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Raymond J. Madachy



445 Hoes Lane Piscataway, NJ 08854

IEEE Press Editorial Board

Mohamed E. El-Hawary, Editor in Chief

R. Abari T. G. Croda R. J. Herrick

S. Basu S. Farshchi S. V. Kartalopoulos

A. Chatterjee B. M. Hammerli M. S. Newman

T. Chen

Kenneth Moore, Director of IEEE Book and Information Services (BIS)

Catherine Faduska, Senior Acquisitions Editor

Jeanne Audino, Project Editor

Technical Reviewers

Raman Aravamudham, University of Iowa Márcio Barros, UNIRIO/Brazil




Raymond J. Madachy



Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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v .


Foreword xiii

Barry Boehm

Preface xvii


Chapter 1 Introduction and Background 3

1.1 Systems, Processes, Models, and Simulation 6

1.2 Systems Thinking 8

1.2.1 The Fifth Discipline and Common Models 9

1.2.2 Systems Thinking Compared to System Dynamics 9

1.2.3 Weinberg’s Systems Thinking 10

1.3 Basic Feedback Systems Concepts Applied to the Software Process 10 1.3.1 Using Simulation Models for Project Feedback 13

1.3.2 System Dynamics Introductory Example 14

1.4 Brooks’s Law Example 16

1.4.1 Brooks’s Law Model Behavior 19

1.5 Software Process Technology Overview 22

1.5.1 Software Process Modeling 22

1.5.2 Process Lifecycle Models 29

1.5.3 Process Improvement 40

1.6 Challenges for the Software Industry 45

1.7 Major References 47

1.8 Chapter 1 Summary 48


Chapter 2 The Modeling Process with System Dynamics 53

2.1 System Dynamics Background 54

2.1.1 Conserved Flows Versus Nonconserved Information 55 2.1.2 The Continuous View Versus Discrete Event Modeling 55

2.1.3 Model Elements and Notations 56

2.1.4 Mathematical Formulation of System Dynamics 56

2.1.5 Using Heuristics 60

2.1.6 Potential Pitfalls 60

2.2 General System Behaviors 61

2.2.1 Goal-Seeking Behavior 61

2.2.2 Information Smoothing 63

2.2.3 Example: Basic Structures for General Behaviors 63

2.3 Modeling Overview 64

2.3.1 An Iterative Process 68

2.3.2 Applying the WinWin Spiral Model 70

2.4 Problem Definition 73

2.4.1 Defining the Purpose 73

2.4.2 Reference Behavior 74

2.4.3 Example: Model Purpose and Reference Behavior 75

2.5 Model Conceptualization 75

2.5.1 Identification of System Boundary 78

2.5.2 Causal Loop Diagrams 79

2.6 Model Formulation and Construction 83

2.6.1 Top-Level Formulation 84

2.6.2 Basic Patterns and Rate Equations 90

2.6.3 Graph and Table Functions 96

2.6.4 Assigning Parameter Values 99

2.6.5 Model Building Principles 101

2.6.6 Model Integration 103

2.6.7 Example: Construction Iterations 104

2.7 Simulation 110

2.7.1 Steady-state Conditions 112

2.7.2 Test Functions 113

2.7.3 Reference Behavior 115

2.8 Model Assessment 116

2.8.1 Model Validation 117

2.8.2 Model Sensitivity Analysis 121

2.8.3 Monte Carlo Analysis 125

2.9 Policy Analysis 126

2.9.1 Policy Parameter Changes 127

2.9.2 Policy Structural Changes 128

2.9.3 Policy Validity and Robustness 129

2.9.4 Policy Suitability and Feasibility 130

2.9.5 Example: Policy Analysis 130

2.10 Continuous Model Improvement 131


2.10.2 Feedback Loops 132

2.10.3 Hypotheses 132

2.10.4 When to Stop? 133

2.10.5 Example: Model Improvement Next Steps 133

2.11 Software Metrics Considerations 134

2.11.1 Data Collection 134

2.11.2 Goal–Question–Metric Framework 135

2.11.3 Integrated Measurement and Simulation 136

2.12 Project Management Considerations 138

2.12.1 Modeling Communication and Team Issues 139

2.12.2 Risk Management of Modeling Projects 140

2.12.3 Modeling Documentation and Presentation 141

2.12.4 Modeling Work Breakdown Structure 142

2.13 Modeling Tools 142

2.14 Major References 145

2.15 Chapter 2 Summary 146

2.15.1 Summary of Modeling Heuristics 148

2.16 Exercises 149

Chapter 3 Model Structures and Behaviors for Software Processes 155

3.1 Introduction 155

3.2 Model Elements 157

3.2.1 Levels (Stocks) 157

3.2.2 Rates (Flows) 159

3.2.3 Auxiliaries 159

3.2.4 Connectors and Feedback Loops 160

3.3 Generic Flow Processes 160

3.3.1 Rate and Level System 160

3.3.2 Flow Chain with Multiple Rates and Levels 161

3.3.3 Compounding Process 162

3.3.4 Draining Process 163

3.3.5 Production Process 163

3.3.6 Adjustment Process 163

3.3.7 Coflow Process 164

3.3.8 Split Flow Process 165

3.3.9 Cyclic Loop 165

3.4 Infrastructures and Behaviors 166

3.4.1 Exponential Growth 166

3.4.2 S-Shaped Growth and S-Curves 167

3.4.3 Delays 169

3.4.4 Balancing Feedback 175

3.4.5 Oscillation 177

3.4.6 Smoothing 180

3.4.7 Production and Rework 182

3.4.8 Integrated Production Structure 183

3.4.9 Personnel Learning Curve 183


3.4.10 Rayleigh Curve Generator 185

3.4.11 Attribute Tracking 186

3.4.12 Attribute Averaging 187

3.4.13 Effort Expenditure Instrumentation 187

3.4.14 Decision Structures 188

3.5 Software Process Chain Infrastructures 192

3.5.1 Software Products 193

3.5.2 Defects 196

3.5.3 People 200

3.6 Major References 203

3.7 Chapter 3 Summary 204

3.8 Exercises 204


Introduction to Applications Chapters 211

Chapter 4 People Applications 217

4.1 Introduction 217

4.2 Overview of Applications 221

4.3 Project Workforce Modeling 222

4.3.1 Example: Personnel Sector Model 222

4.4 Exhaustion and Burnout 224

4.4.1 Example: Exhaustion Model 224

4.5 Learning 227

4.5.1 Example: Learning Curve Models 231

4.6 Team Composition 234

4.6.1 Example: Assessing Agile Team Size for a Hybrid Process 235

4.7 Other Application Areas 252

4.7.1 Motivation 252

4.7.2 Personnel Hiring and Retention 256

4.7.3 Skills and Capabilities 260

4.7.4 Team Communication 260

4.7.5 Negotiation and Collaboration 261

4.7.6 Simulation for Personnel Training 263

4.8 Major References 265

4.9 Chapter 4 Summary 265

4.10 Exercises 267

Chapter 5 Process and Product Applications 269

5.1 Introduction 269

5.2 Overview of Applications 273

5.3 Peer Reviews 274


5.4 Global Process Feedback (Software Evolution) 291 5.4.1 Example: Software Evolution Progressive and 293

Antiregressive Work

5.5 Software Reuse 299

5.5.1 Example: Reuse and Fourth-Generation Languages 301 5.6 Commercial Off-the-Shelf Software (COTS)-Based Systems 309 5.6.1 Example: COTS Glue Code Development and COTS 310


