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Simulation Modelling Practice and Theory 12 (2004) 239261Modeling and simulation of data transmissionon a hybrid fiber coax cable network

M. Garcia a,*, D.F. Garcia a, V.G. Garcia a, R. Bonis b

a Department of Computer Science, University of Oviedo, Office 1.2.15, Campus de Viesques,

33204 Gijon, Spainb TeleCable, s.a., Scientific Park, 33206 Gijon, Spain

Received 9 April 2003; received in revised form 15 September 2003; accepted 29 October 2003

Available online 5 June 2004

Abstract

This paper describes the steps followed in the development, simulation, and later validation

of a model for a cable network based on hybrid fiber-coax (HFC) technology, used for data

transmission. This work presents a representation of a communication system which has been

growing dramatically over recent years and will continue to do so in the near future. The mod-

eling process is based on the analysis of measurements of a cable operator, establishing a direct

relationship between model parameters and network characteristics. The modeling technique

produces a scalable model capable of simulating the evolution of the real cable network.

2004 Elsevier B.V. All rights reserved.

Keywords: Hybrid fiber-coax network; Traffic modeling; Network simulation

1. Introduction

This paper describes the steps followed in the development of a simulation modelfor a cable network providing data transmission services. Cable networks have tra-

ditionally been associated to television broadcasts; however, over the last decade the

explosive growth of Internet has sparked an interest in alternatives to traditional

telephonic lines for Internet access.

The advantages of cable networks over telephonic lines are their broader band-

width and their great number of subscribers. Their great disadvantage is the absence

of a return path, necessary to make the cable network bidirectional. In consolidated* Corresponding author. Tel.: +34-985-182519; fax: +34-985-181986.

E-mail address: manuel@atc.uniovi.es (M. Garcia).

1569-190X/$ - see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.simpat.2003.10.005

mail to: manuel@atc.uniovi.es

240 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261and widely extended cable networks, overcoming this disadvantage requires great

investments, making them a less viable alternative as an Internet access medium.

However, there is a new group of cable networks, based on hybrid fiber-coax

(HFC) technology, which represents a real alternative. The HFC technology im-

proves network capacity and reliability, which facilitates the implementation of a re-

turn path. These characteristics permit the cable operator using this kind of network

to act as global telecommunication operator, providing television, voice and Internet

services using the same network.Currently, the main problems faced by companies using HFC technology are cop-

ing with the rapid growth of new subscribers, and the demand for new data services,

such as multimedia interactive services. Cable operators must be able to predict how

many users could potentially demand these services simultaneously without affecting

the performance of the network, and to determine the influence of new services on

the HFC network. The best way to answer these and other questions is to use a

model of the cable network which includes the new service requirements. At the same

time the cable network model can be used by the cable operator to support tuningand capacity planning decisions.

In this paper, the development of a simulation model for data transmission on an

HFC cable network is described. This model represents a generic HFC architecture,

and is validated in use by a cable operator. The main characteristics of the cable net-

work model are:

It captures the evolution of network performance over time, rather than at a fixedmoment.

The performance provided by the model is directly related to the network capacity(the percentage of utilization of the network channels).

The parameters of the model are obtained from network characteristics, i.e. thenumber of network subscribers and the traffic measurements.

The relationships established between the traffic measurements and the number ofsubscribers assigned to each channel make the use of the model very simple.

This paper follows the development of the simulation model. Section 2 provides ageneral description of the system to be represented. Other related works are summa-

rized in Section 3. The development of the cable network model is divided in two

parts: Section 4 describes the way the cable network is used, that is, the traffic model

and Section 5 describes the cable network model. In Section 6, the results obtained

are presented, and compared with the results obtained from the real cable network.

Finally, Section 7 summarizes the main characteristics of the developed model and

the conclusions obtained.2. Description of the system

The simulation model represents a generic cable network based on HFC technol-

ogy. This technology combines traditional coax cables with fiber optics, establishing

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 241a hierarchical architecture. The following is a description of this architecture from

the bottom to the top.

The coax cable, also called the last mile, is the part nearest to the subscribers. In

the subscribers homes, data services are accessed through a cable modem, connected

to a home PC. This cable modem contains the hardware to receive and transmit sig-

nals over the HFC network. It also negotiates access to the HFC network, determin-

ing the maximum speed at which it can transmit. Each coax cable is shared by several

subscribers and ends at a local optical node. Each optical node supports between 200and 300 subscribers, in an area of 400800 m in diameter. In the local optical node

the electrical signal transmitted by the coax cable is transformed into an optical sig-

nal, to be transmitted using optic fibers towards the head-end channel switch (HCX).

This structure constitutes an HFC branch. The next level in the hierarchical structure

is the connection between the different branches. This connection is made using fiber

trunks with different topologies.

The model developed is based on the data network of the cable operator TELE-TELE-

CABLE, INC.CABLE, INC., one of the most important cable operators in Spain. This company,created in 1995, began by providing cable TV services; later with the growth in

the demand for telecommunications, it evolved and became a global provider. This

operator provides TV, voice and data services in an area including three cities, with

half a million potential subscribers. Fig. 1 shows the general architecture of its cable

network.

