Teletraffic Engineering

Department of Electrical Engineering

Traffic Theory Covers specific types of random processes

intelecommunications– Average connection duration– Average number of users– Busy time– Service time– Call arrival

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Traffic Engineering Required in telecommunications network planning to ensure

that network costs are minimized without compromising the quality of service (QoS) delivered to the user of the network.– It is based on probability theory and can be used to analyze mobile radio networks as well as other telecommunications networks.

Mobile radio networks have traffic issues that do not arise in the fixed line PSTN. A mobile handset, moving in a cell, receives a signal with varying strength. This signal strength is subject to:– slow fading,– fast fading– interference from other signals,

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Traffic Engineering• Traffic engineering balances the following factors based on given

amount of traffic • Grade of Service (GOS)

• Resources (e.g. trunk channels)• Two types of systems implemented to provide voice

communications– Blocking

• Voice or data is blocked (by a busy signal) if network resource (e.g trunk channel) is not available.• GOS = Blocking probability

– Delay System• Voice or data is queued until network resource is

available• GOS = Queuing Probability and average time in

queue

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Traffic Engineering

Holding Time - the length of time that a resource is being held(e.g the duration of a phone call)

Traffic volume - for an interval is the sum of all the traffic holding times for that interval

Traffic intensity = traffic volume / time interval which is a measure of demand

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Traffic Engineering

Erlangs - describe traffic intensity in terms of the number of hours of resource time required per hour of elapsed time

CCS( Centum Call Seconds) - measures the exact same traffic intensity as the Erlangs but expresses it as the number of 100 second holding times required per hour. Traffic registers sample stations every 100 seconds per hour to check for busies. Since there are 36 sets of hundred seconds in an hour36 CCS = 1 Erlangs

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Traffic Measurement Unites Erlangs:

Traffic intensity (named after of a Danish mathematician) is the average number of calls simultaneously in progress over a certain time. It is a dimensionless unit.– Erlang

• one hour of continuous use of one channel = 1 Erlang• 1 Erlang = 1 hour (60 minutes) of traffic

– In data communications, an 1 E = 64 kbps of data– In telephone, 1 Erlang = 60 mins = 1 x 3600 call seconds

% of Occupancy

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Erlangs - Example For example, if a group of user made 30 calls in

onehour, and each call had an average call duration of 5minutes, then the number of Erlangs this represents isworked out as follows:

Minutes of traffic in the hour = number of calls x duration

Minutes of traffic in the hour = 30 x 5Minutes of traffic in the hour = 150Hours of traffic in the hour = 150 / 60Hours of traffic in the hour = 2.5Traffic figure = 2.5 Erlangs

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◦ Call holding time is the length of time during which a traffic source engages a traffic path or channel. 1 – 3 minutes typical, >10 minutes infrequent for voice.

Call Holding Time

H = average holding time, 3 minutes.Negative exponential

Busy Hour Busy hour is that continuous 60 minutes

time span of the day during which the highest usage occurs.

Traffic Intensity over Day

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Busy Hour… Note:

◦ may not occur at the same time every day◦ weekly variation◦ week day /weekend variation◦ seasonal variation

Mathematical formulas assume the busy hour traffic intensity is the average of an infinite number of busy hours.

Busy Hour ADPH (Average Daily Peak Hour)

◦ − one determines the busiest hour separately for each day (different time for different days), and then averages over e.g. 10 days

◦ − the resolution of the start time of the busy hour may be either a full hour (ADPH-F) or a quarter of an hour (ADPH-Q)

TCBH (Time Consistent Busy Hour)◦ − a period of one hour, the same for each day, which gives the

greatest average traffic over e.g. 10 days

FDMH (Fixed Daily Measurement Hour)◦ − a predetermined, fixed measurement hour (e.g. 9.30-10.30);

the measured traffic is averaged over e.g. 10 days

aFDMH ≤ aTCBH ≤ aADPH

Traffic Density / Intensity Traffic Density is defined as the number of

simultaneous calls at a given moment. Traffic Intensity,A represents the average

traffic density (occupancy) during any one hour period.

