Aditya P. Mathur Professor, Department of Computer Science, Associate Dean, Graduate Education and International Programs Purdue University Monday December 20, University of Paderborn, Paderborn, Germany. Software Cybernetics: Progress and Challenges

Cybernetics [n] the field of science concerned with processes of communication and control (especially the comparison of these processes in biological and artificial systems)

Software Cybernetics [n] the field of science concerned with processes of communication and control in software systems.

Sample Problems Control of the software test process: How much and what additional effort is to be applied to achieve the desired quality objective under time/cost constraints? Optimal selection of tests: What is an optimal set of tests for achieving the desired quality objective given time constraints?

Sample Problems (continued) Software performance control How best to adjust software parameters so that an optimal level of performance is maintained? Control of the software development process: What is an optimal set of process variables required to achieve delivery objectives within cost/time constraints?

Approaches 1.Use instinct and experience. 2.Use (1) supported by quantitative tools. (b)Use simulation: “forward” approach. (c)Use (a) plus feedback control: “inverse” approach. Software cybernetic approach.. (a)Use simulation: “forward” approach.

Closed Loop (feedback) Control Specifications Program Effort + f(e) Additional effort What is f ? - Required Quality Observed Quality

Sample Problem Scenario cp 1 cp 2 cp 3 cp 4 cp 5 cp 6 cp 7 cp 8 cp 9 cp i = check point i rfrf schedule set by the manager Approximation of how r is likely to change r0r0 observed deadline r - number of remaining errors t- time t0t0

Our Approach Controller r error (t)  ’  w’ f + + wf+wfwf+wf  +  wf+wfwf+wf r observed (t) r expected (t) Actual STP scsc r0r0 STP State Model scsc r0r0 Initial Settings (w f,  )  wfwf Test Manager w f : workforce  : quality of the test process

Decision Support via Feedback Actual Process Parameter Estimation Progress Metrics Process Model Parameters Feedback Controller Estimated Future Schedule Deviation Suggested Decision Changes Mgmt. Control Management Decisions - Predicted Schedule   - + Desired Schedule Actual Schedule + Estimation Error

Challenges (Sources of difficulty) PhysicalLogical (software) Laws of physicsYesNo Object controlledPhysicalLogical (and Humans) Time dependenceStationary and non- stationary Non-stationary Rate of changeVery slow to very fast Slow Parameter variabilityRelatively lowHigh

Overcoming the challenge: Understanding the problem Partnership amongst researchers and practitioners. Is the problem real? Are the existing solutions adequate?

Overcoming the challenge: Solving the problem Parternership amongst researchers and practitioners. Develop realistic models Develop parameter estimation methods. Develop ways to incorporate parameter estimation into the development process.

Details and Case Studies Razorfish Guidant Corporation Sun Microsystems

Physical and Software Systems: An Analogy Dashpot Rigid surface External force Xequilibrium X: Position Number of remaining errors Spring Force Effective Test Effort Block Software Mass of the block Software complexity Quality of the test process Viscosity Xcurrent Spring To err is Human

Physical Systems: Laws of Motion [1] First Law: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. Does not (seem to) apply to testing because the number of errors does not change when no external effort is applied to the application.

Physical Systems: Laws of Motion [2] Newton’s Second Law: The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. CDM First Postulate: The relationship between the complexity S c of an application, its rate of reduction in the number of remaining errors, and the applied effort E is E=S c. r..

Physical Systems: Laws of Motion [3] Third Law: For every action force, there is an equal and opposite reaction force. When an effort is applied to test software, it leads to (mental) fatigue on the tester. Unable to quantify this relationship.

CDM First Postulate The magnitude of the rate of decrease of the remaining errors is directly proportional to the net applied effort and inversely proportional to the complexity of the program under test. This is analogous to Newton’s Second Law of motion.

CDM Second Postulate The magnitude of the effective test effort is proportional to the product of the applied work force and the number of remaining errors. for an appropriate . Analogy with the spring: Note: While keeping the effective test effort constant, a reduction in r requires an increase in workforce.

CDM Third Postulate The error reduction resistance is proportional to the error reduction velocity and inversely proportional to the overall quality of the test phase. for an appropriate . Analogy with the dashpot: Note: For a given quality of the test phase, a larger error reduction velocity leads to larger resistance.

State Model : Disturbance x(t) = Ax(t) + B u(t). Force (effort) balance equation:

Computing the feedback: Question Question: What changes to the process parameters will achieve the desired r(T+  T) ? r(T): the number of remaining errors at time T r(T+  T): the desired number of remaining errors at time T+  T Given:

Computing the feedback: Answer From basic matrix theory: The largest eigenvalue of a linear system dominates the rate of convergence. Hence we need to adjust the largest eigenvalue of the system so that the response converges to the desired value within the remaining weeks (  T). This can be achieved by maintaining: Obtain the desired eigenvalue.

Computing the feedback-Calculations ( max ) Compute the desired max Given the constraint: We know that the eigenvalues of our model are the roots of its characteristic polynomial of the A matrix.

Computing the feedback-Calculations ( max ) We use the above equation to calculate the space of changes to w and  such that the system maintains its desired eigenvalue. f

A Flow Model of Incremental Software Development/Test Test Specs Test Authoring Feat. Specs Test Code Coding Test Verification & Correction Reg. Cases Regression Testing Known Defects Code Debugging Project Code Latent Defects

Workforce Allocation Workforce allocated to particular tasks Effort is split across all active tasks

State-Model [Example] Equations System State Progress Feature Coding (fc) Code Debugging (dr) Test Authoring (ta) Test Debugging (td) Regression Testing (rr) Defect Model Development Testing

Variable Productivity Equation Human Productivity Workload Dependent (Csikszentmihalyi,’88) r b – Base Work rate c – Fractional size- dependent increase w c – Current workload size w n – Nominal workload size

The “Productivity” Eqns. Process Productivity (E.g. Feature Coding) Defect Introduction Defect Detection (Cangussu et al., ’02)

Control Strategy Model Predictive Control

Select Cost Functional E.g. Q 1,Q 2 := positive definite Calculate where S[x k, u k,k+P ]  x p k,k+P