5.6.2 Example: COTS-Lifespan Model 317

5.7 Software Architecting 319

5.7.1 Example: Architecture Development During Inception and 319 Elaboration

5.8 Quality and Defects 327

5.8.1 Example: Defect Dynamics 328

5.8.2 Example: Defect Removal Techniques and Orthogonal 330 Defect Classification

5.9 Requirements Volatility 333

5.9.1 Example: Software Project Management Simulator 337

5.10 Software Process Improvement 343

5.10.1 Example: Software Process Improvement Model 346

5.10.2 Example: Xerox Adaptation 354

5.11 Major References 362

5.12 Provided Models 363

5.13 Chapter 5 Summary 363

5.14 Exercises 364

Chapter 6 Project and Organization Applications 369

6.1 Introduction 369

6.1.1 Organizational Opportunities for Feedback 371

6.2 Overview of Applications 372

6.3 Integrated Project Modeling 373

6.3.1 Example: Integrated Project Dynamics Model 373

6.4 Software Business Case Analysis 395

6.4.1 Example: Value-Based Product Modeling 396

6.5 Personnel Resource Allocation 411

6.5.1 Example: Resource Allocation Policy and Contention Models 411

6.6 Staffing 416

6.6.1 Example: Rayleigh Manpower Distribution Model 418

6.6.2 Example: Process Concurrence Modeling 423

6.6.3 Integrating Rayleigh Curves, Process Concurrence, and 441 Brooks’s Interpretations

6.7 Earned Value 442

6.7.2 Example: Earned Value Model 450

6.8 Major References 460

6.9 Provided Models 460


6.10 Chapter 6 Summary 460

6.11 Exercises 462

Chapter 7 Current and Future Directions 469

7.1 Introduction 469

7.2 Simulation Environments and Tools 472

7.2.1 Usability 473

7.2.2 Model Analysis 473

7.2.3 Artificial Intelligence and Knowledge-Based Simulation 474

7.2.4 Networked Simulations 475

7.2.5 Training and Game Playing 475

7.3 Model Structures and Component-Based Model Development 476

7.3.1 Object-Oriented Methods 478

7.3.2 Metamodels 478

7.4 New and Emerging Trends for Applications 479

7.4.1 Distributed Global Development 480

7.4.2 User and People-Oriented Focus 482

7.4.3 Agile and Hybrid Processes 482

7.4.4 Commercial Off-the-Shelf Software 484

7.4.5 Open Source Software Development 486

7.4.6 Personnel Talent Supply and Demand 488

7.5 Model Integration 489

7.5.1 Common Unified Models 489

7.5.2 Related Disciplines and Business Processes 490

7.5.3 Meta-Model Integration 491

7.6 Empirical Research and Theory Building 492

7.6.1 Empirical Data Collection for Simulation Models 493 7.7 Process Mission Control Centers, Analysis, and Training Facilities 494

7.8 Chapter 7 Summary 496

7.9 Exercises 498

Appendix A: Introduction to Statistics of Simulation 501

A.1 Risk Analysis and Probability 502

A.2 Probability Distributions 503

A.2.1 Interpreting Probability Distributions 505

A.2.2 Measures of Location, Variability and Symmetry 506

A.2.3 Useful Probability Distributions 508

A.3 Monte Carlo Analysis 515

A.3.1 Inverse Transform 515

A.3.2 Example: Monte Carlo Analysis 516

A.4 Analysis of Simulation Input 521

A.4.1 Goodness-of-Fit Tests 521

A.5 Experimental Design 523


A.6 Analysis of Simulation Output 525 A.6.1 Confidence Intervals, Sample Size, and Hypothesis Testing 525

A.7 Major References 527

A.8 Appendix A Summary 527

A.9 Exercises 529

Appendix B: Annotated System Dynamics Bibliography 531

Appendix C: Provided Models 565

References 571

Index 593



The pace of change in software-intensive systems continues to accelerate at a dizzying rate. This presents a huge challenge for people trying to develop useful software. In the early days of software development, developers could freeze the requirements for the software, develop the software to the requirements, and deliver the resulting software two years later with confidence that the requirements would still be relevant and the software would be useful. Most of our software engineering processes, methods, and tools were developed and used under the assumption of relatively stable requirements. Examples are formal specification languages, performance-optimized point-solution designs, fixed-requirements software-cost estimation, earned-value management sys-tems, requirements traceability matrices, fixed-price/fixed-requirements contracts, and a general attitude that “requirements creep” was bad in that it destabilized software de-velopment.

However, as these practices became increasingly institutionalized, the accelerating rate of software change made them increasingly risky to use. Projects would use them for two years and become extremely frustrated when the users were not interested in the obsolete capabilities that resulted. Projects would fall behind schedule and use sta-tic models (time to complete = work remaining divided by work rate) to try to make up time by adding people, and run afoul of Brooks’s law (adding people to a late software project will make it later). Or they would sprint for the finish line using a point-solu-tion design that satisfied the initial requirements but was extremely difficult to modify when trying to satisfy users’ changing requirements.

Ironically, even with all of these difficulties, organizations would increasingly turn to software and its ability to be electronically upgraded as their best way to adapt their products, services, and systems to the increasing pace of change in their business or operational environment.


In order to keep up with this increased demand for software and the rapid pace of change, software organizations and projects need better ways to reason about the ef-fects of change on their software products, projects, and processes. This is often very difficult to do, as software changes often have complex second-order and higher-order interaction effects that are hard to visualize and reason about. Thus, for example, a project with high rates of change in its requirements, being developed by a team with high rates of change in its personnel, will need to understand and control the interac-tions of decreased productivity due to change processing, decreased productivity due to new staff members’ unfamiliarity with the project and product, and loss of produc-tivity when key staff members are diverted from project work to train and mentor new people in order to develop increased downstream productivity.

