03 17th October Traffic Engineering

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Teletraffic Engineering

Dr. Hicham Aroudaki

Damascus, 17th October 2009


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Traffic Engineering

Pur ose

Traffic theory is used to perform cost-effective

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Traffic Engineering

Interestin Questions

Given the system and incoming traffic, whatis the quality of service experienced by the

user?

quality of service, how should the system be

dimensioned?

2

ven e sys em an requ re qua y o

service, what is the maximum traffic load?


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Traffic Engineering

Interestin Questions

Qualitativel the relationshi s are as follows:

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To describe the relationships quantitatively,

mathematical models are needed.


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Traffic Engineering

Disci lines & Goals

Traffic theor is based on Practical oals:

the following disciplines: probability theory Network planning

s oc as c processes

queueing theory

statistical analysis

mens on ng

Optimization

performance analysis

(analysis of measurement

data)

operations analysis

Network management and

control

efficient o eratin

optimization theory

decision analysis (Markov

fault recovery

traffic management

4

simulation techniques rout ng


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Demand for additional capacity

Problem of the initial approachDefining terms

Offered vs. carried traffic

Offered traffic:

traffic as it is originallygenerated in the

Carried traffic:

Network

offered

traffic

carried

traffic

the network

blocked

traffic


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Demand for additional capacity

Problem of the initial approach

Characterization of carried traffic

Circuit-switched traffic

number of ongoing calls or active connections (Erl) may be converted into bit rate in digital systems (e.g. a

tele hone call reserves 64 kb s = 8000*8 b s in a PCM

system)

Packet-switched traffic bit stream (bps, kbps, Mbps, Gbps, )

packet stream (pps)

number of active flows (Erl)


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Defining terms

Bus Hour

It is the given period within a

110

100

Busy Hour

ay a ears e g es

traffic intensity.

This period usually has the

.of

Ca

lls80

70

60

lost calls.

The 'busy hour' traffic is used

to work out the equipment

No

50

40

30

quantities of the network.

If the dimensioning of

equipment at this period is

0 3 6 9 12 15 18 21 24

10

be minimized, all other non-

busy hour traffic should then be

handled satisfactorily.

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Dail traffic rofile measured in S ria

9%

6%6% 6%

7%

8%

7%7%

8%

ic

# of Minutes

# of Calls

4%

5%

6% 6% 6%

4%

4%

5%

6%

geo

ftotaltraf

3%

2%

1%

2%

3%

2%

3%

Percent

1%0% 0%

1%1%

0%

1%

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

:00

8

0 1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

HouroftheDay


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Defining Terms

Blockin

In a loss system some calls are lost

a call is lost if all nchannels are occupied when the call arrives

the term blocking refers to this event

There are two different t es of blockin uantities:

Call blocking Bc= probability that an arriving call finds all nchannels

occupied = the fraction of calls that are lost

Time blocking Bt= probability that all n channels are occupied at an arbitraryme = e rac on o me a a n c anne s are occup e

The two blocking quantities are not necessarily equal

Example: your own mobile

If calls arrive according to a Poisson process, then Bc = Bt

Call blocking is a better measure for the quality of service experienced by the

subscribers but, typically, time blocking is easier to calculate

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Defining Terms

Grade of Service GoS

Is a measure of the call blocking (the ability to make call during the busiest time).

experiencing a delay greater than a certain queuing time. Is determined by the available number of channels and used to estimate the total

number of users that a network can su ort.

In general, GOSis measured by looking at traffic carried, traffic offered, and calculating

the traffic blocked and lost.

.

For cellular circuit groups an acceptable GoS = 0.02. This means that two users of the

circuit group out of a hundred will encounter a call refusal during the busy hour at the

end of the planning period.

GOS = traffic lost / traffic offered

= proportion of time for which congestion exists

= pro a y o conges on or oc ng pro a y

= probability that a call will be lost due to congestion


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Defining Terms

Qualit of Service

Coverage: the strength of the measured signal is used to estimate

.

Accessibility (includes Grade of Service): is about determining theability of the network to handle successful calls from mobile-to-fixed

networks and from mobile-to-mobile networks.

Audio quality: monitoring a successful call for a period of time for

the clarity of the communication channel.