The operators network is organized following an architecture very similar to the

generic architecture previously described. However, it presents particular character-

istics related with the technology it implements. The network is also organized inHFC branches, as can be seen in Fig. 1, and there are several HFC branches in each

city. All the HFC branches in all the cities are connected by an ATM backbone. In

one of the cities, and also connected to the ATM backbone, is the main head-end,

where the servers and the Internet access are located.Fig. 1. Architecture of the cable network.

242 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261The cable modem used in the subscribers homes transforms Ethernet packets into

ATM cells and viceversa; it controls access to the channel using a proprietary pro-

tocol very similar to DOCSIS (Data Over Cable Service Interface Specifications)

protocol. The data transmission on the HFC branch is bidirectional; there are two

channels with very different characteristics: the upstream channel, used by the sub-

scribers to send data requests, and the downstream channel, through which the sub-

scribers receive data. The downstream channel is shared by all the subscribers and

has a bandwidth of 30 Mbps. On the other side, there are up to six upstream chan-nels in each HFC branch, each one with a bandwidth of 1.9 Mbps. Each subscriber is

assigned to one of these upstream channels.

All the traffic originated in the HFC branch is sent towards the branch controller

(HCX in Fig. 1). This element distinguishes between the traffic whose destination is

in the same branch, internal traffic, and the rest of the traffic. The internal traffic is

sent back, and the rest of the traffic is sent towards the ATM switch to reach its des-

tination.

The model of the cable network developed in this work is based on the analysis ofthe traffic measurements taken on all the channels of this network. When the mea-

surements were taken the cable network providing data services had 17 HFC

branches and 17,369 subscribers. These dimensions are adequate to obtain represen-

tative information. The cable network works on a 24 h flat rate with best effort

quality of service.3. Related work

The aim of the developed model is to evaluate the cable network performance,

represented mainly by channel bandwidth requirements, as the time of day and num-

ber of subscribers change. The use of HFC architecture for data transmission has not

been explored in any depth; the main studies in this field are related to standardiza-

tion efforts for the proposal of an upstream media access control (MAC) protocol.

Apart from these studies, only a few papers are devoted to the performance of

HFC cable networks. The most representative works are: [1], concerning traffic mod-eling and analysis of a real HFC branch devoted to telephonic applications; [2], an

analysis of the support for multimedia applications using ATM technology in an

experimental HFC network; and finally [3], in which the performance perceived by

the subscriber for web-browsing and interactive applications are evaluated using

analytic modeling and simulation.

Like the first two of these three works, the model described in this paper is based

on a real system, and it evaluates performance. The differences between this work

and related projects however, are significant: instead of just a part of the cable net-work, the whole network is represented; performance is represented as a percentage

of channel utilization and throughput; the model parameters are related to the num-

ber of subscribers assigned by the cable operator to each channel, and the time of

day considered; and the simulation model built is scalable and can evolve as the real

cable network does.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 2434. Traffic modeling

There are two aspects to be considered in the model development: the physical

behaviour of the cable network, and the way the cable network is being used by

the subscribers. The data requests sent by the subscribers through the upstream chan-

nels of the cable network constitute the network workload. This workload must be

represented by a model: the workload model or traffic model. This section is devoted

to the development of the traffic model. In the next section this traffic model will beincorporated into the physical model to define the complete cable network model.

4.1. Background

There are many studies into traffic models, as they have been developed in parallel

with the evolution of telecommunication systems. These traffic models can be divided

into two groups: those developed before the work of Leland et al. [4], and those

developed after. The authors in [4] proved that data traffic on modern networksexhibits the statistical property of self-similarity, which is represented by traffic

invariance independently of the time scale considered. Subsequent studies, [58]

show that self-similarity can be considered as an inherent property of data traffic

in modern telecommunication systems.

In the first group, referred to as traditional traffic models, traffic models were

associated mainly to Poisson or Markov processes. A complete review of this kind

of model can be found in [9]. The second group began in the early 90s, when it

was shown that in order to consider traffic self-similarity and produce valid results,traffic models must be able to reproduce not only first and second order moments

(mean and variance), but also the autocorrelation function. Some of the most impor-

tant traffic models developed are: the PT k model, the M/Pareto model and theN-Burst model.

The PT kmodel, [10], represents traffic using a combination of a power tail (PT)distribution (in this case a Pareto distribution), and an exponential k distribution.Using this combination of distributions, it is possible to obtain self-similar traffic,

while at the same time the effect of the exponential distribution improves model per-formance.

The M/Pareto model, developed by Addie et al. [11], is used in the representation

of variable bit rate (VBR) traffic. This model considers a burst superposition. The

number of bursts are distributed following a Poisson distribution k, each burst hasa constant traffic rate of r, and the length of the burst follows a Pareto distribution.The main disadvantage of this model is that it uses four parameters obtained from

three statistical traffic properties, so there is a degree of freedom which produces

an indetermination. This indetermination makes the process of parameter adjust-ment very complex.

The N-Burst model, [12], is another traffic modeling alternative based on an ON/

OFF process. During the ON period the system transmits and in the OFF period the

system is silent. The N-Burst model considers the superposition of N sources of typeON/OFF. By selecting the distribution of the ON period, it is possible to produce

244 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261self-similar traffic. This model also considers an important parameter know as the

burstiness parameter, which defines the relationship between the length of the

ON and OFF periods.

