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In order to check the performance in terms of CPU utilization, we designed a benchmark application that represents service logic that is bounded by computation resources. This application is sent and executed in a DINA node. Without any load the application requires about 2 seconds to complete. Then, we added further load by executing a number of load application representing the logic of other (different) services running on the same DINA node. As one can see from Figure 8.6, when the load increases the time it takes the application to complete increases as well. The Total time in this gure is the time taken to load and execute the application, while the Execution time is the amount of

1 For each pair of attributes A and B, search for a set SAB U {A, B}, so that A B | SAB holds, that is, so that A and B are conditionally inde pendent given SAB If there is no such set SAB , connect the two attributes by an undirected edge If a directed acyclic perfect map G = (U, E) is to be found, the following two steps have to be carried out in order to direct the edges: 2 For each pair of nonadjacent attributes A and B with a common neighbor C SAB , direct the edges towards C, that is, A C B / 3 Recursively direct all undirected edges according to the rules: If for two adjacent attributes A and B there is a strictly directed path from A to B not including A B, then direct the edge towards B.

initial knowledge of the cluster boundaries is encoded into the network, the learning time is reduced greatly, with improved performance. The steps involved in the process, as formulated by Pal et al. [64], are summarized below. Step 1. From the initial data set, use the fuzzy discretization process to create the information system. Step 2. For each object in the information table, generate the discernibility function fA a1 ; a2 ; . . . ; a3n ^f_cij : 1 i; j n; j < i; cij 6 ;g 3:77

If there are three attributes A, B, and C with A and B not adjacent, A C, and C B, then direct the edge C B If neither rule is applicable, arbitrarily direct an undirected edge Obviously, the first step of this algorithm implements the idea stated above: only those attributes are connected by an edge for which there is no set of attributes that renders them conditionally independent Note that for this step it is crucial that a perfect map actually exists Otherwise edges may be omitted that are needed in an independence map (see also below) The reasons underlying the second step of the algorithm are as follows: if a set SAB of attributes renders two attributes A and B conditionally independent, it must block all paths from A to B in the graph (otherwise this conditional independence statement would not be represented by the graph).

This work was undertaken as part of the DAME project, with welcome assistance from Rolls-Royce plc, Data Systems & Solutions LLC, and Cybula Ltd and the teams at the Universities of York, Leeds, Sheffield, and Oxford. This research was supported by the UK Engineering and Physical Sciences Research Council (grant GR/R67668/01) and through contributions from Rolls-Royce plc and Data Systems and Solutions LLC.

Delay (s)

It follows that it must also block a path that runs via a common neighbor C of A and B However, if this common neighbor C is not in SAB , the only way in which this path can be blocked (given SAB ) is by the fact that it has converging edges at C (cf the definition of d-separation32 ) The first rule of the third step simply exploits the fact that the resulting graph must be acyclic If there already is a directed path from A to B not including the edge connecting A and B, directing the edge from B towards A would introduce a directed cycle Therefore it must be directed the other way.