tailieunhanh - Switching Theory: Architecture and Performance in Broadband ATM Networks phần 3

Trong một số trường hợp của các mạng đẳng cấu, lập bản đồ đầu vào và đầu ra chỉ là j nhận dạng nếu A và B có chức năng tương đương, tức là thực hiện các hoán vị tương tự. Điều này xảy ra trong trường hợp của . Đó là giá trị quan sát bạn thân và tài sản reachability hạn chế không tổ chức cho tất cả các mạng lưới đa. | Partial-connection Multistage Networks 73 In some cases of isomorphic networks the inlet and outlet mapping is just the identity j ifA and B are functionally equivalent . perform the same permutations. This occurs in the case of the A Q B r and A o B o-1 . It is worth observing that the buddy and constrained reachability properties do not hold for all the banyan networks. In the example of Figure the buddy property holds between stage 2 and 3 not between stage 1 and 2. Other banyan networks have been defined in the technical literature but their structures are either functionally equivalent to one of the three networks Q s and r by applying if necessary external permutations analogously to the procedure followed in Table . Examples are the Flip network Bat76 that is topologically identical to the reverse Omega network and the Modified data manipulator Wu80a that is topologically identical to a reverse SW-banyan. Since each switching element can assume two states the number of different states assumed by a banyan network is N 22log2N NN which also expresses the network of different permutations that the banyan network is able to set up. In fact since there is only one path between any inlet and outlet a specific permutation is set up by one and only one network state. The total number of permutations N allowed by a non-blocking network N X N can be expressed using the well-known Stirling s approximation of a factorial Fel68 N NN e N 2 n N which can be written as log N Nlog2 N - N For very large values of N the last two terms of Equation can be disregarded and therefore the factorial of N is given by N 2Nlog2N N Thus the combinatorial power of the network Ben65 defined as the fraction of network permutations that are set up by a banyan network out of the total number of permutations allowed by a non-blocking network can be approximated by the value N n 2 for large N. It follows that the network blocking probability increases .