27917052 telecommunications traffic engineering by jeremy harvey cissp

8/8/2019 27917052 Telecommunications Traffic Engineering by Jeremy Harvey CISSP

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Telecommunications

Traffic

An Introduction

© JEREMY HARVEY 2010 All Rights Reserved



What is it?

Telecommunications Traffic or ³teletraffic´ is: The combined messages carried between

two or mor e points via transmission links



TeletrafficWe ar e inter ested in the ³intensity of that traffic´ so that we can provide the

right number of transmission links

³Traffic Intensity´ depends on:

The total number of simultaneousmessages in progr ess on the link It is measur ed in ³Er langs´



TeletrafficWhat is an ³Er lang´

If one line is occupied for one hour, it issaid to carry one Er lang of traffic

So if a line carries 0.5 Er lang of Traffic,it is only busy for 50% of the hour, or 30minutes



TeletrafficEr langs ar e used to calculate the percentage of time each hour, that aline will actually be in use.



TeletrafficThe volume of traffic depends on:

The number of messages (or calls)

The duration of each call

For example 10 calls (each lasting 3minutes) is the same as 1 call lasting 30minutes



TeletrafficMathematically we say that:

Traffic Volume is the integral of trafficintensity with r espect to time, and we expr ess it in ³Er lang-hours´



Integrals

Integration is an ar ea of mathematicsthat is used to measur e the ar ea under the line on a graph

Erlangs

Time

(0-3600

seconds

_



Integrals

Traffic Intensity (Utilisation of line each second)

Erlangs

Time

(0-3600

seconds

_



Integrals

Traffic Volume (Traffic intensitymeasur ed each second for an hour)

Erlangs

Time

(0-3600

seconds

_



Integrals

The integral is found by dividing the graph into r ectangles and finding the

ar ea of r ectangle (then adding them all up)

Erlangs

Time

(0-3600

seconds

_



Integrals

Mathematically this is:

v = I(t) dt

Traffic

VolumeIntegral (the

area under the

graph)

Traffic

Intensity

Over time (eg over

3600 seconds)



Integrals

We can have a function that produces a copy of the curve of the line on the graph

v = f(x) dx

Traffic

VolumeIntegral (the

area under the

graph)

Function that produces a

copy of the curve on the

graph

Over time (eg a

changeIn the x axis)



Integrals

We can have a function that produces a copy of the curve of the line on the graph

v = f(x) dx

This is read as ³delta

x´ or change in x(delta means change)



Integrals

We can also limit our ar ea to between twopoints (a and b, or say 10:00 am and 11:00

amb

v = f(x) dxa



Traffic Patterns The traffic can vary from instant to instant ±

as calls ar e established (set up) or

terminated (ended)



Traffic Patterns It can also f luctuate hour ly, often it is:

Less during the night Rises rapidly in the morning (when offices,

shops & factories open for business)

Goes down at lunch time

Falls again in the afternoon between 5 and 7pm as people leave work for the day



Traffic Patterns And it can have seasonal

f luctuations e.g:

Higher just befor e Easter &

Ch

ristmas



Traffic PatternsFinally ther e ar e long term

patterns as the traffic grow year by year



Traffic PatternsHowever of gr eatest inter est to

the traffic planner is the busiesthour of the day (known as the TCBH or Time Constant BusyHour)



Traffic PatternsBecause if we cater for the

busiest hour, ther e will be sufficient lines available for the quieter times of the day



Busy Hour Traffic

Call arriving at a switch may arrive:

At random

In mor e or less r egular patterns

In bursts

Separated by periods in which no callsarrive (eg to an ACD (Automatic Call Distributor) or Call Centr e)



Busy Hour Traffic

Random arrival of calls is typical at a:Subscriber Switching Stage in

Medium to large public exchanges Large PABXs

Calls to an ACD ar e not random asthey ar e usually in r esponse to anevent (eg an advert on TV)



Busy Hour Traffic

How long each call lasts (knownas a ³holding time´ is asimportant as how many callsarrive each second

The

combination of numbe

r of calls and holding time dictatesthe ³Traffic Intensity´



Busy Hour Traffic

The ³messages´ sent on atransmission link can include:

