Reading without meditation is sterile; meditation without reading is liable to error; prayer without meditation is lukewarm; meditation without prayer is unfruitful; prayer, when it is fervent, wins contemplation, but to obtain contemplation without prayer would be rare, even miraculous. Bernhard de Clairvaux (12th century) NobodycandenythatIP-basedtra?chasinvadedourdailylifeinmanyways and no one can escape from its di?erent forms of appearance. However, most people are not aware of this fact. From the usage of mobile phones – either as simple telephone or for data transmissions – over the new form of telephone service Voice over IP (VoIP), up to the widely used Internet at the users own PC, in all instances the transmission of the information, encoded in a digital form, relies on the Internet Protocol (IP). So, we should take a brief glimpse at this protocol and its constant companions such as TCP and UDP, which have revolutionized the communication system over the past 20 years. The communication network has experienced a fundamental change, which was dominated up to end of the eighties of the last century by voice appli- tion.Butfromthemiddleoftheninetieswehaveobservedadecisivemigration in the data transmission. If the devoted reader of this monograph reads the title ‘IP tra?c theory and performance’, she/he may ask, why do we have to be concerned with mod- ing IP tra?c, and why do we have to consider and get to know new concepts.

Professor Dr.- Ing. Christian Grimm has been working for more than ten years with measuring and modelling of data traffic in packet switched networks. In his PhD thesis he investigated complex methods for the traffic modelling in the World Wide Web. At present he is head of the division for research and development and new network services at the regional computing centre for lower saxony. Since 2003 he has an assistant professorship (Juniorprofessur) in computer networks at the faculty of electrical engineering and computer sciences at the university of Hannover.

Professor Dr. rer.nat. Georg Schlüchtermann finished his study in Mathematics in 1984. He habilitated 1994 at the Ludwig-Maximilians-Universität in functional analysis. Since 2001 he is apl. professor at the faculty for mathematics, computer sciences and statistics at the university of Munich. He is lecturing in the fields of traffic theory, mathematical modelling in mobile communication and finance mathematics.