it can be mathematically generalized to a continuous number of channels, i.e. non-integral number of channels. This is useful for the dimensioning to find out the required number of channels and in turn the bandwidth resources for a given offered traffic and desired blocking probability in the system. Moreover, the fundamental assumption for the validity of Erlang-B formula is the Poisson arrival process. According to Palm's theorem [Ive04] this assumption can be taken if the traffic is generated by a large number of independent sources. Theorem 6.1 Palm's theorem: by superposition of many independent point processes the resulting total process will locally be a Poisson process. offered traffic (Erlang) Figure 6.2: Blocking probability pb as a function of the offered traffic A in Erlang for various values of the number of channels n with equation (6.6) 6 Dimensioning for Single ATM-Based lub In normal telephone systems, it is usually the case that the call requests are assumed to be a Poisson arrival process. Thus, the Erlang-B formula was widely applied in telephone systems of both fixed and mobile networks. Due to its insensitivity property as mentioned above, it can be generally applied from voice telephony to other circuit-switched traffic which reserves a certain bandwidth. Traffic characteristics of Erlang-B formula With the Erlang-B formula (6.6), the important traffic characteristics of the loss system and dimensioning can be obtained. The most important performance measures for loss systems are [Ive04]: Carried traffic Y: the total traffic carried in the system. It is equal to the probability of channels being utilized, as shown in equation (6.7). A is the offered traffic, SO the carried traffic is less than A. (6.7) Y=A.(1-p), Lost traffic A1: the lost or rejected traffic due to the blocking. Traffic congestion C: according to the PASTA-theorem, the blocking probability pb is also equal to traffic congestion C [Ive04]. c=1-y=po Channel utilization Furthermore, from the dimensioning point of view, it is 