Telephone Traffic calculations

1. Telephone Traffic
Engineering
TELEPHONY ONLINE NOTES

2. TOPIC LEARNING OUTCOME
• Demonstrate the ability to implement design in according to
quality measurement standards for telephone traffic engineering.

3. Telephone Traffic Engineering
• It is the collection and study of traffic data and the monitoring of the performance of a
network.
• It is a powerful tool for determining the correct size of a network.
• Except for station sets and their associated loops, a telephone network is composed of a
variety of common equipment such as digit receivers, call processors, inter-stage
switching links, and interoffice trunks. The amount of common equipment designed
into a network is determined under an assumption that not all users of the network
need service at one time. The exact amount of common equipment required is
unpredictable because of the random nature of the service requests.

4. Telephone Traffic Engineering
• Networks conceivably could be designed with enough common equipment to
instantly service all requests except for occurrences of very rare or unanticipated
peaks. However this solution is uneconomical because much of the common
equipment is unused during normal network loads.
• The basic goal of traffic analysis is to provide a method for determining the
cost-effectiveness of various sizes and configurations of networks.

5. TERMINOLOGY
• Busy Hour
- The continuous one – hour period that,
on consecutive days in the busy part of
the year, contains the maximum average
traffic intensity.
• Call
- A discrete engagement or occupation of
a traffic path.
• Calling Rate
- The average number of calls placed
during the busy hour.
• Occupancy
- The traffic intensity per traffic path.
100% occupancy means all paths busy.

6. TERMINOLOGY
• Traffic Concentration
- The average ratio of the traffic quantity
during the busy hour to the traffic
quantity during the day.
• Traffic Intensity
- The average number of calls present on
a group of traffic paths over a period of
time.
• Traffic path
- A channel, time slot, frequency band,
line, trunk, switch, or circuit over
which individual communications pass
in sequence.
• Traffic quantity
- The aggregate engagement time or
occupancy time of one or more traffic
paths.

7. TERMINOLOGY
• Call Intensity
- For many traffic – carrying elements, the number of calls making
up the total traffic load is immaterial; the load represented by two
calls or ten minutes duration has the same impact as one call of
twenty minutes duration.

8. TRAFFIC UNIT
• Erlang
- The international dimensionless unit of
traffic intensity. One erlang is the traffic
intensity represented by an average one
busy circuit out of a group of circuits over
some period of time.
• Traffic Unit (TU)
- 1 TU is the average intensity in one or
more traffic paths carrying an aggregate
traffic of 1 call – hour in 1 hour (the busy
hour unless otherwise specified.
• Equated Busy – Hour Call (EBHC)
- 1 EBHC is the average intensity in one or
more traffic paths occupied in the busy –
hour by one 2-min call or an aggregate
duration of 2 min.
- A European unit of traffic intensity equal
to 1/30 of an erlang.
• Call - Hour
- The quantity represented by one or more
calls having an aggregate duration of 1
hour.

9. TRAFFIC UNIT
• Century or Hundred call second per
hour (CCS)
- A unit of traffic intensity equal to 1/36 of
an erlang.
• Call – minute (Cm)
- 1 Cm is the quantity represented by one
ore more calls having an aggregate
duration of 1 minute.
• Call – second (Cs)
- 1 Cs is the quantity represented by one
or more calls having an aggregate
duration of 1 second.
 The term “ccs” is unfortunately in
common usage when traffic intensity, not
traffic volume is described. Strictly
speaking ‘ccs/hr’ should be used for traffic
intensity and ccs for traffic volume.

10. TRAFFIC UNIT
• Relation between different traffic units:
1 Erlang = 1 TU = 1 Ch = 60 Cm = 3600 Cs = 36 CCS = 30 EBHC
The erlang (symbol E) is a dimensionless unit that is used in telephony as a
measure of offered load or carried load on service-providing elements such as
telephone circuits or telephone switching equipment.
A single cord circuit has the capacity to be used for 60 minutes in one hour.
Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang.