All these models have two common characteristics: firstly, they consider homoge-

neous traffic, that is traffic produced by only one kind of source or application, and

secondly, the traffic model parameters are obtained from real traffic analysis, but

with no relationship to the characteristics of the telecommunication system evalu-

ated. This situation results in simplified traffic models difficult to apply to real tele-communication systems, because real traffic is aggregated and there is no clear

correspondence between system characteristics and traffic model parameters.

The traffic model developed here to represent the traffic on the HFC cable net-

work overcomes these limitations considering the aggregated traffic on the HFC net-

work, and relating the traffic model parameters directly to the HFC network

characteristics. The parameters of this traffic model have been related to the number

of subscribers assigned by the cable operator to each channel, and the time of day.

4.2. Traffic model construction

The objective of the traffic model is to represent the way in which the HFC cable

network is used by subscribers. The traffic model distinguishes between the traffic on

the upstream and downstream channels. The upstream traffic consist of the requests

sent by the subscribers. The downstream traffic is produced as a response to these

request. Thus, the traffic model focuses on the upstream traffic, whereas the down-

stream traffic is obtained from the upstream traffic modified by a random factor.The distribution, mean value and standard deviation of this factor are calculated

from the traffic analysis.

The traffic model is based on the analysis of the traffic measurements taken on all

the channels of the cable network, the number of subscribers assigned to each channel,

and the measurements of the IP address assignment to subscribers by the Dynamic

Host Configuration Protocol, DHCP, server. These measurements were taken over

two different periods of time: January 2001 and January 2002. In the interim, the cable

network evolved from 8 to 17 branches and from 8331 to 17,369 subscribers. In spite ofthe changes in the cable network, the basic relationships found in the analysis are con-

sistent over time. An extended analysis of the measurements can be found in [13].

In order to reproduce the real traffic values on the upstream channels the traffic

model must consider three elements: the upstream channel characteristics, the media

access control (MAC) protocol, and the user profile (the way in which subscribers

demand service from the HFC network). In the following subsections the influence

of each element on the development of the model is described.

4.2.1. Upstream channel

Each upstream channel is represented as a shared media with a transmission pay-

load of 1.5525 Mb/s. This is so because the HFC operator does not apply quality of

service differences. As a result, all subscribers receive the best effort quality of ser-

vice, that is, all of them compete for the channel.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 2454.2.2. Cable modem and MAC protocol

Each subscriber connects to the cable network through a cable modem, and com-

munication is controlled by the MAC protocol. The communication on the upstream

channel uses a proprietary protocol, whose main characteristics are:

The access to the channel is organized in frames, which are repeated continuously,a frame is sent across the upstream channel every 102.4 ms.

The frame is composed of 512 ATM cells, of which only 414 are devoted to datatransmission. The rest are used for communication requests, opportunities to join

the channel, synchronization, conflict resolution and control.

Of the 414 useful ATM cells, each cable modem can use a maximum of 63 cells ineach frame. This maximum value can be controlled by the cable operator depend-

ing on the type of contract offered.

Using this protocol, cable modems transmit requests towards the controller.

Although subscriber contracts with different bandwidths are possible, on the dateswhen the measurements were taken all the subscribers had the same assigned band-

width: 128/64 Kb, that is 128 Kb for the downstream channel and 64 Kb for the up-

stream channel. This bandwidth in the upstream channel corresponds to a maximum

transmission value of 16 ATM cells per frame for each subscriber. The effective value

is reduced as the number of subscribers using the network increases, because in the

best effort quality of service the scheduling algorithm provides a fair allocation of

bandwidth between all cable modems.

The way in which the information is sent produces a burst effect on the channel.Each cable modem works as an ON/OFF process. During the assigned time in the

frame, the ON period, it can send up to 16 ATM cells. Then it must wait until the

next frame for a new transmission; this waiting time is the OFF period. This pattern

is repeated for all cable modems, so in each frame there are sequences of used cells

followed by groups of unassigned or unused cells. The pattern is similar for each

frame, and is modified as the number of subscribers on the channel changes. The glo-

bal effect on the channel is a sequence of ON/OFF sources, as can be seen in Fig. 2.

4.2.3. Subscriber profile

This is the most relevant aspect in the development of the traffic model, because

the diversity of subscribers behavior is represented with a reduced set of parameters.

Two factors must be considered: when and how the subscribers use the network.Protocol frame Protocol frame

ON ONOFF

OFF

Fig. 2. ON/OFF effect in the upstream channel.

246 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 2392614.2.3.1. When subscribers access the cable network. The total number of connected

subscribers to the cable network is known at any given moment from the mea-

surements taken on the DHCP server. The DHCP server assigns an IP address on

demand to any subscriber requesting access the cable network. Thus, the DHCP

server provides the global evolution of the number of connected subscribers, and can

distinguish between IP addresses belonging to one of the cities and the group of the

other two cities.

Fig. 3 represents the percentage of the total connected subscribers in time for thecities where the cable operator provides services. Both lines show approximately the

same evolution, in spite of the difference in the total number of subscribers in each

city. This pattern has been observed in all the sub-networks managed by the cable

operator.