Conversations

Data messages Associated control messages

(data)



Busy Hour Traffic

The ³messages´ holding time´ (itsduration) can vary from a f ewseconds to a whole hour



Busy Hour Traffic

The distribution (statistically) of these individual holding time ±that is the number of calls of each duration in the hour ± is importantin determining the number of

outside lines (trunks) and the

waiting time in a queue (eg ACD)



Fundamental

Relationships Our problem is that we can only measur e

the traffic that is actually carried on a link

(known as the Carried Traffic) which hasthe symbol ³´

What we actually want to know is the Offered Traffic (including that which didnot get through) with symbol ³A´



Fundamental

Relationships The traffic that did not get through

(because ther e wer e insufficient lines) is

known as Blocked Traffic and has the symbol ³´



Fundamental

Relationships To calculate the percentage of blocked

traffic:

B = (A-Y) / A

Which is (off er ed traffic ± carried traffic) /(off er ed Traffic)



Fundamental

Relationships And to calculate carried traffic:

Y = A(1-B)

Which is (off er ed traffic) ± (1 ± Blocked

Traffic)



Fundamental

Relationships And to calculate off er ed traffic (A in Er langs) the

formula is:

A = (nh) /T

Wher e n is number of calls

h is avg holding time of each call (in seconds)

T is the number of seconds in the measur ement period(eg 3600 seconds in an hour)



Measuring Teletraffic

The Traffic Engineer is primarily inter estedin the:

Average Traffic intensity at various points in the telephone exchange and the

³Dispersion´ of traffic (wher e the callers ar e

dialling)




Measuring the Offered Traffic is difficult (if not impossible)

So we measur e the Carried Traffic anduse it to estimate the Offered Traffic




We do this by first measuring the Traffic

Dispersion (wher e the callers ar e dialling)

This is done by r ecording the first 4,5 or 6digits dialled by the callers and the total calls duration.



M

easuring TeletrafficWhen the call is completed the telephone

system pr epar es an SMDR r ecord.

This is a text message, wher e details such as extension, called number, duration etcar e in certain field in the text message.

The text message is sent via a serial port

to a PC running a spe

cial

program. The program extracts the information and

places them into a database format.




By running queries on the database it ispossible to compile r eports on the numbers

callers wer e dialling, as well as individual,total, and ther efor e average holding times(call durations) to each of the destinations.




Since it would be uneconomical to provide equipment for every peak every

encounter ed by the telephone system«

The equipment is instead designed to carrythe traffic in the average Time ConstantBusy Hour (TCBH) , which is the twobusiest consecutive 30 minute periods,during the busy season




The busy season is defined as:

T he 4 consecutive busiest weeks in theyear



System Types

Having identified wher e callers ar e dialling(and for how long) it is then necessary to

make a decision as to what callers whoexperience congestion should do:

Do they wait (queue) or r eceive busy tone

(and be forced to hang up and dial again)



System Types

Callers that wait (eg when dialling a call centr e) in a delay will be placed in a

F.I.F.O queue (First In First Out)

This ensur es that callers who have beenwaiting the longest, ar e answer ed first



System Types

The other consideration is the type of switching system being used (eg the type of exchange or PABX

The system can be dir ectly controlled bythe dial impulses (digit dialled) such as in

Ste

p by Ste

p Ex

ch

ange

s Or impulses can be stor ed and analysedlater (as in Crossbar, AXE, Digital PABXs)



Congestion

In a switching system (eg a PABX) ther e ar e often internal traffic r eports (eg

JUNCTOR r eports) that can be run todetermine whether congestion is occurringbetween shelves or cabinets.



System Types

The ratio of incoming or outgoing lines, tothe number of devices or people wanting to

access those lines is known as a Grade of Ser vice

To be mor e specific the Grade of Ser vice

the percentage of calls that we expect to

fail in trying to access an incoming or outgoing line.



System Types

For example a Grade of Service of 0.01 (or 1%) indicates that:

We expect 1 out of every 100 calls toexperience congestion when trying toaccess either an incoming or outgoing line.