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Sim le Generic teletraffic model

Customers arrive at rate (customers per time unit)

1 = average inter-arrival time

Customers are served by nparallel servers

,

1/= average service time of a customer

There are n + mcustomer places in the system a eas nserv ce p aces an a mos mwa ng p aces

It is assumed that blocked customers (arriving in a full system) are lost

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Model Classification

Pure loss s stem

Finite number of servers (n


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Infinite S stem

Infinite number of servers (n =), no waiting places (m = 0)

No customers are lost or even have to wait before getting served

Sometimes,

this h othetical model can be used to et some a roximate results for a

real system (with finite system capacity)

Always,

it ives bounds for the erformance of a real s stem with finite s stem

capacity)

it is much easier to analyze than the corresponding finite capacity models

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Pure ueuin s stem



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Loss ueuin s stem



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Towards detailed modeling

Tele hone traffic model

Telephone traffic consists of calls a call occupies one channel from each of the links along its route

call characterization: holding time (in time units)

Modelin of offered traffic call arrival process (at which moments new calls arrive)

holding time distribution (how long they take)

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Tele hone traffic model

Link model: a pure loss system a servercorres onds to a channel

the service rate depends on the average holding time

the number of servers, n, depends on the link capacity

when all channels are occupied, call admission control rejects new calls so that they

Modeling of carried traffic

traffic process tells the number of ongoing calls = the number of occupied channels

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Traffic rocess

Traffic intensity is the

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simultaneously in

progress during a

particular period of time.


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Traffic Measurement Unites

Agner Krarup Erlang was born in 1878 in Lnborg, Denmark.

Through his studies of telecommunications traffic, he proposed

a formula to calculate the fraction of callers served by a villageexchange who would have to wait when attempting to place a

.

In 1909, he published his first work: The Theory of Probabilities

and Telephone Conversations. He gained worldwide

recognition for his work, and his formula was accepted for useby the General Post Office in the UK.

He worked for the Copenhagen Telephone Company for twenty

years, until his death in 1929. During the 1940s, the Erlang

measurement.

A.K. Erlang, 1878-1929


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An Intuitive Definition

Traffic or traffic intensityis anon-physical measure ofload on a system.

It is thus given by a pure number with no physical unitattached to it.

The load is simply a zero/one matter of a server beingfree/occupied.

, ,

inlet or outlet, signal receiver, radio channel, memory access, etc.).

It has been decided to use the notation Erlangas a traffic unit. Thus a single server carries

a traffic of 1 Erlan if it is continuousl occu ied durin an observation eriod. Two servers

with occupations 1/4 and 3/4 of the time also together carry 1 Erlang.

Traffic is normally related to a traffic carrying system, consisting of a discrete number of

servers. Each of the servers can at any moment carry a load of one or zero. A system ofn

servers can carry an ns an aneous oa o any n eger num er n.

The definition implies that two servers of different capacity (say one line of 9.6 kb/s and

one of 64 kb/s) both carry 1 Erlang as long as they are occupied to their full capacity, even

.

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Basic Definitiont4t2t1 t3

tT

t any po nt o t me t e resource e.g. c anne s oa e or not.

During the observation time the occupation (load) time is:

4

1

tot i

i

T t=

=

Percentage of occupation during the observation time is: By definition, Traffic Intensity (I):

tot

/totI T T=

Measuring unit: Erlang (Erl)

1 Erlang:

1 hour of continuous use of one channel = 1 Erlan

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1 Erlang = 1 hour (60 minutes) of traffic

In data communications, an 1 E = 64 kbps of data


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Traffic Intensity calculation

Littels formula

tt2t t

tT

4

it Traffic Intensity is the product1 cicI n t

T T

== = =Traffic Intensity:o e ca arr va ra e an e

mean duration of calls handled

by the channel (mean holding

time)

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Exam le

,

call had an average call duration of 5 minutes, what isthe corresponding Erlang value ?


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Exam le

Consider the attern of activit in a cell of ca acit 10

channel over a period of 1 hour. The rate of calls er minute is 97/60.

The average holding time per call, in minutes is 294/97.

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Exam le

Consider the attern of activit in a cell of ca acit 10

channel over a period of 1 hour. The rate of calls er minute is 97/60.

The average holding time per call, in minutes is 294/97.

I =(97/60)(294/97) = 4.9 Erlangs.

That is, on average, 4.9 channels are engaged.

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Exam le I

A call was established at 1am between a mobile and MSC.

Assuming a continuous connection and data transfer rate at 30

kbit/s, determine the traffic intensity if the call is terminated at


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Exam le I

A call was established at 1am between a mobile and MSC.

Assuming a continuous connection and data transfer rate at 30

kbit/s, determine the traffic intensity if the call is terminated at

* *

= 0.833 Erlang

Note, traffic intensity has nothing to do with the data rate, onlythe holding time is taken into account.