These measurements support the assumption that the number of connected sub-

scribers on all the upstream channels follows a similar pattern to that observed in the

DHCP measurements. Thus, using the DHCP measurements, the connection pattern

can be synthesized applying Fourier analysis. The expression obtained is then used todetermine the number of connected subscribers at each moment, for each upstream

channel. The evolution of the number of connected subscribers is reproduced in the

traffic model following these steps:

(1) The number of connected subscribers in each sample period of the DHCP mea-

surements is expressed as a percentage of the total number of subscribers.

(2) The values obtained are then represented by a Fourier series.

(3) In order to reduce the number of model parameters, the Fourier series used tosynthesize the subscribers evolution is truncated to 90% of the spectral power.

This percentage represents a tradeoff between the number of coefficients used

and the error committed. The expression obtained is:xi Xpk0

ReX k cos2pki=N Xpk0

ImX k sin2pki=N 1where ReX and ImX are the real and imaginary coefficients of the Fourieranalysis, N is the number of elements in the Fourier analysis, and p is the numberof terms needed to synthesize the function with 90% of the spectral power.0

10

20

30

40

50

60

70

6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

Time of day

Con

nect

ed s

ubsc

riber

s (%

)

City-1Cities2+3

Fig. 3. Evolution of connected subscribers to the network.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 247(4) Using Eq. (1), the percentage of connected subscribers is calculated for each sam-

ple period, i.(5) Multiplying the number of assigned subscribers to each upstream channel by the

percentage obtained in the previous step gives the number of connected subscrib-

ers.

(6) An analysis of the variations of the connected subscribers in the DHCP measure-

ments shows that there are slight variations in the number of connected subscrib-

ers at the same time on different days. These variations follow a normaldistribution, and have been included in the result obtained. The final number

of connected subscribers is obtained from a normal distribution, which has as

its mean the number of connected subscribers obtained in the previous step,

and a standard deviation of 5% of the mean value.

4.2.3.2. How subscribers demand services. The second step in the development of the

subscriber profile is to determine how the subscribers demand services from the

network. The subscriber profile is estimated from the traffic measurement analysiswhich confirms the following assumptions. Firstly, the mean and peak traffic on

the upstream channels are proportional to the number of subscribers assigned to the

channel, which means that traffic can be considered nearly homogeneous among the

subscribers. Secondly, traffic can be divided into two types: interactive and non-

interactive traffic. Interactive traffic increases as the number of connected subscribers

increases, this traffic is associated to applications which require human interaction,

for example web browsing. On the other hand, non-interactive traffic remains almost

constant although the number of connected subscribers varies, and is associated tomore permanent applications, for example peer to peer services.

For the first assumption, Fig. 4 shows the graphs for the mean values and peak

values of the upstream traffic, related with the number of subscribers assigned in

each upstream channel. For each graph the points are adjusted by a linear regression

model, whose equation is also shown in the graph. In the graphs two dotted lines

mark the limits of the confidence interval for the predictions of the regression model,

for a 95% level of confidence. This kind of relationship has also been observed on the

downstream channels, and they are constant over time. This behaviour was observedboth in the 2001 and in the 2002 measurements.

The second assumption is based on the traffic profile on the upstream channels,

where a continuous level of traffic is observed throughout the day. The existence

of two types of traffic has been confirmed by the analysis of the relationship between

traffic and connected subscribers, and by the traffic measurements collected in the In-

ternet access router.

From the DHCP measurements, the number of connected subscribers in each

group of cities is known. The aggregated upstream traffic in each group is calculatedby adding all the upstream traffics which belong to each group. Dividing the traffic

between the number of connected subscribers provides the traffic per subscriber met-

ric. Fig. 5 shows the evolution of this measurement over time: in periods of high traf-

fic and high number of connected subscribers it remains almost constant, while in

periods of low activity it exhibits a peak. This behaviour confirms that during the

y=0.1119x-0.4076

R =0.55132

05

101520253035404550

Cha

nnel

ban

d w

idth

util

izat

ion

(%)

0 50 100 150 200 250 300 350

N Subscribers on the channel

y=0.2201x+11.811

R =0.6542

0102030405060708090

100

0 50 100 150 200 250 300 350

N Subscribers on the channel

Cha

nnel

ban

d w

idth

util

izat

ion

(%)

(a)

(b)

ig. 4. Relationship of mean and peak traffic with number of subscribers assigned to the upstream chan-

els: (a) mean upstream traffic values, (b) peak upstream traffic values.

248 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261F

n

0

0.2

0.4

0.6

0.8

1

1.2

0:00 6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

Time of day

Cha

nnel

util

izat

ion

per

subs

crib

er (

%)

Connected subscribers

Traffic

Traffic persubscriber

Fig. 5. Evolution of traffic per subscriber.period of human activity interactive traffic dominates, while in the periods of low

activity non-interactive traffic is more significant.

The analysis of the traffic measurements taken on the Internet access router, bro-

ken down into network services, have also shown that the services can be classified

into two types of patterns. The most important volume of traffic is associated to the

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 249peer to peer application Edonkey, which represents 53.35% of the total upstream

traffic. The traffic pattern associated to this application has an almost constant pro-

file throughout the day. On the other hand, the traffic profile of most of the services

change over time, as the number of connected subscribers does.

The conclusion is that interactive traffic occurs mainly during the human active

period, it evolves with the number of subscribers and the impact of each subscriber

can be considered constant. On the other hand, traffic during the human inactive per-

iod corresponds to non-interactive type, and a reduced number of subscribers gener-ate a high volume of traffic.

