北邮交换网性能分析习题答案.doc
文本预览下载声明
Chapter 3
1. Compute the crosspoint complexity, logical depth (the number of logical gates in a path), and fan-out (the number of logical gates in a path), and fan-out (the number of logical gates driven by the gate in the network) for the following networks.
A. The full crosspoint switch.
B. The three stage rearrangeable Clos network constructed using
? switches.
C. The Benes network.
解:
A. crosspoint complexity =
logical depth =
fan-out number =
B. crosspoint complexity =
logical depth =
fan-out number =
C. crosspoint complexity =
logical depth =
fan-out number =.
2. Consider the crosspoint complexity of three stage Clos networks.
a. Show that the strict-sense network has roughly twice the complexity of the rearrangeable network.
b. For the rearrangeable network, show that the optimal choice of p (figure 12) for minimizing crosspoint count count is, which gives a crosspoint complexity of
c. For the strict-sense network, show that the minimum crosspoint count is roughly given by .
解:
A. 当时,根据图12
严格无阻塞网络的交叉点复杂度为:
①
可重排无阻塞网络的交叉点复杂度为:
②
当比较大时,大约 ① = ②×.
B.
≥ =
等号成立时, 当且仅当 或 .
C.
根据A. 在 时, .
6. Consider the recursive construction of an rearrangeably non-blocking Clos network using crossbars only.
a. Compute the number of crosspoints as a function of and .
b. For large, show that minimizes the crosspoint count.
解:
a. 考虑Clos网络
crosspoint count:
如果 有, 递归下去后有,
b. 如果,
(一般来说,后者较大)
故倾向于选小的. 当然也可以按照连续函数求解最优值的范围.
, 或时比较得:
因为,则有,
所以,时,crosspoint最小.
8. For the Benes network, using the looping algorithm to find the paths for the following permutation:
Input 1 2 3 4 5 6 7 8
Output 3 6 2 1 8 4 5 7
解:
按照looping 算法可以将connection pattern分解为两个:
和 .
Chapter 4
Consider the Bell System number 5 crossbar network with a network structure shown in figure 15. It is constructed using switches. A switch frame (in dotted boxes) is an network with 2 stages with switches in e
显示全部