1)
Number of residential customers connected to the DSLAM
at the CO not opting for IPTV
NR-nonIPTV
Coefficient deciding the fraction of residential users
(out of total subscribers) not opting for IPTV
fR1 < 1 ¼ NR nonIPTV
NADSL CO
Number of residential non-IPTV users active during peak-hours (NR-nonIPTV)Active
Coefficient deciding the fraction of non-IPTV residential users
(out of total users) active during peak hours
gR1 < 1
ð Þ ¼
NR nonIPTV
ð ÞActive
NADSL CO
Further, suppose an ith active user (of any UBR category) is served by the
DSLAM in a down-stream access mode at a variant speed, (Umin ≤ ui ≤ Umax). Then,
Coefficient deciding the fraction of statistically variant UBR utilized
by non-IPTV residential customers
(hR1<1) = (uR1)i/UMax
5.2 Residential customers opting for IPTV, (identified by the subscript index, R2)
Number of residential customers opting for IPTV
connected to the DSLAM at the CO
NR-IPTV
Coefficient deciding the fraction of residential users
(out of total subscribers) opting for IPTV
fR2 < 1 ¼ NR IPTV
ð Þ
NADSL CO
Number of active IPTV users during peak-hours (NR-IPTV)Active
Coefficient deciding the fraction of IPTV user
(out of total users) active during peak hours
gR2 < 1 ¼
NR IPTV
ð ÞActive
NADSL CO
Coefficient deciding guaranteed and statistically-invariant,
maximum-UBR utilized by IPTV residential customers
(hR1=1) = UMax/UMax
Ex ante forecast on economically engineered bit rates for IPTV 27

8. 5.3 Business customers on UBR service agreement, (identified by the subscript
index, BU)
Number of business customers on UBR connected
to the DSLAM at the CO (and not opting for IPTV)
NB-nonIPTV/UBR
Coefficient deciding the fraction of business users
(out of total subscribers) on UBR (not opting for IPTV)
fBU < 1 ¼
NB nonIPTV=UBR
NADSL CO
Number of UBR business (non-IPTV) users active during
the peak-hours
(NB-nonIPTV/UBR)Active
Coefficient deciding s fraction of UBR business (non-IPTV)
users (out of total users) active during the peak-hours
gBU < 1 ¼
NB nonIPTV=UBR
ð ÞActive
NADSL CO
Coefficient deciding the fraction of statistically variant UBR
used by non-IPTV/UBR business customers
(hBU<1) = (uBU)i/UMax
5.4 Business customers on GBR service agreement, (identified by the subscript
index, BG)
Number of business customers on GBR connected
to DSLAM at the CO (and not opting for IPTV)
NB-nonIPTV/GBR = NBG
Coefficient deciding the fraction of non-IPTV business
users (out of total subscribers) on GBR
fBG < 1 ¼ NBG
NADSL CO
Coefficient deciding the fraction of GBR (non-IPTV)
business users (out of total users) active during the peak-hours
gBG < 1 ¼
NB nonIPTV=GBR
ð ÞActive
NADSL CO
Coefficient deciding statistically invariant,
GBR used by non-IPTV/UBR business customers
(hBG=1) = UMax/UMax
(e) Capacity requirements
Case (1) Customer base: Residential DSL customers with high-speed Internet access and IPTV support
Number of active residential subscribers in this base:
NR
ð ÞCase 1¼ gR1 fR1 þ gR2 fR2
ð Þ NADSL CO ð2Þ
UBR for ADSL-based residential customer 1.5 Mbps
Maximum (bursty) bit rate on down-stream
per customer (accessing IPTV; ADSL2 up to 12 kft)
12 Mbps
Total capacity in demand:
CR
ð ÞCase 1¼ fR1 gR1 hR1
ð Þ 1500 þ fR2 gR2
ð Þ hR2 ¼ 1
ð Þ 12000
½ Š NADSL CO
f gkbps ð3Þ
Case (2) Customer base: Mixed set of residential
(non-IPTV and IPTV) subscribers plus business
customers of UBR and GBR support on DSL
UBR for ADSL-based IPTV
residential/business customer:
1.5 Mbps
Maximum (bursty) bit rate on down-stream
per customer (accessing IPTV) (ADSL2 up to 12 kft)
12 Mbps
28 P.S. Neelakanta et al.