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Erlan s Formula The Erlang B formula is expressed as probability

N B

of the system)occupied.

The assumptions in the Erlang B formula are:

Traffic originates from an infinite number of

A

traffic sources independently.

Lost calls are cleared assuming a zero

holding time.

Number of trunks or service channels is

limited.

Inter-arrival times of call requests are

independent of each other.

channel (called service time) is based on anexponential distribution.

Traffic requests (with rate ) areAlso called:

Erlangs B-formula

implying exponentially distributed call inter-

arrival times.

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Erlangs blocking formula

Erlangs loss formula

Erlangs first formula


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Erlan -B Traffic Table

Servers (Channels)GoS

Offered

Traffic

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Gra hs for Erlan s blockin function

y

cking

Pro

ba

bili

ckin

gPro

ba

bilit

Number of channels

Bl

Blo

offered traffic in tensityOffered traffic intensity


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Usa e of Erlan s formula

Probability0.01

Minimum number ofneeded channels

n5

33

Offered traffic

0.8 Erlang

U f E l f l


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Usage of Erlangs formula

Ca acit vs. traffic

Given the quality of service requirement that B< 1%, the required

capacity N depends on the traffic A intensity as follows:

N(A) = min{i =1,2, . . . | Erl(i,A) < 0.01}

acity(N)

Ca

34Traffic (A)

U f E l f l


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Qualit of service vs. traffic

Given the capacity N= 20channels, the required quality of service

(1 B) depends on the traffic intensity A as follows:

1-B(A) = 1-Erl (20,A)

S(1-B)

Q

35Traffic (A)

U f E l f l


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Qualit of service vs. ca acit

Given the traffic intensity A= 15 Erlang, the required quality of service

(1 B) depends on the capacity N as follows:

1-B(N) = 1-Erl (N,15)

S(1-B)

Q

36Capacity (N)


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Exam le

A single GSM service provider support 10 digital speech

channels. Assume the probability of blocking is 1.0%. From

the Erlang B table find the traffic intensity. How many 3


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Erlan -B Traffic Table

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Exam le

A single GSM service provider support 10 digital speech

channels. Assume the probability of blocking is 1.0%. From

the Erlang B table find the traffic intensity. How many 3

rom e r ang ar e ra c n ens y = . r angs

nc= 4.5 / (3 mins/60) = 90 callscI n t=


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Traffic Intensit Models

Erlang B Formula:

All blocked calls are cleared

Extended Erlang B:

Similar to Erlang B, but takes into account that a percentage of calls are

immediately represented to the system if they encounter blocking (a busy

. .

Erlang C Formula:

Blocked calls dela ed or held in ueue indefinitel .

Poisson Formula:

Blocked calls held in queue for a limited time only.

Binomial Formula:

Lost calls held


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Poissons formula

The Poisson formula is used for designing trunks on a route for a given GoS. It is

used in the United States.

The assumptions in Poissons formula are:

Traffic originates from an infinite number of independent sources

Traffic density per traffic source is equal

Lost calls are held.

A limited number of trunks or service channels exist.

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Erlan s C Formula

The Erlang C formula assumes that a queue is formed to hold all requested

calls that cannot be served immediately.

Customers who find all N servers busyjoin a queue and wait as long as

necessary to receive service. This means that the blocked customers are

delayed. No server remains idle if a customer is waiting.

The assumptions in the Erlang C formula are:

Traffic originates from an infinite number of traffic sources independently. Lost calls are delayed.

Number of trunks or service channels is limited.

The probability of a user occupying a channel (called service time) is basedon an

ex onential distribution.

Calls are served in the order of arrival.

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Ex onential distribution

Exponential distributions are a class of

continuous probability distributions.

Main parameter is: (rate)

used to model the time betweenindependent events that happen at a

constant avera e rate.

Mean:-1

Variance:-2

Usage: If events are assumed to occur

randomly in time (i.e. follow a Poisson

process) and the average time

between events e uals , then the

( ; ) xx e =

time between each consecutive event

will be distributed according to an

exponential distribution.

For exam le, if an insurer sees that

some particular type of natural

disaster occurs on average once

every 5.5 years, the time between

such consecutive disasters can be

. .

Memory less property: the time until

the next event also follows anExponential distribution.43

PDF of Exponential Distribution


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Ex onential distribution

( ; ) 1- xF x e =

44

CDF of the Exponential Distribut ion


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Real exam le for an arrival rocess

Measured distribution of arrivals

in a subscriber group, matching

to an exponential curve.