This is the ³normal´ public network Grade of Service (GOS)



System Types

The calls may fail because ther e ar e:

Insufficient incoming or outgoing lines or Insufficient signalling devices (eg r egisters)

or

Insufficie

nt control

e

quipme

nt (or path

) inthe switching system to set up the call or

A combination of all of the above



Congestion Types

Ther e ar e two types of congestion:

Call Congestion Time Congestion



Call Congestion

The probability that a call will encounter congestion

Eg 1% of calls ar e expected to r eceive busy tone



Time Congestion

The proportion of time during which congestion exists:

Eg for 10% of the hour congestion is likelyto exist



Congestion

When calls arrive at random, and all trunks(lines) in the route ar e fr eely available:

Call Congestion and Time Congestion ar e equal



Congestion

But in small switching systems (or wher e ther e is limited availability of trunks, eg

when the calls have to get between cabinet/ shelves in the system) then:

Call Congestion & Time Congestion ar e

diff er ent (usually the diff er ence is small butcan be significant)



Congestion

If the congestion is inside the switchingsystem (eg getting between cabinets /

shelves) adding extra external lines will notcur e the problem (in fact it will make itworse)

So it is important to understand why the

congestion is occurring, and where it isoccurring



Congestion

In a switching system (eg a PABX) ther e ar e often internal traffic r eports (eg

JUNCTOR r eports) that can be run todetermine whether congestion is occurringbetween shelves or cabinets.



Congestion

If no detailed r eports ar e available it ispossible to estimate traffic from Peg

Count Reports

Peg Count r eports provide details on the number of times a piece of equipment was

accessed (by then estimating the average holding time, the traffic can be calculated inEr langs)



Delay Systems

A delay system (eg a Call Centr e) allows callers towait (queue) rather than r eceive busy tone.

The delay depends on The Traffic Intensity

The number of circuits provided

The distribution of holding times (diff er ent queues to the same system may have diff er ent call durations

de

pe

nding on the

natur e

of the

e

nquiry and the

numbe

r of operators (Agents) available to take the calls



Delay Systems

But if the mean (average) Offered Traffic

does exceed the number of service

devices (eg equipment, trunks etc) then:

The service standard is expr essed in termsof either: Average Delay

Or Percentage of Calls delayed more than

some specified time



Delay Systems

It is often better to use the ³Percentage of

Calls delayed more than some specified

time´ as this is aff ected mor e by what isknown as the Ser vice Discipline

The Service Discipline r ef ers to the way

calls ar e taken out of the queue andpr esented to Agents (operators) eg FIFO



Availability

To gain access to trunks (outside lines) or equipment in the exchange it is necessary

to consider ³availability´

Availability is defined as the number of outlets in a switching stage which can be

r eached from its inlets.



Availability

In an exchange with a single switchingstage (such as Step by Step) the traffic

load has no eff ect on availability, as it isfixed by the mechanical design of the exchange

Likewise if traffic is always sent to a pr e-

assigned route (I.e ther e ar e no alternative path) then traffic load will also not have anyeff ect on availability



Availability

But modern systems connect to a partial switching stage that is shar ed by others,and ther e can be multiple switching stagesthen:

The actual availability under heavy load may be less than some nominal pr e-set value (eg if it

was designed to carry 99% of traffic it may onlycarry 70% because intermediate switchingstages ar e congested).



Availability

Traffic ther efor e is carried most efficientlyby group of circuits having full availability

wher e:

Every idle circuit can be r each all the time from all inlets. However it is often

uneconomical to provide full availability(especially in large systems)



Availability

We ther efor e have to calculate the pr obability that each part of the path will

be available, based on call patterns, trafficloads and traffic intensity to design asystem that will have the r equir ed Grade of Service

And that is wher e Traffic Engineering isused



Factorial

We first have to determine how many waysour circuit (eg trunk or equipment ports)

can be accessed If we have 5 callers and 5 trunks (outside lines) how many ways ar e ther e of arranging the callers on the available

trunks?