One of the best techniques for reasoning about the effects of such complex interact-ing changes is the System Dynamics modelinteract-ing framework that Ray Madachy presents in this book. As I have found in numerous applications of the method, it enables pro-ject personnel to model such effects and run the models to better understand the impli-cations of candidate project strategies and decisions.

From the pioneering application of Jay Forrester’s System Dynamics approach to software project modeling by Tarek Abdel-Hamid and Stuart Madnick in their 1991 book Software Project Dynamics, system dynamics modeling has been applied to many aspects of software development and management. These include the analysis of the effects on software system cost, schedule, and quality of alternative approaches to software process sequencing, software requirements determination, software architec-ture and design, software project organization and staffing, software development and integration, software quality assurance, and software change management. These ap-plications have constituted the major source of solution approaches in the software process simulation community and its annual series of ProSim conferences (recently combined with the Software Process Workshop into the International Conference on Software Process, held concurrently with the International Conference on Software Engineering).

Ray Madachy has been a major contributor to this body of work. His experience in applying system dynamics modeling as a technical leader in such diverse organizations as the aerospace corporation Litton Systems, the e-commerce system development company C-Bridge Institute, and the software tools company Cost Xpert Group have given him a broad and deep perspective on the critical success factors of developing and applying system dynamics models to various classes of software decision situa-tions. His experience in teaching and researching these techniques at USC has enabled him to develop an integrating framework and set of techniques that make system dy-namics modeling much easier and cost-effective to learn and apply to a software deci-sion situation.


chapter provides and explains a full range of model structures from modeling mole-cules to large infrastructures and flow chains that can be used in new models. Once this framework is established, there are three chapters that apply it to the most signifi-cant classes of system dynamics applications.

The first of these chapters covers useful applications to software personnel deci-sions: workforce levels and team composition, learning, burnout, skills, motivation, re-tention, and rotation effects. The second chapter covers software process and product decision situations: peer reviews, software reuse, COTS-based system development, software architecting, and software process improvement effects. The third chapter covers project and organization applications, such as business case analysis, defect re-duction strategies, and staffing management strategies. The final chapter projects like-ly future uses and research challenges in software process modeling and simulation, including how system dynamics models can add value via integration with other class-es of models.

The appendices also provide important and one-of-a-kind material. The first appen-dix covers statistics of simulation, which is not covered in traditional references on system dynamics. Next is a thorough annotated bibliography of work using system dy-namics for software processes, and is the definitive compendium for the field. Finally, the last appendix lists executable models provided with the book. These are used in ex-amples and can be used for further exercises or for incorporation into your own mod-els. These are valuable, reusable, and fun assets to go along with the book.

Overall, the book brings together a tremendous amount of useful process modeling material and experience in using it in practical software decision situations. It orga-nizes this material into a unifying framework that makes it easier to apply and explain, and illustrates it with a wide variety of useful examples. I believe that the book will serve as a standard reference for the software process dynamics field and a great help to practitioners and researchers for a good long time.

BARRYBOEHM Los Angeles, California University of Southern California June 2006



This book is designed for professionals and students in software engineering or infor-mation technology who are interested in understanding the dynamics of software de-velopment, or in assessing and optimizing process strategies. Its purpose is to improve decision making about projects and organizational policies by making its readers better informed about the dynamic consequences of decisions. Decisions may involve setting project budgets and schedules; return-on-investment analysis; trade-offs between cost, schedule, and quality or other factors; personnel hiring; risk management decisions; make, buy, or reuse; process improvement strategies; and so on.

The importance of process dynamics is hard to refute given the well-known (but too often ignored) combined effects of schedule pressure, communication overhead, changing business conditions, requirements volatility and user requests, experience, work methods such as reviews and quality assurance activities, task underestimation, bureaucratic delays, organizational shifts, demotivating events, other sociotechnical phenomena, and the feedback therein. These complex and interacting process effects are elegantly modeled with system dynamics using continuous quantities interconnect-ed in loops of information feinterconnect-edback and circular causality. Knowlinterconnect-edge of the interre-lated technical and social factors coupled with simulation tools can provide a means for organizations to improve their processes.

The objectives of this book are to:

앫 Provide methods, tools, models, and examples to improve management decision making at all levels. Simulation can support corporate strategy and investment analysis, business case development, project and portfolio management, and training, for example.


앫 Illustratesystems thinkingin action to develop increasingly deep understandings of software process structures and behaviors.

앫 Describe the modeling process, including calibration of models to software met-rics data.

앫 Show basic building blocks and model infrastructures for software development processes.

앫 Review the field of software process modeling with system dynamics. Show how others have used the principles of system dynamics to analyze and improve processes in organizations.

앫 Provide practical lessons learned about the dynamics of software processes. 앫 Provide sufficient introductory material, including exercises and executable

models on the Internet. Software practitioners who are brand new to simulation can immediately get their hands dirty and start modeling. Students can learn at their own pace, delving into the models as deeply as time and interest dictate. 앫 For those experienced in software process simulation, provide more detail of

critical implementation issues and future research motivations.

The book is mostly new material, except for some example applications, and syn-thesizes previous work in the area. There has been much growth in the field; it has evolved to a state of maturity, and this book addresses the need to communicate find-ings. It draws from over 100 publications from practitioners and researchers experi-enced in system dynamics modeling of processes in organizations (all of them summa-rized in Appendix B). It is written to be a self-contained learning experience, and a comprehensive reference for modeling practitioners. The sections are structured so that readers can approach the subject from different perspectives and gain valuable knowl-edge for further study and practice depending on their needs.

A constructive understanding of process dynamics is provided by the illustrated models. Where appropriate, guidelines are presented for process improvement and general software management strategies (common threads include risk management and concentrating on people). The perspective in the book addresses the dynamicsof software development, and best practices are described from that view. Some of these practices are illuminated through simulation experiments herein, and some will be-come foci of further study.

Readers may be involved in software process improvement, project planning and management, software development, testing, quality assurance, strategic corporate planning, organizational learning, education, or simply desire to understand the inter-related factors of software development. There is no need for sophisticated math skills, but a passing knowledge of numerical integration concepts will make the introductory material easier. Readers will increase their understanding of the complexities of soft-ware development and be able to use system dynamics for modeling and improving processes in their particular organizations. They will gain insight into the real-world mechanics behind the modeling equations.


cur-riculums in Software Engineering, Software Project Management, Software Quality Assurance, Systems Engineering or related subjects.

Part 1 of the book presents modeling fundamentals for software processes. These chapters may constitute an entire course for those new to system dynamics modeling. Advanced students should cover applications and future directions in Part 2. These topics can be studied in whole or as selected subjects. Other disciplines or focused studies may choose relevant application topics. For example, researchers in organiza-tions or sociology might want to cover people applicaorganiza-tions, engineering process groups might investigate selected process applications, while senior managers could focus on project or organizational applications.