11. Calling Rate (C)
• The number of times a route or traffic path is used per unit period, or more
properly defined, “the call intensity per traffic path during the busy hour.”
• Average number of calls initiated per unit time (e.g. attempts per hour) a.k.a.
Arrival Rate
• For n receive calls from a terminal in time t:
𝑪 =
𝒏
𝒕
• For n receive calls from m terminals in time t:
a) Group calling Rate: 𝑪𝒈𝒓𝒐𝒖𝒑 =
𝒏
𝒕
b) Per terminal calling rate : 𝑪 =
𝒏
𝒎𝒙𝒕

12. Holding time (T) Departure Rate ()
• The duration of occupancy of a
traffic path by a call.
• Sometimes used to mean the average
duration of occupancy of one or
more paths by calls.
•  =
1
𝑇
, calls per hour
Where: T = mean holding time per call
• The reciprocal of Holding Time
• Also known as Service Rate

13. Traffic Volume (usually in ccs)
V = n x T
Where:
V = volume of calls in time t
n = # of calls in time period t
T = mean holding time per call

14. Traffic Intensity (A)
• Traffic Intensity or traffic flow is a total traffic volume divided by the
duration of time
• For a single terminal:
- The traffic in Erlang is the average occupancy of the terminal while
the traffic intensity or traffic flow is just the percentage of time the
terminal is busy.

15. Traffic Intensity (A)
• For a group of circuits or terminal:
a) The average number of circuits simultaneously busy within a group
b) The expected number of call arrivals per unit holding time
c) The number of circuits required to completely carry the offered
traffic if each circuit were operating at 100% occupancy.

16. Traffic Intensity (A)
• Formulas:
• Where: A = Traffic intensity in Erlang n = # of calls in time period t
T = mean holding time per call t = time period of observations
C = calling rate  = departure rate
V = volume of calls

17. TO TC TL
• Offered Traffic (To)
- Offered traffic is the traffic intensity that would occur if all traffic submitted to a group of
circuits could be processed.
- The volume of traffic offered to a switch.
• Carrier Traffic (Tc)
- Carried traffic is the traffic intensity handled by the group of circuits
- The volume of traffic actually carried by a switch
• Lost Traffic (TL)
- Blocked traffic is that portion of traffic that cannot be processed by the group of circuits.
- The difference between the offered traffic and carried traffic

18. TO , TC , TL
• Relation between TO , TC , and TL
where P = Blocking Probability or Call Congestion

19. Grade of Service (GOS) or Blocking Probability(P(B))
• A measure of probability that, during a specified period of peak traffic, a call
offered to a group of trunks of circuits will fail to find an idle circuit at the first
attempt.
• Usually applied to the busy hour of traffic.

20. Grade of Service (GOS) or Blocking Probability(P(B))
• is the probability of a call in a circuit group being blocked or delayed for more
than a specified interval, expressed as a vulgar fraction or decimal.
• This is always with reference to the busy hour when the traffic intensity is the
greatest.

21. Illustration of Basic Relation between Offered Traffic, Carried Traffic,
Grade of Service and Trunk Utilization

22. BLOCKING PROBABILITY
• Call-blocking probabilities are among the
key performance measures in mobile
communications networks.
• For their analysis, mobile networks can
be modelled as networks of Erlang loss
queues with common capacity
restrictions dictated by the allocation of
frequencies to the cells of the network.

23. 1. Lost Calls Cleared (Blocked Calls Cleared)
• The LCC concept, which is used primarily in Europe or those countries accepting
European practice, assumes that the user will hang up and wait some time
interval before reattempting if the user hears the congestion signal on the first
attempt. Such calls, it is assumed, disappear from the system.
• The assumption that calls not immediately satisfied at the first attempt are
cleared from the system and do not reappear during the period under
consideration.
• Used in the Erlang B Loss probability equation.

