1.0 Introduction

2.0 Traffic Models

3.0 Traffic Analysis

4.0 Traffic Analysis in Circuit Switched Systems

 1.0 Introduction

Teletraffic engineering is the application of probability theory to the solution of problems concerning planning, performance evaluation, operation, and maintenance of telecommunication systems. Teletraffic engineering c covers all kinds of circuit switched and packet switched traffic. The theory will primarily be illustrated by examples from telephone and data communication systems. The tools developed are, however, independent of the technology and applicable within other areas such as road traffic, air traffic, manufacturing, distribution, workshop and storage management, and all kinds of service systems.


The objective of teletraffic theory is to make the traffic measurable in well defined units through mathematical models and to derive relationships between grade-of-service and system capacity in such a way that the theory becomes a tool by which investments in telecommunication infrastructure can be efficiently developed and deployed.


The theory is used to design cost effective systems with a predefined grade of service when we can estimate the future traffic demand. The theory is also used to specify methods for controlling and ensuring  that the actual grade of service is fulfing the requirements, and also to specify emergency actions when systems are overloaded or technical faults occur. This requires methods for forecasting the demand (for instance based on traffic measurements), methods for calculating the capacity of the systems, and specification of quantitative measures for the grade of service.



Except for user terminals, the telephone network is composed of a variety of common equipment such as call processors and trunks. The quantities of the common equipment is usually determined under the assumption that not all users of the telecommunication network require service at the same time. The basic goal in traffic analysis is therefore  to provide a method for determining the cost effectiveness of the number of common network equipment and their configurations.


Teletraffic can be divided into two categories depending on how the system treats overload traffic. These are:

(a) Loss systems where overload traffic is rejected

(b) Delay systems where overload traffic is held in a queue until a facility is available to service the load.


2.1 Loss Systems

In loss systems, excess traffic is blocked and not serviced without a retry by the user.

In most cases the lost calls during blockage represent a loss of revenue by the telecommunications operator. Conventional circuit switched telecommunication systems are loss systems.


2.2 Delay/Queue Systems

Store and Forward Message/Packet Switching possess the characteristics of a delay system. However, in exceptional  cases, packet switched system may have some aspects of a loss system as a result of limited queue sizes and existence of virtual circuits.



In  applied mathematics,  blocking probability analysis are studied under congestion theory while delay probability studies are covered under queuing theory.

In telecommunications, these topics usually referred to as traffic flow analysis. Traffic analysis in circuit switched systems is more concerned with the holding times of network facilities rather than the flow of messages in individual circuits. In message switching and packet switching systems traffic analysis  is more concerned with the actual flow of information.


3.0 Traffic Analysis in Circuit Switched Systems

There are two underlying random processes in circuit switched networks:

(a) Call arrivals  which occur purely by chance and each users arrival is therefore independent from that of other users

(b) Holding times of each call which are usually random in circuit switched systems. Holding times may be made constant by using fixed length packets in virtual switched networks.


Figure 1. Traffic activity in a circuit switched telecommunication network


A common measure of traffic capacity is the volume of traffic carried over a period of time. Traffic volume is the sum of all holding times in an interval. It can be computed by taking the area under the composite activity curve.



Figure 1. Traffic Capacity as the area under the activity curve


Traffic intensity is represents the average activity during a period of time. It can be obtained by dividing Traffic volume  by the length of time during which it was measured. Traffic intensity is measured in erlangs after the Danish pioneer mathematician A.K. Erlang. The maximum capacity of a single server is 1 erlang while the maximum capacity of a group of servers is equal to the number of servers.

Traffic Intensity in erlangs can be calculated as


Where  Lambda is the average call arrival rate and h  is the average holding time.


The busy Hour

Telecommunication systems carry varying traffic during the day. The traffic pattern generally follows the average activity of people during the day. Generally, these are times at night when most people are asleep and traffic is very low. Early in the morning, most people are travelling to their places of work or engagement, e.g offices, industries, schools worshiping and traffic is average. In the mid morning and mid afternoon business-based telephone traffic creates peak traffic. Early in the evening most people are likely call friends and relatives yielding above average traffic. Figure x shows a typical traffic graph for fixed telecommunication traffic.


The result is that there is varying traffic intensities on a normal day which must be captured by planners of telecommunication systems. To capture the above, telephone traffic is usually analysed based on traffic activity in the busiest hour of the day (commonly referred to as busy hour). Busy hour is defined as the sliding 60-minute period when  the maximum total traffic load occurs  in a  24-hour period.

                                                                                                                                                        ©  Prof. Ambani Kulubi May-Aug 2015