Subject Name: Digital Switching Systems
Subject Code:10EC82
Prepared By: Aparna.P, Farha Kowser
Department: Electronics and Communication
Date:3-3-2015
3/14/2016
Unit 3
Telecommunication Traffic
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Unit of traffic
Congestion
Traffic measurement
GOS
Mathematical Model of traffic
Lost call systems
Queueing systems
TRAFFIC DESIGN REQUIREMENTS
• In the study of tele traffic engineering, to model a
system and to analyze the change in traffic after
designing, the static characteristics of an exchange
should be studied. The incoming traffic undergoes
variations in many ways.
• The traffic is unpredictable and random in nature. So,
the traffic pattern/characteristics of an exchange
should be analyzed for the system design. The grade
of service and the blocking probability are also
important parameters for the traffic study.
Traffic Statistics
• The following statistical information provides answer
for the requirement of trunk circuits for a given
volume of offered traffic and grade of service to
interconnect the end offices. The statistical
descriptions of a traffic is important for the analysis
and design of any switching network.
• Calling rate
• Holding time
• Distribution of destinations.
• User behavior
• Average occupancy
Traffic Pattern
• An understanding of the nature of telephone traffic and its
distribution with respect to time (traffic load) which is
normally 24 hours is essential. It helps in determining the
amount of lines required to serve the subscriber needs.
• The variations are not uniform and varies season to season,
month to month, day to day and hour to hour.
• Busy hour. Traditionally, a telecommunication facility is
engineered on the intensity
• of traffic during the busy hour in the busy session.
• Taking into account the fluctuations in traffic, CCITT in its
recommendations E.600 defined the busy hour as follows.
• Busy hour. Continuous 60 minutes interval for which
the traffic volume or the number of call attempts is
greatest.
• Peak busy hour. It is the busy hour each day varies
from day to day, over a number of days.
• Time consistent busy hour. The 1 hour period
starting at the same time each day for which the
average traffic volume or the number of call attempts
is greatest over the days under consideration.
Call completion rate (CCR). Based on the
status of the called subscriber or the design of
switching system the call attempted may be
successful or not. The call completion rate is
defined as the ratio of the number of successful
calls to the number of call attempts.
Busy hour call attempts
Busy hour calling rate.
Day-to-day hour traffic ratio
Units of Telephone Traffic
• Traffic intensity is measured in two ways.
They are (a) Erlangs and (b) Cent call seconds
(CCS).
• Erlangs. The international unit of traffic is the
Erlangs. It is named after the Danish
• Mathematician, Agner Krarup Erlang, who
laid the foundation to traffic theory in the work
he did for the copenhagen telephone company
starting 1908.
• Grade of Service (GOS)
• For non-blocking service of an exchange, it is
necessary to provide as many lines as there are
subscribers. But it is not economical. So, some calls
have to be rejected and retried when the lines are
being used by other subscribers.
• The grade of service refers to the proportion of
unsuccessful calls relative to the total number of calls.
GOS is defined as the ratio of lost traffic to offered
traffic.
Blocking Probability and Congestion
• The value of the blocking probability is one aspect of
the telephone company’s grade of service.
• Based on the number of rejected calls, GOS is
calculated, whereas by observing the busy servers in
the switching system, blocking probability will be
calculated.
• When the number of sources is large, the probability
of a new call arising is independent of the number
already in progress and therefore the call congestion
is equal to time congestion.
MODELLING OF TRAFFIC
• To analyze the statistical characteristics of a
switching system, traffic flow and service time, it is
necessary to have a mathematical model of the traffic
offered to telecommunication systems.
• The facilities of the switching systems are shared by
many users. This arrangement may introduce the
possibility of call setup inability due to lack of
available facilities.
• The mathematical description of the queueing system
characterics is called a queueing model.
Lost Calls Cleared (LCC) System
• The LCC model assumes that, the subscriber who
does not avail the service, hangs up the call, and tries
later.
• The first person to account fully and accurately for
the effect of cleared calls in the calculation of
blocking probabilities was A.K. Erlang in 1917.
• The Erlang loss system can be modeled by birth and
death process with birth and death rate as follows.
Queueing Systems
• In this the call will not lost it will be delayed
• The assumptions are
 Pure chance traffic
 Statistical Equilibrium
 Full availability
 Calls which encounter congestion
enter into a queue and stored until a
server becomes free.
Queueing Systems
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Second Erlang’s Distribution
Let x be the no.of calls in the System.
When x<N ,then x calls are being
served and there is no delay. When
x>N, all the servers are busy and
incoming calls encounter delay; there
are N calls Served and x-N calls in
the queue.
IF x≤N:
There is no queue the system will act
as lost call system in the absence of
congestion.
Queueing Systems
• If x>N:
The probability of a call arrival during time δt is given by
The Probability of a transition from x-1 to x is given by
The probability of call ending is given by
The transition probability from x to x-1 is given by
Queueing Systems
Queueing Systems
If there is no limit for the queue x can have any value between 0 and ∞
We can write
This is second erlangs Distribution formula
Queueing Systems
• Probability of Delay.
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Delay occurs if all servers are busy, the probability that there are at least Z
calls in the system is given by
Queueing Systems
This is called Erlang’s delay formula