The sequence and depth of subjects should be tailored accordingly for any of these uses. The variety of exercises in the book may serve as homework assignments, exam questions, or even major research projects. Except for the introductory chapters, de-tailed equations are generally omitted from the text and left for the reader to study from the models.

Though a primary objective is to instruct in computer-aided analysis, several identi-fied exercises early in the book should be done without a computer. This is to help de-velop intuition of process dynamics, and to strike a balance by not becoming overly re-liant on blindly using the computer during model development and evaluation of simulation results. The structure of the book is explained in more detail below.


This section provides a sequential outline of topics with selected highlights. Each chapter includes numerous graphics, charts, and tables to help illustrate the material. The book is also supplemented on the Internet containing the sample models and sim-ulation tools, exercises, extra references, and updates to the material. The book is di-vided into two major parts per the outline below:

Part 1—Fundamentals

Chapter 1—Introduction and Background

Chapter 2—The Modeling Process with System Dynamics

Chapter 3—Model Structures and Behaviors for Software Processes Part 2—Applications and Future Directions

Introduction to Applications Chapters Chapter 4—People Applications

Chapter 5—Process and Product Applications Chapter 6—Project and Organization Applications Chapter 7—Current and Future Directions Appendices and References

Appendix A—Introduction to Statistics of Simulation Appendix B—Annotated Bibliography

Appendix C—Provided Models References


Chapter 1 establishes the context and foundation of the book, with a goal of helping people use models to quantitatively evaluate processes in order to make better deci-sions. The chapter presents an introduction and background including motivational is-sues and a capsule history of the field. Definitions of terms are provided for reference throughout the book. The concepts of systems thinking are introduced, so one can see how simulation can be used to leverage learning efforts and improve organizational performance. Control systems principles are introduced, and then a simple motivation-al example of modeling Brooks’s Law is shown. A review of software process technol-ogy covers process modeling, lifecycle models, and process improvement.

A description of the iterative modeling process with the system dynamics simula-tion methodology is provided in Chapter 2. Basic modeling elements and classical sys-tem behaviors are shown. The underlying mathematical formulation of syssys-tem dynam-ics is covered with its ramifications for software process models.

The activities of problem definition, model formulation (including calibration), simulation, assessment, communication to others, and challenging the model for the next iteration are elaborated on. Since simulation is both art and science, guidelines and modeling heuristics are discussed. It is seen that there is much in common with software engineering principles in general such as iteration, abstraction, aggregation, and so on, yet there are also aspects of simulation that require somewhat different skills.

This chapter also details the multiperspective validation of system dynamics mod-els, which is of paramount importance before drawing policy conclusions from simula-tion experiments. Different modeling tools and environments are overviewed to help modelers in choosing appropriate tools for their different needs. Also see Appendix A on the use of statistics in the modeling process.

Chapter 3 presents patterns of model structures and behaviors for software process-es. Included is a detailed description of levels, flows, auxiliaries, infrastructures, and feedback loops instantiated for software processes. State variables of interest include software work artifacts, defect levels, personnel levels, effort expenditure, schedule date, and others. Corresponding rates over time include software productivity, defect introduction and elimination rates, financial flows for costs and revenue, and so on. Project reference behaviors for different structures and management policies are intro-duced.

An important contribution of this chapter is the explication of basic flow processes for software development. Common structures for software processes ferreted out of the major models (upcoming in Chapters 4 through 6) are shown. Together with proto-typical feedback loops such as learning and project controlling, these infrastructures can be (re)used to develop models relevant to any software process. This section also illustrates a major advantage in system dynamics models over other modeling tech-niques: inherent cost, schedule, and quality trade-offs by modeling their interactions.


Modeling examples from the field are shown with sample insights. The examples are further instances of the generic structures from Chapter 3.

The application examples show threads of simulation modeling with actual model implementations and worked out examples. These original examples should be of par-ticular value to system dynamics novices, and more experienced modelers can study them for additional ideas. Many also amplify some lessons learned regarding the soft-ware process. Some of the example models are also contained on the accompanying website. Additional exercises are provided for students to work out and practitioners to implement. Note that the applications chapters will also be updated online to keep up with new work.

Chapter 7 presents current and future directions in software process modeling and simulation. These include advances in simulation environments and tools, model struc-tures and component-based model development, new and emerging trends for applica-tion models, model integraapplica-tion (not just system dynamics models), empirical research, theory building, and putting it all together in process mission control centers and train-ing facilities.

Appendix A introduces statistics for simulation as an addendum to the modeling fundamentals about which simulation analysts, researchers, and graduate students studying broader aspects of simulation must be knowledgeable. Statistical methods are used to handle the stochastic inputs and outputs of simulation models. The appendix covers the principles of probability distributions, sample size, confidence intervals, and experimental design applied to continuous system simulation. Monte Carlo simu-lation is described and recommended probability distributions for software process modeling are also provided.

Appendix B is an annotated bibliography of using system dynamics for software processes and is the most complete set of references for the field. It demonstrates well the breadth of applications to date and is a convenient place to start researching partic-ular topics. These same citations are identified in the References in boldface.

Appendix C lists the provided models referenced in the chapters or exercises. These go along with the examples, and can be executed and modified by readers for their own purposes. These models will be updated and replaced on the Internet as improve-ments are made. Models provided by other readers will also be posted.


The referenced models, tools, updates, discussion, and color book information are available on the world wide web at http://csse.usc.edu/softwareprocessdynamics and at a mirror site http://softwareprocessdynamics.org.


I would like to extend sincere appreciation to all the other people who contributed to this work. I initially learned system dynamics for physiological modeling in a graduate


