where (10.11) (10.12) The probability Pwc(H) is difficult to evaluate analytically for the great number of terms composing it. However, it is possible to find an approximation considering that p has to be sufficiently small to have a functional OXC. Thus, in a first approximation, we can neglect in the expression of P(h;(v)), all the terms where h;(v) is greater than one. In this way, only the D' = N(N - 1) (N - H) configuration remains and the approxi- mated expression of Pwc(H), considering also Ps small, becomes (10.13) Next Generation Networking: Enabling Technologies, Architectures, and Performances Coordinate FIGURE 10.23 Blocking probability versus the offered traffic for N = 6 and W = 90. Three cases are considered, no WCs (H = 0), W WCs (H = 1), and 2 W WCs (H = 2). At this point, it is not difficult to evaluate the approximate expression of the blocking probability. The blocking probability P(N,W) is the probability that a new connec- tion request arrives when all the WCs are occupied finding a blocking situation. It is a joined probability that there is no direct internal connection and that all the WCs are occupied; thus, PB(N,W)=WPs(N)[1-Ps(N)W-1]Pwc(H) (10.14) The blocking probability is shown in Figure 10.23 versus the offered traffic for N = 6 and W = 90. Three cases are considered, no WCs (H = 0), W WCs (H = 1), and 2W WCs (H = 2). The strong reduction of the blocking probability is evident even with H = 1, and in many cases, more WCs are really not needed. 10.3.2.4 Final Comparison All the performance parameters that we have evaluated analyzing the three OXC architec- tures are summarized in Table 10.3, where the numerical values correspond to the param- eters reported in the text for each OXC. If one of the expected values of the T-OTN is to drop dramatically the power consump- tion, we have a confirmation from table 10.3 that this is possible. We should not forget that a DXC power consumption is on the order of kW. TABLE 10.3 Comparison among the Three Considered Transparent OXC Architectures 