Factorial

We count each possible way of arrangingthe callers on the 5 trunk as ³n´

The first arrangement would be n1

The 2nd arrangement would be n2

The 3rd arrangement would be n3

The

4th

arrange

me

nt woul

d be

n4 The 5th arrangement would be n5

The total n = n1 n2 n3 n4 n5



Factorial

So ther e ar e:

5 ways to arrange the 1st caller (on 5

trunks) 4 ways to arrange the 2nd (ther e ar e only 4lines left)

3 ways for the 3rd caller

2 ways for the 4th caller

1 way for the 5th caller



Factorial

This mean that ther e ar e the followingpossible way of arranging the callers:

n = 5 x 4 x 3 x 2 x 1= 120 ways

We call this a ³factorial´ with the symbol ³!´

known as ³shriek´

So 5! = 120



Permutation

When we are not worried about the order in which things ar e selected it is a

per mu

tatio

n

A permutation just uses a factorial calculation to calculate the number of ways

ways that things can be arranged but we can choose how many of the ³things we select at a time´



Permutation

For example if we have 5 caller (Fr ed, Joe, Alice, Frank and Kathy) but only two

trunks,h

ow many ways can the

calle

rs be

arrange on the line, if only to can getthrough at a time?



Permutation

We say that we take:

n things r at a time

So we take 5 callers (n=5), 2 at a time (r=2)



Permutation

The formula for a permutation is: n! / (n-r)!

So 5 callers taken 2 at a time is:

5! / (5-2)!

= 120 / (3 x 2 x 1)

= 120/6

= 20 possible ways (permutations) five callers canaccess 2 trunks, two callers at a time



Permutation

This is written mathematically as:

nPr



Combination

When we are worried about the order inwhich thing ar e selected (and we do notwant to count thing twice) we use a³combination calculation´

For example if Fr ed accesses Trunk 1 and Joe Trunk 2

It is the same as if Joe accesses Trunk 1 and Fr ed Trunk 2

We still the same two callers accessing 2 lines at the same time, sowe only count it as one way of accessing the trunks rather than 2ways



Combination

The formula for a combination is: n! / (n-r)! r!

So 5 callers taken 2 at a time is:

5! / (5-2)! 2! = 120 / (3 x 2 x 1) 2x1 = 120/6 x2 = 120 / 12

= 10 possible ways (permutations) five callers canaccess 2 trunks, two callers at a time (each beinga unique arrangement of callers)



Combination

This is written mathematically as:

nCr or (nr )



Probability Theory

Probability theory deal with events thatcannot be pr edicted in advance

For example if I have 3 trunks, which one will a telephone call choose if all ar e equally likely to be chosen?



Probability Theory

We can however list all the possible outcomes

So if ³s´ means the line was chosen and ³f ³means it was not chosen the possible outcomes ar e:



Probability Theory

Lines s f f

f s f

f f s

The list of all possible outcomes is known as a ³sample space´



Probability Theory

Lines s f f

f s f

f f s

The list of individual outcomes (eg s f f , are known as samplepoints



Probability Theory

Lines s f f

f s f

f f s

The sample space is Discrete because the outcomes can be listedone by one, and Finite because there are a finite (limited) number

of sample points



Events

Events ar e groups of sample points(individual outcomes) that can be

r ecorded on a VENN DIAGRAM



Events

Consider Event E as ³throw a 1 or 2with an unbiased dice´

E

1 2



Events

_

Event E (r ead as NOT E) is ³every

other number except 1 or 2´

E

1 2 3 45 6

_

E



Events

If Event E is ³the call is a toll (STD) call´

And Event B is ³that a call has been

progr ess for 2 minutes´We can ask ³what is the probability thatthe call is an STD call and has been in

progr ess for longer than 2 minutes?´



Events

If Event E occurs 0.07 (7%) of the time

And Event B occurs 0.09 (9%) of the

time

A and B occur 0.03 (3%) of the time

We draw it as the following:



Events

E F

0.07 0.090.03



Events

E F

0.07 0.090.03

This is known as conditional probability, it is the probability that

Event F has occurred given that Event E has also occurred.