24. 1. Lost Calls Cleared (Blocked Calls Cleared)

25. Utilization Ratio, 
•  =
𝑡𝑖𝑚𝑒 𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦 𝑖𝑠 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑
𝑡𝑖𝑚𝑒 𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦 𝑖𝑠 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒
or
•  =
(1 −𝐵)(𝐴)
𝑛
Where: B = the probability of blockage, (PB)
n = no. of servers
A = traffic intensity

26. 2. Lost Calls Delayed (Blocked Calls Wait)
• The LCD concept assumes that the user is automatically put in queue (a
waiting line or pool). For example, this is done when the operator is
dialed. It is also done on most modern – controlled switching systems,
generally referred to under the blanket term stored program control
(SPC).
• The assumption that calls not immediately satisfied at the first attempt
are held in the system until satisfied.
• Used in the Erlang C delay – probability equation

27. 2. Lost Calls Delayed (Blocked Calls Wait)

28. 3. Lost Calls Held (Blocked Calls Held)
• The LCH concept, which is the principal traffic formula used in North America,
assumes that the telephone user will immediately reattempt the call on receipt of a
congestion signal and will continue to redial. This concept further assumes that such
lost calls extend the average holding time theoretically, and in this case the average
holding time is zero, and all the time is waiting time.
• The assumption that calls not immediately satisfied at the first attempt are held in
the system until served or abandoned.
• Used in the Poisson loss – probability equation.

29. 3. Lost Calls Held (Blocked Calls Held)

30. CONGESTION
• TIME CONGESTION
- Proportion of time a system is congested (all servers busy)
- Probability of blocking from point of view of servers
• CALL CONGESTION
- Probability that an arriving call is blocked
- Probability of blocking from point of view of calls

31. Sample Problems:
1. If there exist a total of 151 calls in the BH and the average holding time is 3 minutes per call,
Determine the traffic density.

32. 2. Twenty customers are to be handled in the peak hour; the operator takes 2 minutes per client.
Determine the following:
a) Traffic Intensity in Erlang, ccs.
b) Traffic Quantity in Cmin, Cs.
c) Utilization Ratio, 

33. 3. Customers come to a payphone center (with 3 phone booths) at a rate of 3 persons every 6
minutes and make a call on an average of 4 minutes. Determine:
a) GoS
b) utilization ratio, 

34. 4. Given a message switching node that normally experiences 4 arrivals per minute, what is the
probability that 8 or more arrivals occur in an arbitrary chosen 30 second interval?

35. 5. Suppose the average holding time is 2.5min per call and the calling rate in the BH for a particular day
is 237. Determine the traffic flow (A) in Cm and Ch.
6. Call established at 2AM 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 2:45 AM?

36. 7. A group of 20 subscribers generate 50 calls with an average holding time of 3 minutes, what is the
average traffic per subscriber?
8. Calculate the trunk efficiency for a group of 26 trunks that offers 10 Erlangs of traffic and a blcking
probability of 0.2%.

37. 9. If we know that there are 354 seizures (lines connected for service) and 6 blocked calls (lost calls)
during the BH, what is the GoS?
10. Suppose we use 5 trunks, and the route offered 1.66 Erlangs of traffic. Calculate the GoS required to
implement this configuration.

38. 11. On a particular traffic relation the calling rate is 461 (calls in a 1-hr period) and the average call
duration is 1.5 minutes during the busy hour. What is the traffic intensity in Erlangs? ccs?

39. 12. Company X has 10 employees, each placing an average of 20 minutes of long – distance calls per day.
The average call lasts 5 minutes. It has been determined that 20% of the calls are made during the busy
hour. A total of 4 external phone lines are used to place the pool of calls. Calculate the traffic intensity in
Erlang, during the busy hour.

40. 13. Suppose 100 data terminals are to be connected to a computer by way of leased circuits:
1st plan: the terminals are clustered into four groups that use separate groups of shared circuits.
2nd plan: Traffic from all terminals is concentrated into one group of circuits.
Determine the cluster traffic in both cases assuming each terminal is active 10% of the time