Dynamic Networks

• The Crossbar;
  • the cost of the crossbar system can be measured in terms of the number of switching elements (cross points) required inside the crossbar. The crossbar possesses a quadratic rate of cost (complexity) given by $O(N^ 2)$.
  • The delay (latency) within a crossbar switch, measured in terms of the amount of the input to output delay, is constant.The crossbar possesses a constant rate of delay (latency) given by $O(1)$. It should be noted that the high cost (complexity) of the crossbar network pays off in the form of reduction in the time (latency).
  • The crossbar is however a nonblocking network; that is, it allows multiple output connection pattern (permutation) to be achieved.
  • A fault-tolerant system can be simply defined as a system that can still function even in the presence of faulty components inside the system. The crossbar can be affected by a single-point failure. Nevertheless, segmenting the crossbar and realizing each segment independently can reduce the effect of a single-point failure in a crossbar.
• Multiple Bus;
  • It consists of $M$ memory modules, $N$ processors, and $B$ buses. A given bus is dedicated to a particular processor for the duration of a bus transaction.
  • A processor?memory transfer can use any of the available buses. Given $B$ buses in the system, then up to $B$ requests for memory use can be served simultaneously.
  • A multiple bus possesses an $O(B)$ rate of cost (complexity) growth.
  • The multiple bus possesses an $O(B \times N)$ rate of delay (latency) growth.
  • Multiple bus-multiprocessor organization offers the desirable feature of being highly reliable and fault-tolerant. This is because a single bus failure in a $B$ bus system will leave ($B-1$) distinct fault-free paths between the processors and thememory modules.
  • On the other hand, when the number of buses is less than the number of memory modules (or the number of processors), bus contention is expected to increase.
• Multistage Interconnection Networks;
  • Each stage consists of $N/2$, $2 \times 2$ SEs.
  • The network cost (complexity), measured in terms of the total number of SEs, is $O(N \times log_2N)$.
  • The latency (time) complexity, measured by the number of SEs along the path from input to output, is $O(log_2 N)$.
  • Simplicity of message routing inside a MIN is a desirable feature of such networks. There exists a unique path between a given input?output pair.
  • MINs are characterized as being 0-fault tolerant; that is, a MIN cannot tolerate the failure of a single component.

  Figure 2.10: Performance Comparison of Dynamic Networks.

  
  Based on the above discussion, Fig. 2.10 provides an overall performance comparison among different dynamic interconnection networks. ( N represent the number of inputs (outputs) while m represents the number of buses)