biomedical engineering course at UCSD in 1982 under the excellent direction of Drs. Alan Schneider and James Bush. This book would not be complete without the accom-plishments of other researchers and support of colleagues including Dr. Tarek Abel-Hamid, Richard Adams, Dr. Vic Basili, Dr. James Collofello, Scott Duncan, Dr. Susan Ferreira, Dr. David Ford, Tobias Haberlein, Jim Hart, Dr. Dan Houston, Dr. Marc Kellner, Peter Lakey, Dr. Manny Lehman, Dr. Robert Martin, Dr. Margaret Johnson, Emily oh Navarro, Dr. Nathaniel Osgood, Dr. Dietmar Pfahl, Oliver Pospisil, Dr. David Raffo, Dr. Juan Ramil, Dr. Stan Rifkin, Dr. Howard Rubin, Dr. Ioana Rus, Dr. Walt Scacchi, Dr. Neil Smith, Dr. Greg Twaites, Dr. Wayne Wakeland, Dr. Gerry Weinberg, Dr. Paul Wernick, and Ed Yourdon; Litton personnel including Dr. Denton Tarbet, Wayne Sebera, Larry Bean, Frank Harvey, and Roy Nakahara; Charles Lein-bach from C-bridge Institute; Benny Barbe from Cost Xpert Group; and Dr. Julian Richardson and Dr. Michael Lowry for their support at NASA. USC graduate students who contributed to this work are Ashwin Bhatnagar, Cyrus Fakharzadeh, Jo Ann Lane, Dr. Nikunj Mehta, Kam Wing Lo, Jason Ho, Leila Kaghazian, Dr. Jongmoon Baik (also including post-graduate contributions), and Wook Kim. Profound thanks goes to Dr. Barry Boehm, who has served as a mentor and been my biggest influence since the middle of my Ph.D. studies. This book owes much to his continual support, penetrating insights, and inspiration to contribute. Many thanks to the anonymous IEEE reviewers for their long hours and detailed constructive reviews, and IEEE staff including Jeanne Audino, Cathy Faduska, Chrissy Kuhnen, Cheryl Baltes, and Matt Loeb. I also am most grateful to my wife Nancy for her long-term support and lots of patience, and my young daughters Zoey and Deziree for extra motivation and lessons on adaptation to change.


The field of software process modeling itself is quite dynamic, with much happening in conjunction with other software process work. It has been a challenge keeping up with the times as this book has progressed, and the rate of change in the industry has increased over these years. It is inevitable that some things will continue to change, so the reader is urged to access the Internet site for updates at any time, including new and improved models.

Updates to the chapters will be put on the book’s Internet site until the next pub-lished edition. The application Chapters 4–6 will have substantial updates and entire sections replaced. The goal is to keep the applications current and presented in a uni-form uni-format. Chapter 7 on current and future directions is a wild card in terms of pre-dicted changes, and the annotated bibliography will be updated continuously.


edi-tion. You are encouraged to send any ideas, improvement suggestions, new and en-hanced models, or worked out exercises from this book. They will be included in fu-ture editions as appropriate.

RAYMONDJ. MADACHY Los Angeles, California

November 2007





Software Process Dynamics.By Raymond J. Madachy 3 Copyright © 2008 the Institute of Electrical and Electronics Engineers, Inc.




Everything is connected to everything.


Software and information technology professionals, managers, executives, and busi-ness analysts have to cope with an increasingly dynamic world. Gone are the days when one’s software technology, hardware platforms, organizational environment, and competitive marketplace would stay relatively stable for a few years while developing a system. Thus, the ability to understand and reason about dynamic and complex soft-ware development and evolution processes becomes increasingly valuable for decision making.

Particularly valuable are automated aids built upon knowledge of the interacting factors throughout the software life cycle that impact the cost, schedule, and quality. Unfortunately, these effects are rarely accounted for on software projects. Knowledge gleaned from a global perspective that considers these interactions is used in exe-cutable simulation models that serve as a common understanding of an organization’s processes. Systems thinking, as a way to find and bring to light the structure of the or-ganizational system that influences its dynamic behavior, together with system dynam-ics as a simulation methodology, provide critical skills to manage complex software development.


Forrester at MIT to improve organizational structures and processes [Forrester 1961]. It was not applied in software engineering until Tarek Abdel-Hamid developed his dis-sertation model, which is featured in the book Software Project Dynamics [Abdel-Hamid, Madnick 1991].

Simulation usage is increasing in many disparate fields due to constantly improving computer capabilities, and because other methods do not work for complex systems. Simulations are computationally intensive, so they are much more cost-effective than in the past. Simulation is general-purpose and can be used when analytic solutions are extremely difficult if not impossible to apply to complex, nonlinear situations. Simula-tion is even more powerful with improved data collecSimula-tion for the models. Example areas where increased processing power combined with improved models and data in-clude meteorology to better predict hurricane paths, environmental studies, physical cosmology, chemistry to experiment with new molecular structures, or archaeology to understand past and future migrations. These are practical applications but simulation can also be used for experimentation and theory building.

The simulation process in an organization involves designing a system model and carrying out experiments with it. The purpose of these “what if” experiments is to de-termine how the real or proposed system performs and to predict the effect of changes to the system as time progresses. The modeling results support decision making to im-prove the system under study, and normally there are unintended side effects of deci-sions to consider. The improvement cycle continues as organizational processes are continually refined.

Simulation is an efficient communication tool to show how a process works while stimulating creative thinking about how it can be improved. The modeling process it-self is beneficial; it is generally acknowledged that much of the reward of modeling is gained in the early stages to gather data, pose questions, brainstorm, understand processes, and so on.

There are many practical benefits of performing simulation in organizations. Be-sides individual project planning, simulation can help evaluate long-run investment and technology strategies. Companies can use simulation for continuous process im-provement, regardless of their current process maturity. It can support organizational learning by making models explicit in a group setting, where all participants can con-tribute and buy into the model. Such collaboration can go a long way to effect team-building.

Simulation can also be used in individual training, since participants can interact with executing models in real time to see the effects of their decisions. Simulations are used extensively for training in aerospace, military, and other fields. Student awareness is heightened when virtual “games” with simulations are used, particular-ly when they participate interactiveparticular-ly. Visual dynamic graphs or virtual rendering provide faster and more easily remembered learning compared to the traditional lec-ture format. Exploration is encouraged through the ability to modify and replay the models.


uncertainties of development. Previously unforeseen “gotchas” will be brought to the forefront and mitigated through careful planning.

System dynamics modeling can provide insights by investigating virtually any as-pect of the software process at a macro or micro level. It can be used to evaluate and compare different life-cycle processes, defect detection techniques, business cases, in-teractions between interdisciplinary process activities (e.g. software and nonsoftware tasks), deciding “how much is enough” in terms of rigor or testing, and so on. Organi-zations can focus on specific aspects of development cost, schedule, product quality, or the myriad trade-offs, depending on their concerns.

The issues of software processes are very wide-ranging, so the scope and bound-aries of this book will be defined. The focus is not on technical fundamentals of soft-ware programming or specific methodologies, but on the dynamics of software processes. The second definition from Webster’s dictionary describes the prime focus of this book, particularly the relations between forces:

Dynamics—1. The branch of mechanics dealing with the motions of material bodies un-der the action of given forces2. a) the various forces, physical, moral, economic, etc. operating in any field b) the way such forces shift or change in relation to one anoth-er c) the study of such forces.