◦ Occupancy is any use of a traffic resource regardless of whether or not a connection (call) is completed.

◦ Occupancy is the probability of finding the trunk busy is equal to the proportion of time for which the trunk is busy

Loss and Delay Systems A Loss System is one in which a call attempt

is rejected when there is no idle resource to serve the call. (BCC – Blocked Call Cleared)◦ Blocked calls…

A Delay System is one in which call attempts are held in a waiting queue until resource are available to serve the calls.◦ Delayed calls…

Offered, Carried and Blocked Traffic Offered traffic is the traffic intensity that

would occur if all traffic submitted to a group of circuits could be processed.

Carried traffic is the traffic intensity actually handled by the group.

Blocked traffic is that portion of traffic that cannot be processed by the group of circuits (I.e. offered traffic minus carried traffic).◦ Blocked traffic may be rejected, retried or offered

to another group of circuits (overflow).

System Utilization

Let

◦ A be the offered traffic

◦ C be the carried traffic,

◦ B is blocking probability

◦ Lost traffic (A- C) = B*A

◦ Probability of blocking

◦ System utilization: A

CB 1

N

BA

1

N channels

Lost traffic; (BxA)

Offered traffic (A)Carried traffic (C)

Traffic Intensity

Is a measure of the average occupancy of a resource during a specified period of time, normally a busy hour.The traffic intensity offered by each user is:

A = μH Erlangswhere

H is the average holding time of a callμ is the average number of call requested/hour

If there are U users and an unspecified number of channels.

The total offered traffic intensity is:AT = UA Erlangs

Busy hours traffic: Calls/busy hours *Mean call hold time

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Traffic Intensity - contd.

In a trunks system of C channels and equally Distributed traffic among the channels, the

traffic intensity per channel is:

AC = UA/C Erlangs/channels

The traffic volumeis a measure of the total work done by a

resource orfacility, normally over 24 hours

VT = A * T Erlangs-Hours

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Traffic Intensity

◦ Traffic Flow = (no. of calls)*(mean call holding time)

◦ Example :If 100 calls are generated in 1 hour of 3 minutes average duration we have 3*100 = 300 call minutes or 300/60 = 5 call hours.

Erlangs The international dimensionless unit of

telephone traffic is called the Erlang after A. K. Erlang (1878 – 1929) a Danish scientist.

Defined as one circuit occupied for one hour.◦ 1 Erlang = 1 Call–hour / hour

Busy hour traffic◦ Erlangs = (Calls/busy hour)*(mean call holding time)

(careful with units, all times in hours) 1 Erl = 36 CCS

Example IA call 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 1.50am.Solution:

Traffic intensity = (1 call)*(50 mins)*(1 hour/60 min) = 0.833 Er

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

Note:• If the traffic intensity > 1 Erlang: The incoming call rate exceeds the outgoing calls, thus resulting in queuing delay which will grow without

bound (if the traffic intensity stays the same).• If the traffic intensity is < 1 Erlang, then the network can handle more average traffic.

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Example 2Consider a PSTN which receives 240 calls/hr. Each call lasts an average of 5 minutes. What is the outgoing traffic intensity to the public network.Solution:

A = μ *Hμ = 240 calls/hr and H = 5 minutesA = (240 calls /hr) x (5 min/call) = 1200 min/hr

Erlang cannot have any unit soA= 1200 min/hr * (1 hour/60 minutes) = 20 Erlangs

So 20 hours of circuit talk time is required for every hour of elapsed time. An average

of T1 voice circuits busy at any time is 20. (Or 20 hours of continuous use of 20 channels.)

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Example 3 Call established at 2 am between a central

computer and a data terminal. Assuming a continuous connection and data transferred at 34 kbit/s. What is the traffic if the call is terminated at 2-45am?Solution:

Traffic = (1 call)*(45 min)*(1 hour /60 min) = 0.75 Erlangs.