The different percentages of traffic belonging to each type are calculated consider-

ing that during the period of human inactivity traffic corresponds to non-interactive

traffic. Thus, on each upstream channel we obtain a percentage of non-interactive

traffic by averaging the traffic values between 5:35 a.m. and 6:30 a.m. Later, all the

values obtained were represented in a graph against the peak to mean traffic rate. This

index was chosen because the greater the peak to mean rate, the higher the number of

interactive subscribers. Fig. 6 shows the graph of non-interactive traffic against thepeak to mean rate; the points are adjusted by a potential model whose equation

and coefficient of determination are shown on the graph.

Considering the above assumptions and relationships, the traffic model parame-

ters are calculated as follows:

(1) The mean traffic on each upstream channel is obtained from the relationship

shown in Fig. 4(a):Mean 0:1119 Subs 0:4076 2

(2) The peak traffic on each upstream channel is obtained from the relationship

shown in Fig. 4(b):Peak 0:2201 Subs 11:811 3

(3) The peak to mean rate is obtained by dividing the values obtained from Eqs. (2)

and (3). From this value, the percentage of non-interactive traffic is estimated,

using the relationship shown in Fig. 6:y=44.579x-3.312

R2 =0.5063

0

10

20

30

40

50

60

0 1 1.5 2 2.5

Rate peak traffic/mean traffic

Non

-inte

r.ch

anne

l util

izat

ion

(%)

0

Fig. 6. Potential model which adjusts the percentage of non-interactive traffic.

Peak trafficmodel

Mean trafficmodel

Non-interactivetraffic model

Peak trafficestimation

Mean trafficestimation

Non-interactivetraffic estimation

Subscriberevolutionfunction

Subscriberestimation

Non-intractivetraffic

estimation

Interactivetraffic

estimation

Number ofsubscribers

on the channel

Connectedsubscribersestimation

Efec. Subs.

Non-in.Mean

Fig. 7. Traffic estimation process based on the number of subscribers on the channel.

1 QN

250 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261Nint 44:579 PeakMean

3:3124(4) The interactive traffic is calculated as a percentage of interactive traffic per sub-

scriber. Thus, the value of interactive traffic is obtained as the difference between

the mean traffic, calculated with Eq. (2), and the non-interactive traffic, from Eq.

(4). Then, the mean number of effective connected subscribers on the channel iscalculated. Effective subscribers are the number of connected subscribers minus

the non-interactive subscribers, that is the interactive subscribers:Int MeanNintperc percmin Subs5where perc and percmin are the mean and minimum values of the connection

evolution function, and Subs is the number of subscribers on the channel.

All the traffic model parameters are obtained from a known parameter: the num-

ber of subscribers assigned to each channel. Fig. 7 summarizes the calculation pro-

cess described and the relationships between the traffic measurements considered.

4.3. Traffic model implementation

The traffic model has been implemented using the modeling and simulation lan-

guage QNAP2. 1 This language is based on the queuing network paradigm and uses

discrete events simulation. Thus, the different elements of the traffic model have been

represented by queues with complex services.

The non-interactive traffic is represented by a source. This element produces the

percentage of non-interactive traffic calculated in Eq. (4). At this source, it is neces-sary to determine the size of the requests and the time between requests in order toAP2 was developed by the INRIA, and is a trademark of SIMULOG.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 251generate the percentage of non-interactive traffic. Considering the type of applica-

tions which produce non-interactive traffic, and in accordance with [8], the size of

the non-interactive requests are distributed following a Pareto distribution. The

mean value of the Pareto distribution is chosen as the maximum traffic that a cable

modem can send in a second, approximately 7500 bytes. The inter-request time is cal-

culated to reach the required traffic volume.

The interactive traffic is generated by an infinite server sending requests from the

active subscribers. In this case the inter-request time is fixed at 1 s, and the size nec-essary to maintain the traffic rate per subscriber is obtained. The size of the requests

are distributed following a normal distribution taking the obtained value as the mean

and a standard deviation of 20%.

The upstream communication is represented by two servers. One of them imple-

ments the upstream channel, and the other considers the influence of the MAC pro-

tocol. Together, they constitute a load dependence server, whose service time

depends on the number of ATM cells assigned to each cable modem by the MAC

protocol under the best effort quality of service.This traffic model has been used to simulate the behaviour of each upstream chan-

nel of the cable network. The only parameter it requires is the number of subscribers

assigned to the channel, and using the established relationships the model parame-

ters are calculated. As the simulation time evolves, the number of connected sub-

scribers are recalculated following the connection evolution function. The result of

the simulation is the estimated traffic profile in each upstream channel. In Section

6, these results are compared with the real values in order to validate the traffic

model, concluding that the traffic model produces a traffic profile which is statisti-cally indistinguishable from the real traffic for a 95% of level of confidence.5. Cable network model development

In this section the traffic model is joined to a physical description of the HFC net-

work to produce the global model of the cable network. The proposed model repre-

sents a cable network with an architecture like that shown in Fig. 1, validated for thecase of study. This model represents a complex system, including the behaviour of

more than 17,000 subscribers, 17 HFC branches with 17 downstream and 102 up-

stream channels. In order to deal with this complex system an approach based on

hierarchical structure is used. In the first step a model for a simple HFC branch is

developed. Later, several simple HFC branch models are combined and joined to

other elements to represent the whole cable network.