Essentially, this book is about understanding the dynamics of software processes with the help of simulation modeling. Software process dynamics is a more general term than software project dynamics, which is limiting in the sense that dynamics oc-cur outside of project boundaries such as continuous product line development, organi-zational reuse processes contributing to many projects, or other strategic processes. A project is also considered an execution of a process, roughly analogous to how a pro-gramming object is an instance or execution of a class.

When simulation is used for personnel training, the term process flight simulationis sometimes used to invoke the analogy of pilots honing their skills in simulators to re-duce risk, with the implicit lesson that software managers and other personnel should do the same. Use of the system dynamics method may on occasion be referred to as dy-namic process simulation, dydy-namic simulation, orcontinuous systems simulation.

Alternative titles for this book could be The Learning Software Organization or Software Process Systems Thinking, depending on the camp de jour. System dynamics and, particularly, organizational learning gained wider public exposure due to Peter Senge’s bestselling book The Fifth Discipline [Senge 1990]. Organizational learning in the context of a software process involves translating the common “mental model” of the process into a working simulation model that serves as a springboard for in-creased learning and improvement. This learning can be brought about by applying system dynamics to software process and project phenomena.

There are other excellent references on system dynamics modeling that one could use to learn from, but why should a busy software engineer studying the software process spend so much time with examples outside of his/her field? This book uses ex-amples solely from the software process domain to minimize modeling skill transfer time. Organizational learning and systems thinking are also well documented


where (see the popular books by Peter Senge and collaborators [Senge 1990], [Senge et al. 1994]).


Important terminology for the field is defined in this section. A systems orientation is crucial to understanding the concepts herein, so system will first be defined generally as a subset of reality that is a focus of analysis. Technically, systems contain multiple components that interact with each other and perform some function together that can-not be done by individual components. In simulation literature, a system is typically defined as “a collection of entities, e.g., people or machines, that act and interact to-gether toward the accomplishment of some logical end” [Law, Kelton 1991]. For-rester’s system definition is very close: “a grouping of parts that operate together for a common purpose” [Forrester 1968].

Systems exist on many levels; one person’s system is another person’s subsystem. Since systems are influenced by other systems, no system is isolated from external fac-tors. How to define system boundaries for meaningful analysis is discussed later in this book.

Systems are classified as “open” if the outputs have no influence on the inputs; open systems are not aware of their past performance. A “closed” system is also called a feedback system; it is influenced by its own behavior through a loop that uses past actions to control future action. The distinction between open and closed systems is particularly important in the context of system dynamics.

A system can be characterized by (1) parameters that are independent measures that configure system inputs and structure, and (2) variables that depend on parameters and other variables. Parameters in human systems are directly controllable. The collection of variables necessary to describe a system at any point in time is called the stateof the system. Examples of state variables for a software process are the number of personnel executing the process; the amount of software designed, coded, and tested; the current number of defects; and so on.

Real-world systems can be classified as static or dynamic depending on whether the state variables change over time. The state of a static system does not change over time, whereas the state of a dynamic system does. Dynamic systems can be further classified as continuous, discrete, or combined, based on how their variables change over time.

Variables change continuously (without breaks or irregularities) over time in a con-tinuous system, whereas they change instantaneously at separated time points in a dis-crete system. A lake is an example of a continuous system since its depth changes con-tinuously as a function of inflows and outflows, whereas a computer store queue would be considered discrete since the number of customers changes in discrete quan-tities. A software process arguably has continuous quantities (personnel experience, motivation, etc.) and discrete ones (lines of code, defects, etc.)


de-pends on the modeling purpose, and some discrete systems can be assumed to be con-tinuous for easy representation. For example, some would consider a software process to be a system with discrete entities since it can be described by the number of people working, number of units/lines/objects produced, defects originated, and so on, but much difficulty will be avoided if each entity does not need to be traced individually. Hence, the approach in this book and system dynamics in general is to treat the “flow” of the software process as continuous.

A software process is a set of activities, methods, practices, and transformations used by people to develop software. This is a general definition from the commonly accepted Software Engineering Institute’s Capability Maturity Model (SEI CMM) [Paulk et al. 1994]. In the context of this book, the software process is the system un-der study.

A system must be represented in some form in order to analyze it and communicate about it. A modelin the broadest sense is a representation of reality, ranging from physical mockups to graphical descriptions to abstract symbolic models. Software pro-grams are themselves executable models of human knowledge. A model in the context of this book is a logical, quantitative description of how a process (system) behaves. The models are abstractions of real or conceptual systems used as surrogates for low cost experimentation and study. Models allow us to understand a process by dividing it into parts and looking at how they are related.

Dynamic process models can be discrete, continuous, or a combination of the two. The essential difference is how the simulation time is advanced. Continuous systems modeling methods such as system dynamics always advance time with a constant delta. Since variables may change within any time interval in a continuous system, the delta increment is very small and time-dependent variables are recomputed at the end of each time increment. The variables change continuously with respect to time. Discrete modeling normally is event based. State changes occur in discrete systems at aperiodic times depending on the event nature, at the beginning and end of event activities. The simulation time is advanced from one event to the next in a discrete manner.

All classes of systems may be represented by any of the model types. A discrete model is not always used to represent a discrete system and vice versa. The choice of model depends on the specific objectives of a study. Models of the software processes are either static,1in which time plays no role, or dynamic, in which a system evolves

over time. The dynamic process models described this book are classified as symbolic, or mathematical ones.

Models may be deterministic, with no probabilistic components, or stochastic, with randomness in the components. Few, if any, software processes are wholly de-terministic. Stochastic models produce output that is random and must be handled as such with independent runs. Each output constitutes an estimate of the system char-acteristics.


1A cost model such as COCOMO II [Boehm et al. 2000] is traditionally a static model since the cost factors


Simulationis the numerical evaluation of a mathematical model describing a sys-tem of interest. Many syssys-tems are too complex for closed-form analytical solutions, hence, simulation is used to exercise models with given inputs to see how the system performs. Simulation can be used to explain system behavior, improve existing sys-tems, or to design new systems too complex to be analyzed by spreadsheets or flow-charts.

Finally,system dynamics is a simulation methodology for modeling continuous sys-tems. Quantities are expressed as levels, rates, and information links representing feed-back loops. Levels represent real-world accumulations and serve as the state variables describing a system at any point in time (e.g., the amount of software developed, num-ber of defects, numnum-ber of personnel on the team, etc.) Rates are the flows over time that affect the levels. See Table 1.3-1 for a preview description of model elements. System dynamics is described in much more detail in Chapter 2.

A complete and rigorous reference for terms related to modeling and simulation can be found at [DMSO 2006].


