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Problem Analysis and Structure II

Problem Analysis and Structure II. Multi-frame problems. Composite Frames. Using only elementary frames means Decomposing problems such that each subproblem fits one elementary frame Don’t build repository of experience about problem and solution composition

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Problem Analysis and Structure II

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  1. Problem Analysis and Structure II Multi-frame problems

  2. Composite Frames • Using only elementary frames means • Decomposing problems such that each subproblem fits one elementary frame • Don’t build repository of experience about problem and solution composition • Building a car is about more than understanding its component parts • We need composite frames

  3. Package Router Problem • See Jackson, M.A. “Problem Analysis and Structure” from where this example is taken (pointer on web site) • A realistic problem • See the problem description on the handout • Package router delivers packages to different bins by scanning bar codes on the packages and routing them accordingly • What frame does this seem to fit?

  4. Frame Diagram • C1 = flip • C2 = read, hit, position of switches • C3 = arrive, package, bin, destination

  5. Recognising sub-problems • Looks like a control problem • M/c must flip switches to ensure correct destination • Switch is flipped when package passes a sensor at bottom of a pipe • However, consideration of the phenomena exposes difficulties

  6. Connection difficulties • Destination read at the source station • Destination no longer available when package passes the sensor • M/c and sensors share only the penomena • SensorOpen and SensorClosed [state] • Pckg causing state change is unknown • We need a dynamic model

  7. Dynamic model • State of pckgs and pipes regarded as a set of queues • Pckg arriving at a sensor above switch is at the head of the queue in the pipe to which sensor is attached • Destinations (read at source station) are attached to pckg objects in this queue model • To flip a switch, m/c consults queue model to identify destination and hence switch setting

  8. Dynamic Model • Use model to answer question: what is the barcoded destination of the package that participated in the most recent hit event in which this particular sensor participated?

  9. Further problem • The switch to be set is determined by the router topology • i.e. the positioning of sensors on pipes, and the pipe and switch layout. • We need a static model here • i.e. a map of the router and its bins • Using the map, m/c can determine the correct route and hence set the switch correctly.

  10. Static Model • Provides necessary information • Which sensors are on which ends of which pipes? Which pipes feed and leave which switches? Which pipe leaves the reading station? Which bins guarded by which sensors?

  11. Information Display • Signalling arrival of package at wrong bin is a Simple Information System Display problem

  12. Composing the Solution • How do we schedule the machines from each sub-problem? • Run the static-model machine to completion first • Run the other machines in parallel synchronised by the read and hit events

  13. Summary • Problems located in real world not computer • Large (realistic) problems can be seen as compositions of small problems • Small problems must be of recognised classes • Problem structure often a parallel composition of subproblems

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