responds to a traffic stream, thus several traffic streams are offered to the same channel group. When the system is extended to receive a group of independent traffic streams each with its respective arrival rate Ai and service rate Mi, then the Erlang-B formula is expanded to a general case of a network with multiple traffic streams. The general form of the Erlang-B formula is the multi-dimensional Erlang-B formula. Now consider a group of n bandwidth units (channels, trunks, etc.), which is offered to two independent traffic streams with arrival and service rates (A1, M1) and (A2, M2). Then, the offered traffic is A = 21/111 for the stream 1 and A2 = A2/M2 for the stream 2. Let (i, j) denote the state of the system when there are i calls from stream 1 and j calls from stream 2. Each call is allocated to one and only one channel (assuming all channels are identical). And the following restrictions hold: 0 n, O<j<n, , and j <n. For this case, the two- dimensional state transition diagram is shown in Figure 6.4, which corresponds to a reversible Markov process. 0, n-1 1,n-1 (n-1)uz (n -1)u2 n-1,1 (n-1)u, n-1,0 (n-1)u, Figure 6.4: Two-dimensional state transition diagram for a loss system with n channels offered to two traffic streams [Ive04] Under the assumption of statistical equilibrium in the system, the state probabilities can be obtained by applying the global balance equations. As the state transition diagram corresponds to a reversible Markov process, the state probabilities can be written in product form [Ive04]. Let p(i,j) denote the probability that the system is in state (i,j), it is expressed in (6.10) in product form [Ive04]: 6.2 Dimensioning for Circuit-Switched Traffic (6.10) where p(i) and p(j) are the state probabilities of the one-dimensional Poisson distribution and K is normalization constant to conserve the state probabilities. By the Binomial expansion by convolving two Poisson distributions, the following aggregated state probabilities can be obtained: (6.11) Where K is obtained by normaliz