Teletraffic Theory

Teletraffic Theory is a branch of engineering mathematics that studies the behavior and performance of telecommunication networks. While it provides a solid theoretical foundation to evaluate the performance of existing networks, the most important practical aspect of teletraffic theory is its use in the network dimensioning process.

A.K. Erlang

History of Teletraffic Theory goes back to the early 20th century, when Danish schoolmaster A.K. Erlang (1878-1929) worked out a formula, now known as Erlang's formula, to evaluate the performance of the village telephone exchange.

In simple terms teletraffic theory forms a relationship between the following three quantities:

traffic offered to the network/system
quality/grade of service
network/system resources

For example teletraffic theory tells us how many users will be refused service if a given number of users (with well defined call arrival and call length distributions) try to access a certain set of telephone lines or what is the average packet delay for a certain Internet user. On the other hand it tells a network designer how many lines are required to serve a certain user population given that they must not experience blocking probabilities greater than a given threshold. During the early to mid 1900's teletraffic theory was developed as an application of queuing theory in the area of telecommunication systems. Simple telephone networks were modelled using distributions with Markovian properties, which simplifies the modelling process to a great extent. However, with the introduction of new types of networks and applications, such as video conferencing over the Internet, teletraffic theory has been broaden to a accommodate a diverse range of probability distributions as well as queuing strategies and networks.

Recent research has shown that packet traffic, including Internet traffic, shows Self-Similar behavior over a wide range of time scales. This opened up a range of new research into teletraffic analysis of the Internet which resulted in much improved general understanding of the Internet. It also helped make predictions on future resource requirement of the Internet. However the study of self-similarity in a queuing network is extremely complicated and currently efforts are being made to approximate the self-similar traffic models with higher order Markovian models.

Proper understanding of the behavior of traffic is essential in controlling or regulating the traffic in networks. Over the years teletraffic theory has been successfully used in devising mechanisms to control congestion in ATM networks and currently efforts have been made to apply mechanisms based on teletraffic theory to regulate Internet traffic.

Key Research Challenges

One of the key current challenges for the Teletraffic Theory is to define simple but accurate traffic models to describe the traffic patterns of data networks, including the Internet. Furthermore the study of complex structures of current data networks is essential in dimensioning them to satisfy the needs of future generations. Some of the specific projects that can be considered under the program may include:

Modelling Self-Similarity as a higher order Markovian Models
Modelling modern data networks
Traffic modelling in cellular/satellite communication networks
Dimensioning high-speed data networks
Mathematical methods for congestion control in Internet
Modelling service expectations of users and service provision capabilities of network providers