It’s nothing to do with the data rate of communication, only the call holding time.

A group of 20 subscribers generate 50 calls with an average holding time of 3 minutes, what is the average traffic per subscriber?

Example 4

Solution:Traffic = (50 calls)*(3min)*(1 hour/60 min)

= 2.5 Erlangs Average traffic per subscriber = 2.5 / 20

= 0.125 Erlangs per subscriber.

Individual (residential) calling rates are quite low and may be expressed in milli-Erlangs, i.e. 0.125 Erlangs = 125 milli-Erlangs.

There are 100 subscribers with the following telephone traffic

profile: 20 make 1 call/hour for 6 minutes; 20 make 3 calls/hour for half a minute; 60 make 1 call/hour for 1 minute.

Example 5

Solution:The traffic they generate is:

20x1x (6/60) = 2 E20x3x(0.5/60) = 0.5 E60x1x(1/60) = 1 E

a total traffic of 3.5 E.

On average, each subscriber generates 3.5/100 = 35 mE.In practice on average telephone subscribers generate between 25 to 35 mE during the busiest hour

Grade of Service, GoS Grade of Service is a measure of the probability

that a percentage of the offered traffic will be blocked or delayed. ◦ the ability to interconnect users ◦ the rapidity with which that connection is made

Commonly expressed as the fraction of calls or demand that◦ fails to receive immediate service (blocked

calls)◦ is forced to wait longer than a given time

(delayed calls)

For example, if GOS = 0.05, one call in 20 will be blocked during the busiest hour because of insufficient

Grade of Service, B

B = Lost traffic Offered traffic

OrB = Lost call

Offered call

Grade of Service (GoS)

Grade of Service (GoS)A measure of the performance of a telephone

systemGOS is a measure of the ability of a user to

access a trunked system during the busiest hourAlso an indication of the user not being able to

secure a channel during the busiest hourTelephone networks are designed with specified

GOS, usually for the busiest hour. If a subscriber is able to make a call during the busiest hour, he will be able to make a call at any other time

Grade Of Service, B is used to observe and measure how many calls are offered, carried and lost in the system.

The lower this number, the higher the GOS.

B = Number of calls lost

Number of calls offered

B = Traffic lost

Traffic offered

Offered TrafficThe offered traffic: Volume of traffic offered to a switch

that are all processed is defined as:

Offered traffic = carried traffic + overflow

The carried traffic: The actual traffic carried by a switch.

Overflow (blocked) traffic: Portion of the traffic not processed.

Busy Hour Call Attempts (BHCA)• Used to evaluate and plan capacity for telephone networks• Is the number of telephone calls made at the peak hour• The higher the BHCA, the higher the stress on the network processors.• Not to be confused with Busy Hour Call Completion (BHCC), which truly measures the throughput capacity of the network.

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For example, if GOS = 0.05, one call in 20 will be blocked during the busiest hour because of insufficient capacity

For 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.

Example 6 1200 calls are offered to a channel and 6

calls are lost. Duration of a call is 3 minutes. Find:a) Offered traffic, Ab) Carried trafficc) Lost trafficd) GOS, Be) Congestion time

Solution:

a) A = CH/T = (1200 x 3) / 60 = 60 Eb) Carried traffic = [(1200-6) x 3] / 60 = 59.7 Ec) Lost traffic = (6 x 3) / 60 = 0.3 Ed) B = Lost traffic / Offered traffic

= 6/1200 = 0.005

e) Congestion time = B x 1 hours (second)= 0.005 x 60 x 60

= 18 seconds

On average during the busy hour, a company makes 120 outgoing calls of average duration 2 minutes. it receives 200 incoming calls of average duration 3 minutes. Find;◦ A. The outgoing traffic◦ B. The incoming traffic◦ C. The total traffic

Example 7

A. The outgoing traffic is 120 x 2/60 = 4E B. The incoming traffic is 200 x 3/60 = 10E C. Total Traffic is 4E + 10E = 14E

Solution: