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 Building a car is about more than understanding its component parts We need composite frames

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?

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

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

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

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

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?

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.

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?

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

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

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