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Traffic Theory

Traffic denotes the aggregate flow of massage thought a

telecommunications system. Traffic engineering applies mathematical tools for

dimensioning telephone facilities so that they can accommodate the massage

flow in a way that provides satisfactory service to the user while making

economical use of the facilities providing the service.

Agner Krarup Erlang was born in 1878 in Lonborg, Denmark.   He was a

pioneer in the study of telecommunications traffic and, through his studies,

proposed a formula to calculate the fraction of callers served by a village

exchange who would have to wait when attempting to place a call to someone

outside the village.

1.1. Definitions of Some Common Telephone Traffic Terms/Assumptions

Lost Call Cleared (LCC): Call not immediately satisfied at first attempt are

cleared from the system and do not reappear during the period of

consideration [used with the Erlang B formula (Section 1-4) and the Engset

formula (Section 1-6)

Lost Call Delayed (LCD): Calls not immediately satisfied are held in the system

until satisfied [used with the Erlang C formula (Section 1-5)].

Lost Call Held (LCH): Calls not immediately satisfied at first attempt are held in

the system for a period not to exceed the average holding time of all calls and

thereafter cleared from the system [used with the Poisson formula (Section 1-3)

and the Binomial formula (Section 1-6)].

Busy Hour (BH): The continuous 1-hours period of the day that has maximum

average traffic intensity. (See the four BH definitions at the end of this section.)

Call: A disserted usage or occupation of a traffic path, real or virtual.

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Call-Hour (CH or ch): A unit of traffic density. One call-hour is the quantity

represented by one or more call having an aggregate duration of 1 hour.

1 CH = 36ccs = 60 call-minutes = 3600 call-seconds.

Calling Rate: The call intensity per traffic path during the BH.

Call-Minute (Cmin): A unit of traffic density (or intensity). It is the quantity

represented by one or more calls having an aggregate duration of 1 minute.

Call-Second (Cs): A unit of traffic density (or intensity), where 1 Cs is the

quantity represented by one or more calls having an aggregate duration of 1

Second.

CCS (“Centum” Call-Second): A unit of traffic intensity used primarily in USA

and Canada. 1 ccs is the quantity represented by one 100 Cs of traffic (centum

derived from the Latin meaning 100, and C being the Roman numeral indicating

100).

Equated Busy-Hour Call (EBHC): A unit of traffic density (or intensity) used in

European practice, where 1 EBHC is the traffic intensity in one or more traffic

paths occupied in the BH by one 2-minute call or for an aggregate duration of 2

minutes. 30 EBHC=1 Erlang.

Erlang (E): The internationally accepted dimensionless unit of traffic intensity,

where 1 E is the intensity in a traffic path occupied continuously or in one or

more paths carrying an aggregate traffic intensity of 1 call-hour per hour, 1 call-

minute per minute , and so forth,

Full-Availability Group: A group of traffic-carrying trunk or circuits in which

every circuit is accessible to all the traffic sources.

Grade of service: A measure of the probability that during a specified period of

peak traffic, usually the BH, a call offered to a group of trunks or circuits will fail

to find an idle circuit at first attempt.

Holding Time: The duration of occupancy of a traffic path by a call. At times it

is used to mean the average duration of occupancy of one or more paths by

calls.

Infinite Sources: The assumption that the number of traffic source offered to a

group of trunk or circuits is large in comparison with the number of circuits. A

ratio of 20 or greater is considered infinite.

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Limited-Access Group: A group of traffic-carrying trunks or circuits in which

only a fraction of the circuits accessible to any one group of the traffic sources.

Limited Sources: The assumption that the number of sources offering traffic to

a group of trunks or circuits does not exceed a specified number.

Occupancy: An expression of traffic intensity (or density) in one or more traffic

paths. By definition, 100% occupancy of one path equals 1 Erlang.

Traffic Density, Traffic Load: Synonymous with traffic intensity. Sometimes in

the literature, only the term traffic is used.

Traffic Path: A channel, time slot, line, trunk, frequency slot, switch, or circuit

over witch individual communications pass in sequence.

Traffic Quantity: The aggregate engagement time or occupancy of one or more

traffic paths.

Traffic Rate: The intensity per traffic path during the BH.

Traffic Unit (TU): A unit of traffic intensity (density), where 1 TU is the average traffic intensity in one or more traffic paths carrying an aggregate traffic of 1 call-hour in 1 hour. This is the BH unless otherwise specified. Numerically, 1 TU=1 ErlangUnit Call (UC): A unit of traffic intensity (density), where 1 UC is the average traffic intensity in one or more traffic paths occupied during 1 hour by one 100-second call or for an aggregate duration of 100 second. 36 UC=1 Erlang.

(From Freeman, Telecommunication System Engineering [Ref.1]

SOME ACCEPED DEFINTIONS OF THE BUSY HOUR (BH)

The average of the BH traffic on the 5 busiest day of the year. CCITT Recommendations Q.80 and Q.87 referring to traffic on “exceptionally busy day.”

The average of the BH traffic on the 10 busiest day of the year. A standard often used in North America.

The average of the BH traffic on the 30 busiest day of the year. CCITT Recommendations Q.80 definition of “mean busy-hour traffic.”

The average weekday (Monday through Friday) reading over 1 or 2 weeks in the (know) busy session. Normal practice for manual traffic observation.

From Telecommunication Planning, Section 3, “Networks” [Ref. 2]

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1.2 An Erlang is a unit of telecommunications traffic measurement.  Strictly speaking, an Erlang represents the continuous use of one voice path.  In practice, it is used to describe the total traffic volume of one hour.

