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calculation, and may then distribute the results of its calculation back to its neighbors It is iterative in that this process continues on until no more information is exchanged between neighbors (Interestingly, we will see that the algorithm is self terminating -- there is no "signal" that the computation should stop; it just stops) The algorithm is asynchronous in that it does not require all of the nodes to operate in lock step with each other We'll see that an asynchronous, iterative, self terminating, distributed algorithm is much more "interesting" and "fun" than a centralized algorithm The principal data structure in the DV algorithm is the distance table maintained at each node Each node's distance table has a row for each destination in the network and a column for each of its directly attached neighbors Consider a node X that is interested in routing to destination Y via its directly attached neighbor Z Node X's distance table entry, Dx(Y,Z) is the sum of the cost of the direct one hop link between X and Z, c(X,Z), plus neighbor Z's currently known minimum cost path from itself (Z) to Y That is: Dx(Y,Z) = c(X,Z) + minw{Dz(Y,w)} (4-1)



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Figure 10.29. Emission intensity and linewidth of laser emission as a function of pumping energy with a second harmonic light of Nd-YAG laser. Source: Kurihara et al., 2006.





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The minw term in equation 4-1 is taken over all of Z's directly attached neighbors (including X, as we shall soon see) Equation 4-1 suggests the form of the neighbor-to-neighbor communication that will take place in the DV algorithm -- each node must know the cost of each of its neighbors minimum cost path to each destination Thus, whenever a node computes a new minimum cost to some destination, it must inform its neighbors of this new minimum cost Before presenting the DV algorithm, let's consider an example that will help clarify the meaning of entries in the distance table Consider the network topology and the distance table shown for node E in Figure 42-3 This is the distance table in node E once the Dv algorithm has converged Let's first look at the row for destination A

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Clearly the cost to get to A from E via the direct connection to A has a cost of 1 Hence DE(A,A) = 1 Let's now consider the value of DE(A,D) - the cost to get from E to A, given that the first step along the path is D In this case, the distance table entry is the cost to get from E to D (a cost of 2) plus whatever the minimum cost it is to get from D to A Note that the minimum cost from D to A is 3 -- a path that passes right back through E! Nonetheless, we record the fact that the minimum cost from E to A given that the first step is via D has a cost of 5 We're left, though, with an uneasy feeling that the fact the path from E via D loops back through E may be the source of problems down the road (it will!) Similarly, we find that the distance table entry via neighbor B is DE(A,B) = 14 Note that the cost is not 15 (why )

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Figure 12.15 shows the typical A629 20 bit data word format. The rst three bits are related to word time synchronisation as already described. The next 16 bits are data related and the nal bit is a parity bit. The data words may have a variety of formats depending upon the word function; there is provision for general formats, systems status, function status, parameter validity, binary and discrete data words. Therefore although the data format is simpler than A429, the system capabilities are more advanced as the bit rate is some 20 times faster than the fastest (100 kbit/sec) option for A429. The only aircraft utilising A629 data buses so far is the Boeing 777.The widespread application of technology such as A629 is important as more widespread application drives component prices down and makes the technology more cost-effective. Certainly that has been the case with A429 and MIL-STD-1553B. For more detail on A629 see references [6], [7] and [8].

A circled entry in the distance table gives the cost of the least cost path to the corresponding destination (row) The column with the circled entry identifies the next node along the least cost path to the destination Thus, a node's routing table (which indicates which outgoing link should be used to forward packets to a given destination) is easily constructed from the node's distance table In discussing the distance table entries for node E above, we informally took a global view, knowing the costs of all links in the network The distance vector algorithm we will now present is decentralized and does not use such global information Indeed, the only information a node

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