Systems thinking is a way to ferret out system structure and make inferences about the system, and is often described as an overall paradigm that uses system dynamics prin-ciples to realize system structure. Systems thinking is well suited to address software process improvement in the midst of complexity. Many organizations and their models gloss over process interactions and feedback effects, but these must be recognized to effect greater improvements.

Systems thinking involves several interrelated concepts:

앫 A mindset of thinking in circles and considering interdependencies. One realizes that cause and effect can run both ways. Straight-line thinking is replaced by closed-loop causality.

앫 Seeing the system as a cause rather than effect (internal vs. external orientation). Behavior originates within a system rather than being driven externally, so the system itself bears responsibility. It is the structure of a system that determines its dynamic behavior.

앫 Thinking dynamically in terms of ongoing relationships rather than statically. 앫 Having an operational vs. a correlational orientation; looking at how effects

hap-pen. Statistical correlation can often be misleading. A high correlation coeffi-cient between two factors does not prove that one variable has an impact on the other.



The Fifth Discipline and Common Models

Senge discusses five disciplines essential for organizational learning in [Senge 1990]: personal mastery, mental models, shared vision, team learning, and systems thinking. Systems thinking is the “fifth” discipline that integrates all the other disciplines and makes organizational learning work. Improvement through organizational learning takes place via shared mental models.

Mental models are used in everyday life for translating personal or organizational goals into issues, questions, and measures. They provide context for interpreting and acting on data, but seldom are stated explicitly. Mental models become more concrete and evolve as they are made progressively explicit. The power of models increases dramatically as they become more explicit and commonly understood by people; hence, process modeling is ideally suited for organizational improvement.

For organizational processes, mental models must be made explicit to frame con-cerns and share knowledge among other people on a team. Everyone then has the same picture of the process and its issues. Senge and Roberts provide examples of team techniques to elicit and formulate explicit representations of mental models in [Senge et al. 1994]. Collective knowledge is put into the models as the team learns. Elaborated representations in the form of simulation models become the bases for process im-provement.


Systems Thinking Compared to System Dynamics

Systems thinking has been an overloaded term in the last 15 years with many definitions. Virtually any comparison with system dynamics is bound to be controversial due to se-mantic and philosophical issues. Barry Richmond addressed the differences between systems thinking and system dynamics mindsets in detail in [Richmond 1994a]. His ma-jor critique about “the historical emphasis of system dynamics” is that the focus has been on product rather than transferring the process (of model building). Only a privileged few developed models and presented them to the world as “the way” as opposed to edu-cating others to model and letting them go at it.2His prescription is a systems thinking

philosophy of providing skills rather than models per se. Relevant aphorisms include “Give a fish, eat for a day; teach to fish, eat for a lifetime,” or “power to the people.”

His definition of systems thinking is “the art and science of making reliable infer-ences about behavior by developing an increasingly deep understanding of underlying structure.” It is both a paradigm and a learning method. The paradigm is a vantage point supplemented with thinking skills and the learning method is a process, language, and technology. The paradigm and learning method form a synergistic whole. System namics inherently fits in as the way to understand system structure. Thus, system dy-namics is a methodology to implement systems thinking and leverage learning efforts.

We prefer not to make any hard distinctions between camps because it is a semantic issue. However, this book is architected in the spirit of systems thinking from the per-spective of transferring the process. The goal is to teach people how to model and give


2It should be noted encouragingly that the system dynamics pioneer Jay Forrester and others at MIT are


them tools to use for themselves, rather than say “here is the model for you to use.” This is a major difference between Software Project Dynamics and this book. Abdel-Hamid and Madnick present a specific model with no guidance on how to develop a system dynamics model, though very few organizations are content to use the model as-is. Their work is still a seminal contribution and it helped make this book possible.


Weinberg’s Systems Thinking

Gerry Weinberg writes about systems thinking applied to software engineering in Quality Software Management, Volume 1: Systems Thinking [Weinberg 1992]. It is an insightful book dealing with feedback control and has a close kinship with this book, even though it is almost exclusively qualitative and heuristic. Some academic courses may choose his book as a companion to this one. It provides valuable management in-sights and important feedback situations to be modeled in more detail.

Weinberg’s main ideas focus around management thinking correctly about devel-oping complex software systems—having the right “system model” for the project and its personnel. In a restatement of Brooks’s dictum that lack of schedule time has doomed more projects than anything else, Weinberg writes in [Weinberg 1992], “Most software projects have gone awry from management’s taking action based on incorrect system models than for all other causes combined.”

One reason management action contributes to a runaway condition is the tendency to respond too late to deviations, which then forces management to take big actions, which themselves have nonlinear consequences. In order to stay in control of the soft-ware process, Weinberg advises to “act early, act small.” Managers need to continual-ly plan, observe the results, and then act to bring the actuals closer to planned. This is the prototypical feedback loop for management.

Weinberg was working on his book at the same time that Abdel-Hamid and Mad-nick were working on theirs, unknown to each other. The day after Weinberg submit-ted his work to the publisher, he met Abdel-Hamid and realized they were working on parallel and complementary paths for years. Weinberg describes the relationship be-tween the two perspectives as follows. He starts from the low end, so projects get sta-ble enough so that the more precise, high-end modeling exemplified by system dynam-ics can be even more useful.

Much of Weinberg’s book discusses quality, on-the-job pressures, culture, feedback effects, dynamics of size and fault resolution, and more. He proceeds to describe the low-level interactions of software engineering, which are the underlying mechanics for many of the dynamic effects addressed by various process models described in this book. His work is referenced later and provides fodder for some exercises.




processes of communication and control (especially the comparison of these processes in biological and artificial systems) [Weiner 1961]. Cybernetic principles are relevant to many types of systems including moving vehicles (ground, air, water, or space), bi-ological systems, individuals, groups of individuals, and species.

We are all familiar with internal real-time control processes, such as when driving down a road. We constantly monitor our car’s position with respect to the lane and make small adjustments as the road curves or obstacles arise. The process of monitor-ing actual position against desired position and makmonitor-ing steermonitor-ing adjustments is similar to tracking and controlling a software project. The same mathematics apply, so system dynamics can be used to model the control aspects of either human driving or project management.

Control systems theory provides a rigorous framework for analyzing complex feed-back systems. This section will introduce some basic system notations and concepts, and apply to them to our system of study—the software process. The purpose is to re-alize a high-level analogy of control principles to our domain, and we will forego mathematical formulae and more sophisticated feedback notations.3System dynamics

is our chosen method for modeling feedback systems in a continuous-time fashion, as used in the rest of this book.

Figure 1.1 shows the most basic representation of an open system, whereby a black-box system transforms input to output per its internal processing functions. Input and output signals are treated as fluxes over time. It is open because the outputs have no system influence (frequently, it is also called an open-loopsystem despite the absence of any explicit loops). Figure 1.2 shows the closed-loop version with a controller im-plementing feedback. A decomposition of the controller shows two major elements: a sensor and a control device, shown in Figure 1.3.