9. Total capacity in demand on the access side:
CRB
ð ÞCase 2¼ fR1 gR1 hR1 ¼ 1
ð Þ
f g 1500 þ fR2 gR2
ð Þ hR2 ¼ 1
ð Þ 12000
½ Š
NADSL CO þ fBU gBU
f g hBU ¼ 1
ð Þ 1500
½ Š NADSL CO
þ
X
NBGgBG
i¼1
GBRi
ð Þkbps hBG ¼ 1
ð Þ
#
kbps
ð4Þ
With reference to algorithms on capacity demands as above, the access network
has to be designed with constraints posed by the total (worst case) demand on the bit
rate as specified by customers of different service classes. This is necessary to
evaluate optimally engineered bit rates (EEBRs) for each service category
provisioned.
(f ) Determination of: { fR1, gR1}, { fR2, gR2}, {fBU, gBU} and, { fBG, gBG}
It can be observed that, in the algorithms indicated above, there is a set of three
fractions (for each category of service rendered), namely, { fR1, gR1, hR1}, { fR2, gR2,
hR2}, { fBU, gBU, hBU} and { fBG, gBG, hBG}; and, these coefficients should be
estimated a priori and known explicitly in order to ascertain eventually the EEBRs of
interest. These coefficients (and hence EEBRs) are not per se, parameters that can be
calculated deterministically solely from inventory data. The underlying consider-
ations invariably bear random attributes with probabilistic norms that correspond to
the following three statistics:
– Demographic statistics of users opting for a specified class of interest
– Statistics on active usage profile of a specified class by the subscriber
– The spatiotemporal UBR statistics involved; (that is, the varying bit rates (peak
and slackened) across the service area during different times of the day).
Specifically, for example, considering residential customers of two categories,
namely those not opting for IPTV and those who do, the associated probability
distributions of the fractional customer populations can be denoted as p( fR1)
and p( fR2) respectively; here, p( fR1) ≡ p(NR-nonIPTV*) and, p( fR2) ≡ p(NR-IPTV*),
where the asterisk depicts the normalized value of populations, NR-nonIPTV and
NR-IPTV. Likewise, with respect to business customers, p( fBU) ≡ p(NB-nonIPTV/UBR*)
and p( fBG) = p(NB-nonIPTV/GBR*). Consistent with these probability distributions,
the parameters of the set { fR1, fR2, fBU, fBG} are rather required in the
computational exercise and can be elucidated in terms of the associated fractions
of respective populations (as indicated before).
In general, the xDSL growth rate at each wire-center pertinent to a service area is an
inventory data normally available in the database of a telco. The trend of this growth
depends on social habits, economic profile (such as per capita income), residential
outlays (locations) and business proliferation in that service area. Hence, when the set of
data on NR-nonIPTV
, NR-IPTV
, NB-nonIPTV/UBR and NB-nonIPTV/GBR (versus time, expressed
in yearly quarters or semiannual terms) is available, the corresponding fractions fR1,
fR2, fBU and fBG can be determined at any desired period of service deployment along
the temporal trend-line. (Such values, should however, be weighted proportionally so
that, the defined fractions conform to: fR1 + fR2 + fBU + fBG = 1.)
Ex ante forecast on economically engineered bit rates for IPTV 29

