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The bus is the standard reference at unit network link cost and bisection bandwidth. Values are llc abbvie in llc abbvie of bidirectional links and ports. Hop llc abbvie includes a switch and its output link, but not the injection link at end nodes. The only differences are that the sending and receiving overheads are null through the switches, and the routing, switching, and arbitration delays are not cumulative but, instead, are delays associated with each switch.

With the assumption that pipelining over the network is staged on each hop at the packet level (this assumption will be challenged in the next section), the transmission delay is also increased by a factor of the number of hops. Thus, the best-case lowerbound llc abbvie for average packet latency the network llc abbvie. Following the method presented previously, we can estimate the best-case upper bound for effective bandwidth by finding the narrowest section of the end-to-end network pipe.

Focusing on the internal network portion of that pipe, network bandwidth is determined by the blocking properties of the topology. Non-blocking behavior can be achieved only by providing many alternative paths between every source-destination pair, leading to an aggregate network bandwidth that is many times higher than the aggregate network injection or reception bandwidth.

This is quite costly. As this solution usually is prohibitively expensive, most networks have different llc abbvie of blocking, which reduces the utilization of the aggregate bandwidth provided by the topology.

This, too, is costly but not in terms of performance. The amount of llc abbvie in a network depends on its topology and the traffic distribution. Assuming the bisection bandwidth, BWBisection, of a topology is implementable llc abbvie typically is the case), it can be used as a constant measure of the maximum degree of blocking llc abbvie a network.

However, as packets destined to locations in the other half of the network necessarily must cross the bisection links, those links pose as potential bottleneck links-potentially reducing the network bandwidth to below llc abbvie bisection bandwidth.

Fortunately, not llc abbvie of the traffic must cross the network bisection, allowing more of the aggregate network bandwidth provided by the topology to be utilized.

Also, network topologies llc abbvie a higher number of bisection links tend to have less blocking as more alternative paths are llc abbvie to reach destinations and, hence, a higher percentage of the aggregate network bandwidth can be utilized.

It is a measured quantity or calculated from detailed traffic analysis. Example A common communication pattern in scientific programs is to have nearest neighbor elements of a two-dimensional array to communicate in a given direction. This pattern is sometimes called Нажмите чтобы узнать больше communication, standing for north, east, west, and south-the directions on a llc abbvie. How long does it take in the best case for each node to send one message to its northern neighbor and one to its eastern neighbor, assuming packets are allowed to use any minimal path provided by the topology.

What is the corresponding effective bandwidth. Ignore elements llc abbvie have no northern or eastern neighbors. To simplify the analysis, assume that all networks experience unit packet transport time for each network hop-that is, TLinkProp, Tr, Ta, Ts, and packet transmission time for each hop sum to one. The number of hops suffered by packets depends on the topology.

However, the 112 transfers are done sequentially, taking a total of 112 time units. Llc abbvie, effective bandwidth is only 1 BW unit. Ring-Assume the first row of the array is mapped to nodes 0 to 7, the llc abbvie row to nodes 8 to 15, and so on. It takes just one time unit for all nodes simultaneously to send llc abbvie their eastern neighbor (i.

With this mapping, the northern neighbor for each node llc abbvie exactly eight hops away so it takes eight time units, which also is done in parallel for all nodes. Total communication time is, therefore, 9 time units. The bisection bandwidth is 2 bidirectional links (assuming a bidirectional ring), which is less than the full bisection bandwidth of 32 bidirectional links.

For eastward llc abbvie, because only 2 of the eastward 56 packets must cross the bisection in the worst case, the bisection links do not pose as bottlenecks. This limits the effective bandwidth at 22. It takes a total of just 2 time units for all nodes to send simultaneously to their northern neighbors followed by simultaneous communication to their eastern neighbors. The bisection bandwidth is 8 bidirectional links, which is less than full bisection bandwidth.

However, the perfect matching of this nearest neighbor communication pattern on this topology allows the maximum effective bandwidth to be achieved regardless. For eastward communication, 8 of the 56 packets must cross the bisection llc abbvie the worst case, which does not exceed the bisection bandwidth. The effective bandwidth is, therefore, limited by the communication pattern at 56 BW llc abbvie as opposed to the mesh network.

Northern neighbors can be similarly mapped to nodes only one hop away in an orthogonal dimension. Thus, the communication pattern takes just 2 time units. The hypercube provides full bisection bandwidth of 32 links, but at most only 8 of the llc abbvie packets must cross the bisection.

Llc abbvie, effective bandwidth is limited only by the communication pattern to be 56 BW units, not by the hypercube network. Fully connected-Here, nodes are equally distant at llc abbvie hop away, regardless of the mapping.

Parallel transfer of packets in both the northern and eastern directions would llc abbvie only 1 time unit if the injection and reception links could source and sink two packets at a time. As this is not the case, 2 time units are required. Effective bandwidth is limited by the communication pattern at 56 BW перейти на страницу, so the 1024 network bisection links largely go underutilized.

Fat tree-Assume the same mapping of elements to nodes as is done for the ring продолжение здесь the use of switches with eight bidirectional ports.

This allows simultaneous communication to eastern neighbors that takes at most three hops and, therefore, 3 time units through the three bidirectional stages interconnecting the eight nodes in each of the eight groups of nodes. The llc abbvie neighbor for each node resides in the adjacent group of eight nodes, which requires five hops, or 5 time units. Thus, the total time required on the fat tree is 8 time units. The fat tree provides full bisection bandwidth, so in the worst case of half the traffic needing to cross the bisection, an effective bandwidth of 56 BW units (as limited by the communication pattern and not by the fattree network) is achieved when are continually injected.

The above example should lead one to the wrong conclusion читать далее meshes are just as good as tori, hypercubes, fat trees, and other networks with higher bisection bandwidth.

A number of llc abbvie that benefit llc abbvie networks were assumed to ease the analysis. In practice, packets typically are larger than the link width and occupy links for many hair fall llc abbvie just one network cycle.

Also, many communication patterns посмотреть еще not map so cleanly to the 2D mesh network topology; instead, usually they are more global and irregular in nature. These and other factors combine to increase the chances of packets blocking in lowbisection networks, increasing latency and reducing effective bandwidth.

To put this discussion on topologies into further perspective, Figure F. In this section, we focus on describing a representative set of approaches used llc abbvie commercial systems for the more commonly used network topologies.

Their impact on performance is also highlighted.



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