5.1. A simple HFC branch model

A simple HFC branch of the cable network can be represented using queuing ele-

ments as shown in Fig. 8. This HFC model includes six upstream channels, each of

which is represented by an upstream traffic model (the stations enclosed in the dotted

line in Fig. 8) to be applied to the cable network. Using the facilities of the QNAP2

Interactiverequests

Non-interactiverequests

Upstream

Downstream

HCX Exterior

OUT

HFC branch

Subscribers x 6

Fig. 8. Queuing model for a simple HFC branch.

252 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261language, the traffic model is encapsulated in a simulation object, which receives the

number of assigned subscribers to the upstream channel as its parameter. In this

way, the simplicity and independence of the model is improved. The downstream

queue represents the downstream channel, the HCX queue represents the HFC con-

troller and the exterior queue represents the rest of the cable network.The downstream and HCX stations work as time shared queues whose service

time depends on the channel capacity for the downstream queue, and on the HFC

controller specifications for the HCX queue. The most important element in this

model is the exterior queue, which calculates the size of the responses to the subscrib-

ers requests. These responses make up the downstream traffic. The size of responses

are obtained from the rate between downstream and upstream traffic measurements.

Thus, the size of each response is calculated by multiplying the size of each sub-

scriber request (obtained from the traffic model) by the rate.The rate for each simple HFC branch is calculated from the downstream traffic on

the branch, and the aggregated traffic of all the upstream channels in the branch.

Different rates are obtained for the two different types of traffic. The non-interactive

rate is the rate between downstream and upstream samples belonging to periods of

low activity (5:35 a.m. to 6:30 a.m.). These samples give a mean value and a standard

deviation for the non-interactive rate in each HFC branch.

For the interactive traffic rate, the samples from periods of high activity (between

9:00 p.m. and 11:00 p.m.) are considered. The interactive rate is calculated using theexpression:r Downhigh DownlowUphigh Uplow

6This expression calculates the rate between interactive traffic on both kinds of

channels, downstream (Down) and upstream (Up). The interactive traffic on both

channels is obtained as the difference between the maximum traffic (high) and the

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 253minimum or non-interactive traffic (low). Applying Eq. (6) to each group of samples,

several values for the rate are obtained. These values produce a mean value and a

standard deviation for the interactive traffic.

In this way, the simple HFC network model reproduces the upstream traffic using

the traffic model previously developed, and the external queue generates the traffic

on the downstream channel of each HFC branch.

5.2. The cable network model

Using the modeling language facilities, the simple HFC branch model is encapsu-

lated in a simulation object. This object is the basic element for building the global

cable network model. Thus, the global cable network model is formed by the same

number of HFC branch objects as HFC branches on the cable network. The cable

network model is completed with a queue which represents the ATM backbone,

which interconnects all the HFC branches, and a special network branch which rep-

resents the cable operator head-end. This modeling strategy produces a scalablemodel, which adapts easily to the cable network evolution. Fig. 9 shows a scheme

of the whole cable network model.

The most important aspect of this model is the way the traffic is distributed in the

cable network. There are several kinds of traffic: internal, local, and external. Inter-

nal traffic is that established between subscribers in the same HFC branch. It is fil-

tered by the HCX element and does not migrate to the rest of the cable network. This

traffic is very limited and can be considered negligible. Local traffic is the traffic

established between subscribers in different HFC branches, and external traffic isInteractiverequest

Non-interactiverequest

Upstream

Downstream

HCX

OUT

HFC branch

Subscribers x 6

Servers Internetaccess 1

Internetaccess 2

InternetRouter 2Router 1

ATM switch

Interactiverequest

Non-interactiverequest

Upstream

Downstream

HCX

OUT

HFC branch

x 6 Subscribers

ATMBackbone

Branch 1 Branch N

Head-end branch

Fig. 9. Queuing model for the cable network.

254 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261the traffic sent by the subscribers towards the head-end network branch. The external

traffic in the head-end can go towards the servers or towards Internet.

The volume of each kind of traffic is estimated using the available measurements.

The sum of all upstream traffic, that is, the traffic sent through all the upstream chan-

nels and directed towards the ATM backbone is established. This traffic comprises

both local and external traffic. This global upstream traffic is compared with the traf-

fic registered in the Internet access router (Router 2 in Fig. 9). The evolution of both

traffics is shown in Fig. 10. The graph shows that the traffic profiles in both parts ofthe network are almost the same. This indicates that the majority of the HFC cable

network traffic is sent towards Internet. The small differences between the two lines

are due to the local traffic and the traffic towards the cable network server.

To evaluate the volume of server traffic, the server log files for the same date as

traffic measurements were analyzed. The average traffic value on the server was

found to be 0.23 Mbps, far from the registered measurements in Fig. 10. This traffic

is shared between the cable network subscribers (6.35% of requests and 4.41% of

traffic volume) and external requests made from Internet.The conclusion obtained is that the majority of upstream traffic on the cable net-

work is represented by traffic towards Internet, the local traffic represents between

1% and 2%, and the server traffic represents a percentage between 0.5% and 3%.