10. Next considering, the coefficient set, namely, {gR1, gR2, gBU, gBG}, it refers to the
statistics on active usage of lines for different service categories. Considering the so-
called peak-hour traffics, it is logical to surmise that xDSL traffic would mimic more
or less the traditional local access (dial-up modem) traffic on circuit-switched
networks. Such traffics on circuit-switches located at a CO are measurable (or “peg-
counted”) in terms of the so-called centum call second (CCS) load experienced by the
CO switch. But, this CCS load consists of a voice-traffic part (CCS)v and a data-traffic
part (CCS)d. Therefore, the total of CCS measured at the circuit switch, namely
(CCS)T can be written in terms of Lichtenecker and Rother mixture formula [6]:
CCS
ð ÞT¼ CCS
ð Þv
θ
CCS
ð Þd
1 θ
ð5Þ
where θ is a fraction of voice-alone (telephone) lines out of the total network access
lines (NALs) terminated at the CO switch; and, therefore θ is a known inventory
parameter.
Using Eq. 5, (CCS)d can be filtered out assuming that (CCS)v≈3, (which is
typical in telephony). Further, as indicated above, (CCS)T is a measurable (peg-
counted) parameter at the CO during the peak-hours when active sessions of data
traffic prevail. Relevant to the notations adopted, these sessions for gR1 and gR2
correspond to residential areas; and, for gBU and gBG such sessions refer to busy
hours in business districts. Thus, for example,
CCS
ð Þd
CCS
ð ÞT Residential area=UBR traffic
¼ gR1
ð Þ8
gR2
ð Þ1 8
ð6Þ
where 8 is the ratio of non-IPTV users to total xDSL users. The fraction gR1 can
correspond to those measurements at wire centers where IPTV customers do not
exist (or sparingly exist). Hence, gR2 can be evaluated explicitly. And,
gBU ¼
CCS
ð Þd
CCS
ð ÞT Business district=UBR traffic
ð7aÞ
gBG ¼
CCS
ð Þd
CCS
ð ÞT Business district=GBR traffic
ð7bÞ
In the numerical example indicated in Appendix 1, the data furnished on the set {gx}
is gathered from the wire center details described in [9].
(g) Determination of: {hR1, hR2, hBU, hBG}
The third set of parameters, namely, {hR1, hR2, hBU, hBG} of interest refers to the
statistics of application-specific (fluctuating) UBR and (constant) GBR values of
data rates involved in the traffic. That is, under UBR conditions a line could be
supporting sometimes bursty spurts of bits or may pass non-spurt bit rates on
statistical basis. In GBR services, however, a guaranteed (constant) rate is always
assured and supported on the line. Consistent with the two-state model of UBR
fluctuation, the parameter set, {hR1, hR2, hBU}can be determined by a method
proposed in [8, 10] and described below. The parameter, hBG, however, is equal to 1
due to the constancy of GBR provisioned.
30 P.S. Neelakanta et al.

11. As indicated earlier, an ith active user (of any UBR category) is served by the
DSLAM in a down-stream access mode at a speed, Umin ≤ ui ≤ Umax. This
statistical variable ui across the entire ensemble of user base can be specified by the
following heuristics: Considering the downstream access, the function of a
DSLAM can be regarded as a queueing-service that enables bits being received
from the feeding side and buffered as well as (de)multiplexed to n active users.
Hence, any ith active user (of UBR category) is served by the DSLAM in question
to have a (down-stream) access at a speed of Umin ≤ ui ≤ Umax of the user type/
service category, x (denoting explicitly, the service category R1, R2, BU or BG).
Further, since the bit rate ui being considered is a time-dependent statistical
variable, Umin and Umax respectively define its minimum and maximum bounds for
a given service category x.
And, as defined earlier, (ux)i = (hx × Umax)i with an average rate of (Ra–x)i = (μx)i
and a standard deviation (σx)i. Also, this variable ui can be assumed to be uniformly
distributed, inasmuch as any value between Umin and Umax is equally likely to occur
in any active session. Hence, the prescription of Laplace’s assumption namely, a
uniform probability distribution as regard to this variable in question is a valid
proposition.
(h) Determination of ui and EEBR evaluation
Next, the objective is to decide the value of ui that can be used in EEBR designs.
Suppose pertinent to any ith customer of service category x, the following relation is
defined:
(x ¼ (o nx= nR1 þ nR2 þ nBU þ nBG
ð Þ
½ Š ð8Þ
with x ⇒ (non-IPTV service: R1), (IPTV service: R2), BU or BG; and, nx depicts
the number of lines (users) being active, for example, nR1 = gR1 × NADSL-CO.
Further, (o = (ρx × p) where, ρx is the user-side utilization (that is, the probability
that a user is in an active, spurt state); and, (p=1) denotes explicitly the critical
state of the DSLAM being at its full service activity, (namely, the feed-side
capacity is fully flooded). So, p1, implies a prorated condition on the full service
activity. As described in [8, 10], the index (i=1, 2,…,n) refers to multiplexed
connections supporting traffics of average rate (μx)i in each ith connection (of any
category x).
Now, an “equivalent bandwidth” can be defined such that, the probability that the
instantaneous aggregate bit rate exceeding a certain value (cx)i is less than (x; and,
the entity (ux × cx) thereof, depicts an “equivalent capacity” per user of the service
category, x. Corresponding analysis in [8, 10], further stipulates elucidating an
inverse Gaussian distribution αx specified by the following approximation in order to
determine cx:
αx 2 ln 1= (x
ð Þ
f g ln 2 π
ð Þ
½ Š1=2
ð9Þ
When αx→0, it depicts the critical condition (that the feed-side been fully
flooded). It leads to ((x)critical = (o=0.39894. Hence explicitly, (x=0.39894 × [nx/
(nR + nBU + nBG)]. Further, under this critical condition, p→1; therefore, ρx can be
implicitly specified by: 0.39894 × (user occupation fraction of time). Suppose this
Ex ante forecast on economically engineered bit rates for IPTV 31