Events

E F

0.07 0.090.03

We represent it as P(E | F)



EventsE F

0.07 0.090.03

If 3% of calls are

STD and last

longer than 2

minutes

What is the

probability that acall is STD given

it has

been in progress

for longer than 2

minutes



Events

E F

0.07 0.090.03

We calculate P(E|F) = P(EF) / P(F) where mean ³and´



Events

E F

0.07 0.090.03

We calculate P(E|F) = 0.03 / 0.03 + 0.09) = 0.25 (or 25%)



Events

E F

0.07 0.09

If however nocalls were STD

and longer than 2

minutes we

say the Events E

and F aremutually

exclusive (they

have no

sample points incommon)



Independent Events

To calculate the probability of callsbeing ³blocked´ and not getting through

(to determine the number of lines for aparticular Grade of Service´) usingEr langs Poisson formula ± the events(the call) need to be independent of

each other



Independent Events

Two events ar e independent if one (sayE) has the same probability of occurring

whether or not another event F hasoccurr ed.



Independent Events

As an example ± what is the probabilitythat a household with a car, also has a

phone«in other words can we determine how many phones ther e ar e in an ar ea by measuring the number of households that have a car?



Independent Events

Households in town

Phone No Phone

Car 844 284

No Car 1477 497



Independent Events

P (Car|Phone) = 844 (Car and phone) /(844 (Car and Phone) + 1477 (No Car

and Phone) = 4/11

P (Car) = (844 (Car and phone) +

284(Car + no phone))/ (844 + 1477 +284 + 497) = 4/11



Independent Events

Since both probabilities ar e the same (4/11) they ar e said to be independent

of each other

Possessing a car does not make it mor e

or less likely that the household will have a phone



Probability Distribution

We can graph the individual probabilities of an eventoccurring, we end up with a pr obability distributioncur ve

This can be described mathematically with a functionP(X = x ) wher e X is random variable and x is the value that variable can take

If the value if x can be any random number, known asa continuously random variable (eg time spent ona call), then it is known as a Pr obability DensityFunction



The story of e

Befor e looking at the Poisson ProbabilityDistribution curve (used by Er lang) we firsthave to look at a curious curve made by

plotting ³e´

³e´ is a number that has the approximate

val

ue

of 2.71828



The story of e

In 1683 Jacob Bernoulli (a Swissmathematician) got to work in trying tocalculate compound inter est

Imagine that you invest $1 over 1 year, andyou get a massive 100% inter est on your

inve

stme

nt



The story of e

At the end of the first six month you will have $1.50($1 principal and $0.50 inter est)

But at the next six months you will have $1.50 plusanother $0.75 giving you $2.25

You made an extra 25c just by compounding. Now if

our original investment was 1000 times bigger youwould make an extra 25,000c or $250 than if the inter est was paid just once a year.



The story of e

³e´ is the amount the $1 would grow to if the compounding took place continuously ± it isknown as exponential growth

It is used to calculate population growth,radioactive decay and much much mor e

e it turns out can be calculated by:

e = 1 + 1/1! + (1 / 2!)) + (1/3!) + (1/4!)«. And equals 2.717828 (approx)



The story of e

e = 1 + 1/1! + (1 / 2!)) + (1/3!) + (1/4!)«.might look familiar

The 1!..2!«3!«. Ar e all factorials..and couldbe saying how many way ar e ther e to seize agroup of lines 1 at a time, 2 at a time, 3 at atime etc.



How to calculate

Traffic

An Introduction



Weighting

Probabilities



Weighting Probabilities

We first have to decide on how likely anevent is to occur.

Using ³e´ for what is known as³exponential distribution´ we can do the following?




For calls of 2 minutes average durationwe can work out how likely calls will be

in 30 second intervals from 0.5 to 3minutes

It is known that call durations ar e

³ex

pone

ntiall

y distribute

d´ (th

ish

asbeen shown by experimentation)




We first take the call duration (t) and divide it by the average conversation time ±h (2 minutes)

So it becomes t/h

The formula to find the probability of each call duration t is:

P(T <=t) = 1 ± e-t/h

t (min) (h) min ± t/h P(T<=t)



avg call duration

0.5 2 0.25 0.221

1.0 2 0.5 0.393

1.5 2 0.75 0.528

2.0 2 1 0.6323.0 2 1.5 0.777




We then multiply the weightedprobabilities

So for our pr evious example the weighted probability is:

0.221(0.5) + 0.393(1.0) + 0.525(1.5) +0.632(2.0) + 0.777(3.0) = 4.886 %

27917052 telecommunications traffic engineering by jeremy harvey cissp

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