Trafico

An introduction to teletraffic
BY ARNE MYSKJA

1 Introduction
This article is intended to be a broad introduction to the subject of teletraffic, particularly written for a special teletraffic issue of the journal Telektronikk. The presumed readers are primarily telecommunications engineers, but also others who have an interest in the subject of teletraffic, without being – or wanting to be –an expert in that particular area. Traffic theory is covered by numerous textbooks as well as by an impressive amount of papers found foremost in the records of ITC (International Teletraffic Congress). A particular support has been the textbook “Data- og teletrafikteori” [1] by Villy Bæk Iversen. With this stated intention it might seem an easier task, since the burden of mathematical rigor tosome extent is relieved. On the other hand, the development of mathematical theory for the purpose of modelling, dimensioning and optimisation of telecommunications systems has turned out to be among the most powerful tools available. A non-mathematical description can never catch some of the most important aspects of the task. The question I have posed is: Can one make easy reading out of acomplicated matter? My pragmatic choice is to aim at simple textual explanations and to use fairly simple mathematics supplemented by illustrations in the forms of functional diagrams, curves, tables, etc. Some elaboration on distributions, as well as deduction of formulas, have been put into “boxes” that can be studied separately. Even there the reader will find little use of “higher” mathematics. Basicarithmetic is supplemented by simple integrals, exponential functions and a limited use of Laplace- and Z-transforms. Some readers may be unfamiliar with – and even a little scared by – transforms. I want to stress the simplicity of concept and the usefulness of those transforms. The presentation is coloured by my particular interests. Thus, my background in telephone traffic measurements as wellas modelling by moment matching and repeated calls studies has certainly had its influence. Still, I hope the general view of traffic is predominant. There is, of course, the risk that many knowledgeable people will find the presentation trivial, since they already know much more about traffic. I do apologise, and suggest that they only browse through this introduction and rather concentrate onthe more specific articles in the issue.

An obvious cause of criticism will be that of the length of the article. Who will read one article of about 30 journal pages? In fact I was incited by the chief editor to attempt to write a comprehensive introduction of such extent. I assume my target readers to belong to some of the following categories: - the “browse through” experts - those who lookfor basic formulas - those who look for development of basic formulas - those who want to study particular sections in more detail - those who want to read the complete text as a condensed book. I wish all my readers a pleasant journey, whether it is an initial tour, or it is the nth repetition.

cussed in relation with data communication and various bit rates. In general practice A is consideredan average number over a given time interval. This average will in general be a non-integer (continuous) value. When needed, it should be stated whether traffic means an instantaneous value or an average one. In the latter case much more specification about the way the traffic varies may be necessary. The number of servers, n, on the other hand is an integer. The load of a traffic carrying systemhas to be generated by some set of traffic sources. In general, the traffic sources are individuals, customers, that ask for service in a co-ordinated or rather an uncoordinated manner. A request for service is a call attempt, which, if granted, will occupy one server as a call. Often the term call is used as a synonym for call attempt, when no ambiguity arises. (See list of terms below.) In...