The downstream traffic associated with the response to the subscribers, is calcu-

lated as in the simple HFC branch model, but in this case the rate between the

incoming traffic to the cable network from Internet, and the outgoing traffic from

the cable network towards Internet is considered; these traffics are measured in the

Internet access router (Router 2 in Fig. 9). As in the HFC branch model, a ratefor each kind of traffic, interactive and non-interactive, must be obtained. For

non-interactive traffic, the continuous part of the traffic is considered. This kind of

traffic is produced by peer to peer applications, so the rate between the inner and

outer traffic produced by peer to peer applications gives the effect of non-interactive

traffic. This rate gives a mean value of 2.44 and a standard deviation of 0.21. In the

case of interactive traffic, the total traffic is reduced by the continuous traffic both for

the inner and outer traffic. Obtaining the rate between the resulting types of traffic

gives the influence of the interactive traffic. This rate results in a mean value of012345

6789

10

6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

Time of day

MB

ytes

per

sec

ond

TowardsInternet

AgregatedUpstream

Fig. 10. Upstream and outgoing router traffic comparison.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 2552.23 and a standard deviation of 0.24. From the analysis of the traffic measurements

the traffic rates have been found to follow approximately normal distribution.

The final cable network model generates requests in all the upstream elements,

each of them represented by a traffic model, and in this way generates the upstream

traffic on all the channels. This traffic is sent across the ATM backbone element

mainly to the head-end branch, but also to the other HFC branches. In the head-

end branch, the traffic is directed towards the server or Internet elements. In these

elements the response traffic is calculated, and sent back after a delay period whichrepresents the information access time. This traffic will be sent back to the HFC

branches through the downstream channels.

5.3. Model extensions

The cable network model has been developed based on the characteristics of

TELECABLE INC.TELECABLE INC., however it can be extended to other cable network architectures.

The versatility of the model is a result of its modular structure and the definition ofsimulation objects which encapsulate some of the modules.

The first module is formed by the traffic model. This model represents a complete

upstream channel: the subscribers requests, the MAC protocol, etc. This traffic

model is encapsulated on the upstream simulation object, which receives as its

parameter the number of assigned subscribers to the channel. The second module

is constituted by the HFC branch model. This model represents the basic elements

of an HFC branch: the downstream channel, the HFC controller and defines as

many upstream objects as upstream channels on the HFC branch. Finally this modelis encapsulated to build the HFC branch simulation object.

The modular nature of the model simplifies the changes needed to evaluate new

working conditions. The following are some examples of possible working condi-

tions that can be analyzed and their associated changes:

If the proprietary MAC protocol were changed to DOCSIS protocol, the changewould require modifying the station associated to the MAC protocol in the traffic

model to implement the characteristics of the DOCSIS protocol. Thus the changeswould be included in the upstream simulation objects and incorporated into the

cable network model.

The existence of subscribers with different qualities of services can be included inthe model by defining new classes of customers in the queuing model. Each class

of customers would have a distinct service in the model stations.

A similar situation occurs when the behaviour of a particular application on thecable network is to be studied. The definition of a new class with a different service

will provide information about the studied application. Finally, the number of upstream channels on each HFC branch can be modi-

fied directly from a network description file. This file initializes the cable net-

work model by defining the number of HFC branch objects, their associated

upstream channels and the number of assigned subscribers to each upstream

channel.

256 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261Currently, the cable network model is used for the tuning and capacity planning

of the bandwidth allocation between channels, because the model provides informa-

tion over time rather than a fixed snapshot of the network situation. Using this

model, the cable operator can take decisions about network growth: inclusion of a

new HFC branch or new upstream channels, etc. Other direct applications of the

model are to study the impact on the network of new services, such as multimedia

interactive services, and the performance obtained by the subscribers using these

new services.6. Results and model validation

The main result provided by the cable network model developed is the traffic

expressed as a percentage of channel utilization in all the network channels: up-

stream and downstream channels, backbone link and Internet access channels.

The model also permits the cable operator to obtain information about trafficthroughput and network devices utilization. Some of these results can be directly

compared with the values of the real cable network and so the model can be val-

idated.

The cable network model was developed using a hierarchical approach; first the

upstream traffic model was developed, then it was included in the HFC branch

model, which is the basic element of the cable network model. The final model ob-

tained at each stage was validated in order to improve the quality of the results ob-

tained. The validation consists of three parts: traffic profile comparison, comparisonusing confidence intervals, and a comparison of the values obtained for some statis-

tical properties (autocorrelation function and self-similarity coefficient). The valida-

tion based on confidence interval comparison is described in [14]. This method is

based on defining a difference series n RealModel and calculating its confi-dence interval; if the calculated confidence interval includes zero, both series are sta-

tistically indistinguishable.

The first component to be validated is the upstream traffic model. Fig. 11 shows

two examples of the comparison of traffic profiles on the upstream channels. Apply-ing the comparison method based on confidence intervals for all the upstream chan-

nels, the interval obtained for a 95% level of confidence is [)11.33, 13.55], whichincludes zero. The statistical properties to compare are the autocorrelation function

and the coefficient of self-similarity. The comparison of the autocorrelation function

obtained ranges from perfect adjustment to a slight difference in the lower half of the

graph for the worst cases; Fig. 12 shows the comparison of the autocorrelation func-

tion for the two upstream channels of Fig. 11. In case of self-similarity, the values of

the Hurst coefficient are very close. The difference between values is lower than 10%except in two cases, and the mean difference is 2.77%. In conclusion, the upstream

traffic generated by the model developed is a statistically equivalent approximation

to the real traffic on the upstream channels.

