Multiprocessors Interconnection Networks - Part -3

The k-ary n-cube network is a radix k cube with n dimensions. The radix implies that there are k nodes in each dimension. An 8-ary 1-cube is simply an eight node ring, while an 8-ary 2-cube is eight 8-node rings connected such that nodes are connected to all nodes with an address that differs in only one digit.
It should be noted that the number of nodes in a k-ary n-cube is N ¼ kn nodes and that when k ¼ 2, the architecture becomes a binary n-cube. Routing of messages in a k-ary n-cube network can be done in a similar way to that used in mesh networks. Notice that, depending on the directionality of links among nodes the possible route(s) will be decided. Another factor involved in the selection of route in a k-ary n-cube network is the minimality of the route, measured in terms of the number of hops (links) traversed by a message before reaching its destination. Notice that other routes exist between S and D but they are longer than the indicated route. The longest distance traveled between any two arbitrary nodes in a k-ary n-cube network is O(n ? k).
Having introduced the main architecture of multiprocessors, we now turn our attention to a discussion on the analysis and performance issues related to those architectures. We provide an introduction to the basic performance issues and performance metrics related to both static and dynamic interconnection networks. For
dynamic networks, we discuss the performance issues related to cost, measured in terms of the number of cross points (switching elements), the delay (latency), the blocking characteristics, and the fault tolerance. For static networks, we discuss the performance issues related to degree, diameter, and fault tolerance