45

Myskja, A, Walmann, O O. A statistical study of telephone traffic data with emphasis on

subscriber behavior. I: 7th international teletraffic congress, ITC 7. Stockholm 1973.


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Poisson Distribution

Poisson distribution is a discrete

probability distribution. k

It expresses the probability of a number

of events occurring in a fixed period oftime if these events

( ; )

!

k e

k

=

,

and

are independent of the time since

the last event.

Mean:

Variance:

The probability that there are exactly k

occurrences (k being a non-negative

inte er k = 0 1 2 ... is:

( ; )!

k

f k ek

=

For instance, if the events occur on average every 4

Probability Mass Funct ion (PDF)

46

min, and you are interested in the number of events

occurring in a 10 minute interval, you would use as

model a Poisson distribution with = 10/4 = 2.5.

is a positive real number, equal to the expected number of

occurrences that occur during the given interval


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Poisson distribution

The Poisson (t)distribution models

the number of occurrences of an k

event in a timetwith an expected

rate of l events per periodtwhen thetime between successive events

follows a Poisson process.

( ; )

!

k e

k

=

Examples

If is the mean time between

events, as used by the

Mean:

Variance:

xponen a s r u on, en =

1/. For example, imagine that

records show that a computer

crashes on average once every

ours o opera on =

hours), then the rate of crashingis 1/250 crashes per hour.

Thus a Poisson (1000/250) =

Probability Mass Funct ion (PDF)

o sson s r u on mo e s

the number of crashes that could

occur in the next 1000 hours of

operation.47


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Poisson in other words

In a Poisson process with rate , the number of points occurring in a fixed length

t has the Poisson distribution, or equivalently, the lengths of the intervalsseparating successive points are independent and have identical, exponential

distributions

Service times

t4t3Ch 1

t2t1

t6 t9Ch 3

t5 t5 t7 t8

Arrival times

Departure timest


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Profile of T ical Cellular usa e 1994


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Ca acit considerations 1

The capacity required in a certain service area is proportional to the traffic which

can be served at a given quality of service (QoS) within this service area.

The traffic generated by the subscribers within the service area is proportional tomean service time and the mean service requesting rate. Thus for circuit

switched services the traffic is given by:

_ _ _ _ _ _traffic mean service time mean arrival rate for service=

for speech services the capacity of a mobile radio network can be defined as:

/capacity traffic area=

tra ic tra ic channels carriers sites

Expanding the above expressions leads to:

50

area channel carrier site area=


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Using the definition ofcluster size for homogeneous networks as the number of

,

equation can be derived:

.

carriersbandwidth

carriers total No o carriers

By combining the equations:

_ _

_ _site cluster size cluster size= =

1

_

traffic channels carriers sitescapacity bandwidth

channel carrier bandwidth cluster size area=

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traffic/channel- physical channel (system) load; this factor takes into

accoun e ac a a c anne usua y canno e u y oa e .

channels/carrier- system dependent parameter (GSM family: 8 TCH forfull-rate channels, 16 TCH for half-rate channels, signalling neglected);

carriers/bandwidth- system dependent parameter (GSM: 5 carriers per 1

MHz);

cluster size- characterizing the frequency reuse in the deployment area,

which depends on propagation conditions, required QoS and the

network structure;

bandwidth- total available frequency bandwidth per operator;

sites/area- describes the base station density in the deployment area.

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A reasonable definition of the spectral capacity is obtained by relating the

capacity to the most severe network investment costs spent for the licensed

spectrum and building up the network infrastructure:capacity

_sites

bandwidtharea

1_

_

traffic channels carriersspectral capacity

channel carrier bandwidth cluster size=

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Capacity considerations (5)


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Capacity considerations (5)Numerical exam les on s ectral efficienc

Parameters: Licensed bandwidth: 7.2 MHz; GoS: 1%

Scenario 1: Omni cells of cluster 12

Scenario 2: Sector cells of cluster 4x3 (4/12)

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4/12 cluster


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Efficienc measures

Spectrum efficiency: a measure of how efficiently frequency, time and

space are used:

anneltraffic/chOfferedellchannels/cofNo.

AreaBandwidth

(Erlang)Traffic

Erlang

se

=

AreaBandwidth2

kmkHz

It depends on:

Number of required channels per cell Cluster size of the interference group

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Efficienc Utilization related

Capacity

nonblockedTrafficEfficiency =

)(channelstrunksofNumber

trafficnonroutedofportionsErlangs =

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03 17th October Traffic Engineering

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