Mixed Trees and LayersCharaceristics of Human Layered OrganizationsOverlaysComplexity and Flexibility:Structural complexityStructural complexity of an implementationMy approach to structural complexity in the analysis belowExamples of FlexibilityWhat is Flexibility?Continuous Notions of FlexibilityWhat is Flexibility -2Flexibility in relation to other goals and characteristics of systemsImplementing FlexibilityWhy are paths important in the definition of flexibility?Complexity and Flexibility of Teams/FamiliesComplexity and Flexibility of Tree StructuresFlexibility and Performance – Tree structured systemsComplexity and Flexibility of Layered StructuresFlexibility and Performance – Layered SystemsAnalysis of a hybrid or mixed trees and layersAnalysis of layered systems that use routersComplexity and Flexibility of NetworksLateralityFlexibility of Linearly Structured SystemsStaging AlternativesFlexibility and RoutersFlexibility, networks and RobustnessFlexibility and Rates of ChangeMeasuring FlexibilityUniversalityLayering as an Algebraic ConceptLandline Telephone ArchitectureAbstractions in Algebra:Simple Algebraic ExamplesIntegration using algebraic abstractionsSimple ExamplesSimple integration examplesAbstraction and Problem SolvingArguments against abstractions and layeringData Abstraction1Mixed Trees and Layers• Layered human organizations are locally relatively horizontal and globally tree structured. Locally they form a team, and rely on leaders to form interconnections resulting in tree structures of clans (see Watts, Chapter 9, also in Dodd, Watts and Sabel’s paper, although they come at it from a very different perspective)2Characeristics of Human Layered Organizations• Members of a given layer can have multiple parents or can relatively easily switch parents at the layer above them• Cooperation and trust are important attributes• Members of a given layer can interact readily with other members at the same layer• I believe that middle managers in such organizations recognize that a significant part of their job is increasing trust between their team members and members of other teams with whom they will need to work at some point3Overlays• Large partnerships (e.g., consulting firms) are often layered, and use project teams that may be best modeled as tree structures which areoverlayed on the base structure• Matrix organizations (two bosses) may be viewed as overlays as well. At MIT we have departments as well as centers, and most faculty members have a department head and a center director as ‘bosses.’4Complexity and Flexibility5Complexity and Flexibility:Structural complexity • Kolmogorov defined the (structural) complexity of a function as the length of its shortest description. This gives a lower bound to the complexity of implementations of the function• The shortest description is, however, hard to determine • Abstractions in an implementation permit you to reduce the length of a description (recall the matrix example in Herb Simon’s chapter)• There is a trade-off between a long description in an implementation and one that has a high number of layers of abstractions, each of which is relatively short• The intricacy (related to messiness)of the interconnection pattern in a system clearly adds to the complexity• The total number of nodes and interconnections also clearly adds to the complexity of an implementation6Structural complexity of an implementation• “Spaghetti stack” – a messy pattern of interconnections of components – people sometimes use graph theory to measure the messiness of the interconnection pattern –systems or software engineering design methodology tends to reduce the messiness of the interconnection pattern –this is one of these methodologies’ biggest advantages• Number of components -clearly related to complexity• Number of interconnections -also clearly related• In a hierarchy, the number of levels or layers is related to complexity (in a system using layers of abstractions which reduce the number of components and their interconnections, the depth of the hierarchy, if large, clearly adds to the complexity)7My approach to structural complexity in the analysis below• I assume that there is regularity in the interconnections structure in a generic structure, such as a tree structure . Thus messiness is not an issue• I assume that the number of layers is not large, so accounting for the increased complexity for a large number of layers is not much of an issue• I assume that the number of interconnections is larger than the number of nodes• Thus I simply count the number of edges or interconnections in a system, and call that the structural complexity of the generic system or organization8Examples of Flexibility(D-design, R-redesign, O-operation, F-function, P-performance)• Using a tuner in a radio to switch stations – O, F• Changing gears in a car or bicycle – O, P• Adding rules in spreadsheets – O, R, F• Creating a new layer of software on top of or in between existing layers – D, R, F• Switching roads to avoid congestion – O, P• Adding connections in infrastructures to increase flexibility (and robustness) – R, P• Switching roles in NE Patriots’ defensive positions – O, F, P9What is Flexibility?• A flexible system presents alternatives, usually many alternatives, to its function, performance or other ilities• Some of these alternatives are obvious in the system’s interface, but most are not• A flexible system also makes it easy to make certain classes of modifications in the system during design, redesign or operation of the system• Not all modifications by an external designer are easily made in a flexible system (largely because these modifications may not rely on flexible parts of the system)10Continuous Notions of Flexibility• Flexibility is assumed here to be a property of discrete systems in the process of making alternative choices• English also uses the term flexibility in continuous systems, such as a flexible bow• One may have a flexible body permitting one to make a large variety of moves and take on a large variety of positions or states• One could model or simulate these large number of relatively continuous positions with a discrete system, but we shall choose to ignore this possibility, and continue to emphasize flexibility in relatively clear-cut discrete situations11What is Flexibility -2• Flexibility is related