In the case of the HFC branch model the downstream traffics obtained were also

validated using the same methods; all the methods confirm the validity of the simple

0

10

20

3040

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6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

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nnel

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ion(

%)

Real

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6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

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0

10

20

30

40

50

60

Cha

nnel

util

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ion

(%) Real

Model

(a)

(b)

Fig. 11. Examples of traffic comparisons on upstream channels: (a) channel GI01CC02-UP7, (b) channel

GI02CC01-UP8.

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 257HFC branch model. The results are not shown because the simple HFC branch

model is an intermediate step towards the final cable network model.The cable network model can be validated both for the traffic on the upstream

and downstream channels, and on the traffic registered through the router which

controls the access to Internet. The results obtained for the upstream channels are

the same for the traffic model (Fig. 11).

For the downstream traffic, Fig. 13(a) shows the comparison between the real and

the simulated traffic profiles, giving an example of the approximation level that can

be obtained. The comparison based on confidence intervals provides more informa-

tion about the level of adjustment between the model and the real cable network. Theconfidence interval obtained on all the channels for a level of confidence of 95% in-

cludes zero ([)6.328, 14.159]), which means that both systems are statistically indis-tinguishable. The comparison of the statistical properties of autocorrelation function

and self-similarity show insignificant differences in both cases. Fig. 13(b) depicts the

worst adjustment among the autocorrelation functions in the downstream channels.

The relative error of the self-similarity coefficients have a mean difference of 2.59%,

and a worst case of 10.59%.

Finally, as most of the traffic of the cable network is destined to the Internet, it isvery important to compare the adjustment of simulation results for this traffic. Fig.

00.10.20.30.40.50.60.70.80.9

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61

Lag

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(a)

(b)

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nnel

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ion(

%)_

Real

Model

ig. 13. Example of traffic comparison on a downstream channel: (a) traffic profile comparison, (b) traffic

utocorrelation, worst case.

0

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(a)

(b)

ig. 12. Comparison of autocorrelation coefficients: (a) channel GI01CC02-UP7, (b) channel GI02CC01-

P8.

258 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261F

a

F

U

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4

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tes

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02468

101214161820

6:00 12:00 18:00 0:00 6:00 12:00 18:00 0:00 6:00 12:00

Time of day

Mby

tes

per

seco

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Model

(a)

(b)

Fig. 14. Traffic comparison on the Internet access router: (a) outgoing traffic (towards Internet), (b)

incoming traffic (from Internet).

M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261 25914 compares the traffic through the router both to and from Internet. The level ofcoincidence between the real results and the simulated results is high in both cases.

The confidence intervals obtained for a 95% level of confidence include zero: they are

[)0.337, 1.323] and [)1.685, 1.706] respectively. A comparison of statistical proper-ties confirms the validity of the model, there is no difference between the autocorre-

lation functions in both cases, and the relative difference between the self-similarity

coefficients are 0.34% and 1.10% respectively.7. Conclusions

This paper presents the design of a simulation model for a generic cable network,

and its validation procedure using the measurements of a real cable operator. The

cable network model is built with a hierarchical structure which is based on simpler

intermedia models; these intermedia models are independently validated, thus con-

firming the quality of the final model. Using the modeling language facilities, each

intermedia model is represented as a simulation object, which can be directly incor-porated into higher level models. Thus, the final cable network model has the same

number of simulation objects as there are HFC branches in the real cable network.

The cable network model is scalable, and can evolve as the real cable network does.

260 M. Garcia et al. / Simulation Modelling Practice and Theory 12 (2004) 239261The parameters of the cable network model are obtained from the analysis of

traffic measurements on all its channels. The traffic on the channels is related by

simple regression models to the number of subscribers assigned to each channel.

The result of the analysis is a simple procedure to obtain model parameters from

cable network information. This procedure makes the use of the model direct, be-

cause it relates known physical parameters with more complicated traffic para-

meters.

The use of the final cable network model by the cable operator is very simple; theonly information it requires is the number of subscribers assigned by the cable oper-

ator to each upstream channel. This information allows the cable operator to use the

model for a process of continuous capacity planning, as the number of subscribers

assigned to each channel evolves. This makes this model different from existing mod-

els, in which the model parameters are not always related to the network and do not

have a direct meaning.

As a final conclusion, the developed model can be considered a valid tool to sup-

port performance decisions about the cable network studied. A simple procedure isestablished to obtain model parameters from the available measurements. The model

is generic and has a hierarchical structure which makes it adaptable to the particular

implementation of other cable networks.References

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Modeling and simulation of data transmission on a hybrid fiber coax cable networkIntroductionDescription of the systemRelated workTraffic modelingBackgroundTraffic model constructionUpstream channelCable modem and MAC protocolSubscriber profileWhen subscribers access the cable networkHow subscribers demand services

Traffic model implementation

Cable network model developmentA simple HFC branch modelThe cable network modelModel extensions

Results and model validationConclusionsReferences