For example, if a group of user made 30 calls in one hour, and each call had an average call duration of 5 minutes, then the number of Erlangs this group represents is worked out as follows:

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

Minutes of traffic in the hour = 30 x 5

Minutes of traffic in the hour = 150

Hours of traffic in the hour = 150 / 60

Hours of traffic in the hour = 2.5

Traffic figure =2.5 Erlangs

1.3 An Introduction to Congestion Theory and a

Summary of Traffic Formulas

The section describes basic congestion theory (or blocking theory) and

introduces related formula as well as traffic behavioural assumptions. The basic

traffic formulas are summarized and their applications are discussed.

Traffic is the aggregate of messages using a group of circuits, trunks, or

other shared equipment or facilities and is define in terms of both the duration

and the number of message. Traffic flow thought a telecommunications system,

or part of it, is the product of the number of massage (calls) during a specified

period of time and their average duration (holding time). Using 1 hour as the unit

of time, traffic flow, A, can be excrescent as follows:

A= CT

Where C is the number of massage (calls) originated in 1 hour and T is

the average holding time.

Basic considerations in traffic engineering are:

the volume and characteristics of traffic to be carried

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the facilities used to meet the demand, and

the grade of service desired.

Traffic theory is a specialized application of mathematical statistics, using

models to simulate actual situations. It is important to remember that the

accuracy of estimates made using traffic theory is no better than the closeness

of the models to reality.

Congestion theory (or blocking theory) is the term used to designate the

various method of evaluating the ability of telephone facilities to handle traffic

loads that may be impose on them.

Several statistics-based formulas have been developed to express the

relationship between traffic loads and grades of service.

The simple computer programs and the traffic capacity tables have been derived

using these formulas.

The chief concerns of the traffic engineer and of the telecommunications

industry are the call, whether it is voice connection between humans or a data

connection between machines, and the ability of the telecommunications system

to complete the. Calls, local and long distance (toll), are made by individual

users in accordance with business and personal needs, whims, and desires.

Individual subscriber lines are associated with:

telecommunications facilities in groups (such as line group),

multiplexer inputs, and

complete switching entities (packet switches, telephone central offices);

the calls; although made individually, occur in groups.

The number of call in progress simultaneously from a group of users in a

unit follows a pattern that fluctuates thought out the day. The traffic engineer

must specify sufficient facilities in each stage of the telecommunications system

to provide a satisfactory grade of service during periods of maximum demand)

busy hour).

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The aforementioned grade of service is usually expressed in terms of lost

calls (or blocked calls). A term used to denote those calls that find all facilities

busy in the group to which they are offered at the instant they are offered. It will

be noted later that there are different interpretations regarding the disposition of

lost calls, which lead to different formulas for congestion.

An Erlang is a unit of telecommunications traffic measurement.  Strictly

speaking, an Erlang represents the continuous use of one voice path.  In

practice, it is used to describe the total traffic volume of one hour.

1.4 Dimensioning Trunks:

So, a way of estimating the number of lines required for a known value of

offered traffic is required. This is available in the form of the Erlang B traffic

mode which requires the following inputs:

Busy Hour Traffic

Blocking

1.5 Busy Hour Traffic (B.H.T.)

This figure represents the quantity of traffic expressed in a unit called

Erlangs. For the purposes of these calculations, 1 Erlang can be considered

equivalent to 1 hour of call.

You will need to provide an estimate for this figure, which represents the

number of hours of traffic which is offered to a trunk group in its busiest hour.

For example, if you know from your call logger that 350 calls are made

on a trunk group, and the average call duration is 180 seconds, then the busy

hour traffic will be:

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BHT = Average call duration (s) * Calls per hour / 3600

BHT = 180 * 350 / 3600

BHT = 17.5 Erlangs

1.6 Blocking

The blocking figure describes the calls which cannot be completed

because insufficient lines have been provided.

A figure of 0.01 means that 1% of calls would be blocked; this is a normal

figure to use in traffic engineering.

For some applications, 0.03 (3%) blocking is used.

It is also called grade of service (GOS). It my be defined as “percentage

of call that may be allowed to fail for optimum utilization of equipment”.

1.7 ERLANG B TRAFFIC TABLE- FULL AVAILABILITY GROUPS

The Erlang B formula is used to determine the number of trunks, switches, and other traffic-carrying facilities required when such facilities are arranged in full availability groups. The Erlang B formula assumes the following:

Traffic source are infinite Calls occur at random

Holding time either are constant or vary exponentially.

Lost calls are cleared(i.e. a call failing to find a channel immediately disappears from the system and the channel through which the call was made becomes idle again, and its holding time is zero; the call will not return in the same study period, such as the busy hour).

In the Erlang B traffic table , the probabilities of loss, as shown in decimals, indicate the proportions of call attempt that will find all facilities occupied. The number of channels (trunks) per group covers a range from 1 to

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200, and the range of probabilities covers the useful limits for most engineering problems. The tables are structured such that for a given grade of service (GOS) i.e. probability of delay or probability of blockage),it is possible to determine:

The number of channels(trunks) required per group if the traffic load (in Erlangs or CCS) is known or

The traffic capacity (in Erlangs or CCS) if the number of channels(trunks) is known.

Example calculation:

Having established these two parameters, an estimate of the number of lines required can be made using the Erlang B Traffic Model. We can use online calculator to work through this example or Erlang B Traffic Table.

BHT = 17.986 Erlangs Blocking = 0.01

No. of trunks required are = 28.