12. user occupation fraction of time (depicting the fraction of average duration of
active period) of a service category x is denoted by bx (so that, ρx=0.39894×bx).
Then, following the details furnished in [9], this bx parameter of the active period/
session time can be evaluated on the basis of ensemble data on CCS compiled at a
wire center. Described in [9] are details pertinent to such active time-slabs
indicating worst-case active sessions of the traffic in terms of CCS-loading
encountered in voice and data transmissions. Relevant considerations yield
approximately the numerical evaluation of the set {bx}(and used in the calculations
of Appendix 1).
Further, pursuing the analysis similar to that in [8, 10], the expression for cx is as
follows:
cx ¼
yx χx
ð Þ þ yx χx
ð Þ2
þ4 χx ρx yx
h i1=2
2 yx
ð10Þ
where, yx = αx × bx × (1−ρx) × Umax and χx is the feed-side capacity (such as DS-3,
OC 3, 4 × DS1 or DS-1) at the DSLAM provisioned per ADSL. Hence, (ui)x due to
all the (i=1, 2,…,n) active users is given by:
u
ð Þx
M
¼ UM
ax
ð Þ
P
n
i¼1
cx
ð Þi
n
8
:
9
=
;
ð11Þ
where the subscript M denotes maximum, average or minimum values on ux,
corresponding to UMax, UMean and UMin respectively. The expression of Eq. 11 can
further be approximated over its entire ensemble set (of large cardinality) as
follows:
u
ð Þx
M Ensemble set i¼1;2;...;n
f g
UM αx
ð Þ cx ð12Þ
Therefore, the set {hR1, hR2, hBU} with hx defined via (ux)i = (hx × Umax)i, can be
duly evaluated; (and, as indicated earlier, hBG=1).
In essence, as stated before, the above algorithm of Eq. 12 is obtained on the basis
of a two-state model (representing active/spurt and silent dichotomy of traffic states
as mentioned earlier). It also includes Gaussian approximation of superimposed
(multiplexed) traffics described in [8, 10].
Now, the EEBRs in question can be computed. Suppose, for example, the mean
values of EEBRs are sought. They can be obtained by the following steps:
– For non-IPTV residential/business customers on UBR-SLA:
EEBR
ð ÞR; BU¼ Average of ebr
ð Þu
mean
and ebr
ð Þg
h i
mean
n o
wR;BU
¼ ebr
ð Þu
mean
þ ebr
ð Þg
h i
mean
n o.
2
h i
wR;BU
¼ r
ð Þu
wR;BU
ð13Þ
32 P.S. Neelakanta et al.

13. – For business customers on UBR- and GBR-SLA:
EEBR
ð ÞBU¼ Average of r
ð Þu and ebr
ð Þg
h i
mean
h i
n o
wBG
ð Þ
¼ r
ð Þu and ebr
ð Þg
h i
mean
n o.
2
h i
wBG
ð Þ
ð14Þ
– For residential customers on high-speed Internet (UBR)- plus IPTV(GBR)-SLA:
EEBR
ð ÞIPTV¼ Average of ebr
ð Þu and ebr
ð Þg
h i
mean
h i
n o
wIPTV
ð Þ
¼ r
ð Þu
wIPTV
ð Þ
ð15Þ
where, (ebr)x denotes the statistical spread of bit rates being economically
engineered. Explicitly, for the service categories of interest:
ebr
ð Þu
M
¼ u
ð ÞR1
M
nR1
½ Š þ u
ð ÞBU
M
nBU
½ Š
nR1 þ nBU
ð Þ ð16aÞ
ebr
ð Þg
h i
M
¼ u
ð ÞBG
M
nBG
½ Š þ u
ð ÞIPTV
M
nR2:IPTV
½ Š
nBG þ nR2:IPTV
ð Þ ð16bÞ
Further, the entity wx in Eqs. 13, 14, 15 represents a prorating coefficient for the
service category x. It is decided by the ratio of maximum (worst case) rate Umax (of
that service category) relative to the highest (bursty) rate Rmax of the system. That is,
with Rmax depicting the maximum of all [Umax]x of all the services provisioned, it
follows that,
wx ¼ U
ð Þx
max
.
Rmax ¼ U
ð Þx
max
.
Max UMax
ð Þx
h i
ð17Þ
6 EEBR calculation: numerical example
Data furnished in Table 2 corresponds to details on types of services
provisioned in a typical wire center and the associated population growth over
a stretch of eleven semiannual terms commencing from December 1999 through
December 2004 [3, 7]. Corresponding trend-line equations on the growth
performance are presented in Table 3. (These trend-line expressions are obtained
on the basis of normalized values of the data set given in Table 2. Relevant
normalization is done as follows: Each data value in a row is normalized with
respect to the total subscriber value (S ) found in the last column for that row. This
normalized variable is denoted by y. For example, considering the residential UBR
population, ( y)Dec-99 =60.6/711.1=0.08522 and so on. The semiannual term
counting from the first is denoted by z; for example, z=1 represents the Dec-99
term and so on, so that an extended value of z=23 depicts the ex ante forecast term
of Dec-2010).
Ex ante forecast on economically engineered bit rates for IPTV 33

14. Corresponding results are presented in Tables 4 and 5 depicting the statistics of
EEBR in terms of 95% level of confidence with respect to the negotiated SLA on
UBR/GBR versus the percentage penetration of IPTV subscribers in the wire center
analyzed.
7 Concluding remarks
Evaluation of EEBR values would assist network designers to use appropriate
considerations in augmenting network resources as a function of growth in
subscriber population and penetration of new services. In worst-case design
considerations, the maximum values of EEBR (that is, [(EEBR)x]max) can be
normally adopted for prudent prescription of required network resources so as to
Table 2 Types of wire center services and the associated subscriber population: Compiled from FCC data
for residential and business subscribers in the USA [3, 7]
Semi-annual
term
z value Types of services
Res-UBR Res-coax
or IPTV
Bus-UBR Cu-bond ×4 Bus-GBR Total
subscribers (S)
Subscriber population in 1000’s
Dec-99 1 60.6 126.9 507.5 12.0 4.1 711.1
Jun-00 2 155.9 205.3 821.1 31.8 7.3 1,221.4
Dec-00 3 324.0 321.9 1,287.7 65.8 15.1 2,014.4
Jun-01 4 441.4 465.8 1,863.2 102.7 22.3 2,895.4
Dec-01 5 646.9 634.3 2,537.3 149.1 30.5 3,998.1
Jun-02 6 835.9 824.2 3,296.8 181.2 41.3 5,179.5
Dec-02 7 1,060.4 1,021.5 4,086.1 228.0 48.6 6,444.7
Jun-03 8 1,257.6 1,229.6 4,918.2 265.2 56.6 7,727.1
Dec-03 9 1,558.1 1,477.7 5,910.9 367.4 67.7 9,381.9
Jun-04 10 1,867.6 1,670.6 6,682.3 443.7 84.0 10,748.2
Dec-04 11 2,264.0 1,919.0 7,676.0 541.0 127.0 12,527.0
Res-UBR residential UBR, Bus-UBR business UBR, Res-coax/IPTV residential service with coaxial and/or
IPTV, Cu-bond ×4 copper-bonding of four DSLs
Table 3 Summary of trend-line equations for the (normalized) data
Type of service Trend-line equation:
y = function of (z)
Subscriber population in 2010
(in 1000’s):
(S extrapolated to z=23)
Res-UBR y=0.0005z3
–0.0102z2
+0.0676z+0.0517 24,337
Res-coax/IPTV y=−0.0497×ln(z)+0.8458 19,085
Cu-bond (×4) y=0.00008z4
–0.0027z3
+0.0293z2
–0.135z+0.9772
Bus-UBR y=0.0107×ln(z)+0.0237 646
y=0.0241z0.3144
Bus-GBR y=0.00009z2
–0.0001z+0.0007 1,817
Total wire center subscribers (extrapolated forecast) in 2010 45,885
34 P.S. Neelakanta et al.

15. reduce the CAPEX and the OPEX economic outlays in the xDSL turf of the wire
center of interest. Otherwise, should raw UBR and GBR values be used in the
design, an overestimate on the needs of resources (versus population growth) would
result imposing an unwanted (and incorrect) burden on CAPEX involved. EEBR-
based design will however, prevent such overestimates without prejudicing the
underlying SLAs.
Determination of EEBR values also indicates the net effect of resource
requirements as a function of subscriber population. For example, viewing
Tables 4 and 5, it can be seen that EEBRs show a characteristic tendency of
variation as a function of IPTV penetration. The underlying variations in the
results are caused by the growing and changing statistics of traffic distribution
across shared network resources improvised with necessary enhancements.
Absence of EEBR evaluation would forbid such deserving details on network
growth and the associated economic implications.
Next, how the evaluated EEBRs can be used in economic planning and
engineering of xDSL systems when requests for new connections are made in a
particular wire center can be understood from the following problem:
Table 4 Statistics of EEBR adopted to support SLA-specified unspecified bit rates (UBR) of residential
and business services as a function of IPTV subscriber penetration
IPTV subscribers Percentage of IPTV/NAL Interval of EEBR (in kbps) supporting UBR with 95%
level of confidence (in relation to the negotiated SLA):
x 2s x : Mean UBR and σ : Standard deviation
ð Þ
From To
5,000 15.72 7.06 30.42
10,000 27.17 9.26 39.90
15,000 35.89 10.81 46.85
19,085 41.59 11.84 51.40
25,000 48.26 13.03 56.83
30,000 52.82 13.88 60.64
35,000 56.63 15.52 63.04
Table 5 Statistics of EEBR adopted to support SLA-specified guaranteed bit rates (GBR) as a function of
IPTV subscriber penetration
IPTV subscribers Percentage of IPTV/NAL Interval of EEBR (in kbps) supporting GBR with 95%
level of confidence (in relation to the negotiated SLA):
x 2s x : Mean GBR and s : Standard deviation
ð Þ
From To
5,000 15.72 147.52 150.96
10,000 27.17 138.78 141.98
15,000 35.89 125.47 128.47
19,085 41.59 117.52 120.67
25,000 48.26 106.69 111.49
30,000 52.82 100.25 105.17
35,000 56.63 94.87 99.35
Ex ante forecast on economically engineered bit rates for IPTV 35

16. It refers to determining whether a new user connection when requested should
be accepted or not by the telco. Relevant decision can be done by enunciating a
pair of bandwidth-check criteria (that use explicitly the deduced EEBR values).
Depending on the criteria-check, provisioning a new line in demand can be
made.
For the underlying computations, relevant data needed and the criteria to be
specified are indicated below. The discussion presented thereof, refers to a typical
ADSL service area consisting of UBR (residential/business) and GBR (business)
customers. (No IPTV penetration is considered here in order to facilitate numerical
simplicity in the illustrative example presented). Relevant preliminary data set
presumed is as follows:
Hypothetical wire center details
Turf: ADSL service area
Total ADSL subscribers supported
at the CO:
NCO-ADSL
Bandwidth of physical feed-line
at the DSLAM:
BWPHY
Guaranteed bit rate (GBR)/business
users (BU)
384 kbps (say, for example)
Umax (maximum/bursty bit rate
of the new subscriber):
BBRNS
Economically engineered bit rates: EEBRx
(x⇒R, BU or BG)
Number of UBR SLA
(residential: R) users
NR = NR-nonIPTV
Number of UBR SLA
(business: BU) users:
NBU = NR-nonIPTV/UBR
Number of GBR SLA users (BG): NBG
Criteria
Condition I: BBRNS BWPHY
P
NBG
i¼1
GBRi
Condition II: EEBRNS BWPHY
P
NR
i¼1
EEBRi þ
P
NBU
j¼1
EEBRj þ
P
NBG
k¼1
EEBRk
!
The first criterion implies that the highest (bursty) bit rate of the new
customer seeking connection will not exceed the bandwidth of the feed line at
the DSLAM minus the total guaranteed bit rate already provisioned at the
DSLAM; and, the second criterion stipulates that the difference between the
bandwidth (capacity) of the feed line at the DSLAM less the sum of already
economically engineered bit rates of existing users (of different classes, R, BU
and BG) should not exceed the EEBR computed for the new subscriber.
Implementation of the aforesaid criteria is illustrated via a flow chart in Fig. 3
where, based on the criteria specified, the status of accepting or rejecting a user
connection is indicated. The method of implementing the connection admission
criteria indicated above is illustrated in Table 7 of Appendix 2 using a numerical
example.
36 P.S. Neelakanta et al.

17. In summary, the present study considers practical aspects of xDSL turf details,
the associated services provisioned and corresponding demography of user
population so as to ascertain the economics of network capacity (observed in
terms of bit rates deployed prudently to the customer base without violating the
SLAs). Designing such economically engineered bit rates is based on user
behavior versus the statistical pattern of sharing the associated network resources.
Such EEBRs are logically adequate to support statistically-fluctuating traffics and
at the same time, economically viable in improvising network resources cost
effectively; above all, the customers will remain transparent to the bit rates on
ply with their SLAs honored effectively.
An illustrative example is furnished (in Appendix 1) to demonstrate the EEBR
computation when IPTV penetration exists in an xDSL service area. Relevant
calculations lead to an ex ante forecast on EEBRs accomplished using ex post
details of the loop.
Another example is presented (in Appendix 2) to show how the estimated values
of EEBR can be profitably utilized in new connection admissions being sought.
Using a hypothetical set of details pertinent to an ADSL service area (with no IPTV
provisioned), a numerical example is elaborated to illustrate the connection
admission procedure.
Input
data
Is
condition I
satisfied?
Is
condition II
satisfied?
Can
BWPHY
increased?
Yes
Yes
No
No
No
Yes
Accept user
connection request
Input the
increased
BWPHY
Reject user
connection request
Fig. 3 Flow-chart on bandwidth provisioning check when a new user connection request is made
Ex ante forecast on economically engineered bit rates for IPTV 37

18. Appendix 1
Table 6 Determination of EEBR values for the wire center details furnished in Tables 4 and 5: a
numerical spreadsheet
38 P.S. Neelakanta et al.

19. Table 6 (continued)
Ex ante forecast on economically engineered bit rates for IPTV 39

20. Table 6 (continued)
40 P.S. Neelakanta et al.

21. Table 6 (continued)
Ex ante forecast on economically engineered bit rates for IPTV 41

22. Table 6 (continued)
42 P.S. Neelakanta et al.

23. Table 6 (continued)
Ex ante forecast on economically engineered bit rates for IPTV 43

24. Appendix 2
Table 7 New connection admission criteria implementation using EEBR values
44 P.S. Neelakanta et al.

25. Table 7 (continued)
Ex ante forecast on economically engineered bit rates for IPTV 45

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46 P.S. Neelakanta et al.