ation in (6.12). (6.12) As the arrival process is Poisson, due to the PASTA property, the time congestion, the call congestion and traffic congestion are all identical for both traffic streams, and they are equal to the aggregated probability p(i+j=n). The above two-dimensional system can be generalized to N traffic streams, then the state probabilities are expanded to a general form as given in equation (6.13). This is the general multi-dimensional Erlang-B formula [Ive04]. osi,sm. (6.13) In the above, it is assumed that each traffic stream requests the same bandwidth corresponding to one channel and thus the restriction of the number of simultaneous calls for each traffic stream is same. But, in many systems, the bandwidth requested by a call is dependent on the traffic stream (class), i.e. each traffic class may have an individual bandwidth requirement. For example, voice service may require one bandwidth unit per call, and video stream may require two or more. Thus, in this case, the maximum number of simultaneous calls allowed for each traffic stream is service specific. Let ij denote the number of simultaneous calls for traffic class j and Nj the maximum number of simultaneous calls for traffic class j. They need to satisfy the following restrictions: (6.14) Due to the above restrictions, the state transition diagram is truncated. Figure 6.5 shows the two-dimensional state transition diagram for the two traffic streams case where the number of maximum calls for traffic stream 1 and 2 is N1 and N2 respectively. It is noted that 6 Dimensioning for Single ATM-Based lub the truncated state transition diagram still is reversible and that the relation in (6.10) still holds, but the normalization constant K is changed. In fact, due to the local balance property, any state can be removed without changing the properties. blocking for stream 1 blocking for stream 2 (i,j) itj=n Figure 6.5: Two-dimensional state transition diagram for a loss system with class limitations: n for the traffic stream 1 and N2 for the traff