The borrowing of these standard depictions from control systems theory can lead to misinterpretation about the “system” of interest for software processes. In both Figures 1.2 and 1.3, the controller is also of major concern; it should not be thought of as being “outside” the system. One reason for problems in software process improvement is that management is often considered outside the system to be improved. Therefore, the boundary for a software process system including management should encompass all the elements shown, including the controller.

Applying these elements to the software process, inputs traditionally represent re-quirement specifications (or capabilities or change requests), the system is the software development (and evolution) process with the management controller function, and the outputs are the software product artifacts (including defects). The sensor could be any means of measuring the output (e.g., analyzing software metrics), and the control de-vice is the management action used to align actual process results with intended. This notation can represent either a one-time project or a continual software evolution process.

If we consider all types of inputs to the software process, the vector includes re-sources and process standards as well as requirements. Rere-sources include people and


3We are not covering signal polarities, integrators, summers, transfer functions, Laplace transforms,


machines used to develop and evolve the software. Process standards include methods, policies, procedures, and so on. Even the process life-cycle model used for the project can be included (see Section 1.3.2). Requirements include functional requirements, project constraints like budget and schedule, support environment requirements, evo-lution requirements, and more. Process control actions that management takes based on measurements may affect any of these inputs.

Substituting software process elements into the generic system description pro-duces Figures 1.4, keeping the controller aggregated at the top level representing inter-nal process management.

However, the management controller only represents endogenous process mecha-nisms local to the development team. These are self-initiated control mechamecha-nisms. In reality, there are external, or exogenous feedback forces from the operational

environ-System Output Input

Figure 1.1. Open system.

System Output Input


Figure 1.2. Closed system with controller.

System Output



Control device



ment of the software—global feedback. The feedback can be user change requests from the field, other stakeholder change mandates, market forces, or virtually any ex-ternal source of requirements evolution or volatility. The exogenous feedback is a very important effect to understand and try to control. An enhanced picture showing the two sources of feedback is in Figure 1.5.

The outer, global feedback loop is an entire area of study in itself. Of particular note is the work of Manny Lehman and colleagues on software evolution, which is high-lighted in Chapter 5 and referenced in several other places (also see their entries in Ap-pendix B).

These feedback mechanisms shown with control systems notation are implemented in various ways in the system dynamics models shown later. Feedback is represented as information connections to flow rates (representing policies) or other parameters that effect changes in the systems through connected flow rates.


Using Simulation Models for Project Feedback

Projects can proactively use simulation models to adapt to change, thereby taking ad-vantage of feedback to improve through models. This is one way to implement opera-tional control through simulation. A simulation model can be used for metrics-based feedback during project execution since its input parameters represent project



Process Software Artifacts Requirements, resources, standards


Figure 1.4. Software process control system with management controller.


Process Software Artifacts Requirements, resources etc.

internal project feedback

external feedback from operational environment Software Development or Evolution Project


tives, priorities, available components, or personnel. It serves as a framework for pro-ject rescoping and line management to reassess risks continuously and support replan-ning.

Figure 1.6 shows a project rescoping framework utilizing metrics feedback and simulation. By inputting parameters representing changed conditions, one can assess whether the currently estimated cost and schedule are satisfactory and if action should be taken. Either rescoping takes places or the project executes to another feedback milestone, where the model is updated with actuals to date and the cycle repeats.


System Dynamics Introductory Example

Table 1.1 is a heads-up preview of system dynamics model elements used throughout this book. The capsule summary may help to interpret the following two examples be-fore more details are provided in Chapter 2 (this table is a shortened version of one in Chapter 2). We are jumping ahead a bit in order to introduce a simple Brooks’s Law model. Novices may also want to consult the system dynamics introduction in Chapter 2 to better understand the model elements.

Throughout this text and in other references, levels are synonymous with “stocks” and rates are also called “flows.” Thus, a stock and flow representation means an elab-orated model consisting of levels and rates.

A simple demonstration example of modeling process feedback is shown in the Fig-ure 1.7 system diagram. In this model, the software production rate depends on the number of personnel, and the number of people working on the project is controlled via a feedback loop. The linear software production rate is expressed as

software production rate = individual productivity · personnel



The management decision that utilizes feedback from the actual work accomplished is the following equation for personnel allocation:

personnel allocation rate = if (completed software < planned completion) then 1 else 0

This highly oversimplified feedback decision says to add a person whenever actual progress is less than planned. If actual progress meets or exceeds the planned progress, than no changes are made to the staff (zero people are added). Presumably, this man-agement policy would keep a project on track, assuming a productivity increase when


Table 1.1. System dynamics model elements (capsule summary)

Element Notation Description

Level A level is an accumulation over time, also called

a stock or state variable. They are functions of past accumulation of flow rates. Examples in-clude software tasks of different forms, defect levels, or personnel levels.

Source/Sink Sources and sinks indicate that flows come from

or go to somewhere external to the process. They represent infinite supplies or repositories that are not specified in the model. Examples in-clude sources of requirements, delivered soft-ware, or employee hiring sources and attrition sinks.

Rate Rates are also called flows. They are the

“ac-tions” in a system. They effect the changes in levels and may represent decisions or policy statements. Examples include software produc-tivity rate, defect generation rate, or personnel hiring and deallocation rates.

Auxiliary Auxiliaries are converters of input to output, and

help elaborate the detail of stock and flow struc-tures. Auxiliaries often represent “score-keep-ing” variables and may include percent of job completion, quantitative goals or planned val-ues, defect density, or constants like average de-lay times.

Information Information linkages are used to represent

Link information flow (as opposed to material flow).


someone is added. It does not consider other ripple effects or nonlinearities of adding extra people, which is addressed in the next example.


A small motivational example of modeling Brooks’s Law is described here. In the ear-ly software engineering classic The Mythical Man-Month (it was also updated in 1995), Fred Brooks stated, “Adding manpower to a late software project makes it lat-er” [Brooks 1975]. His explanation for the law was the additional linear overhead needed for training new people and the nonlinear communication overhead (a function of the square of the number of people). These effects have been widely accepted and observed by others. The simple model in Figure 1.8 describes the situation, and will be used to test the law. Model equations and commentary are in Figure 1.9.4This model is

personnel completed software

personnel allocation rate individual productivity


planned completion software production rate

Figure 1.7. System dynamics representation of simple project feedback. The software production flow chain models productivity as a linear function of the number of personnel. The level of completed software increases according to the production rate flowing into it.

The personnel chain models the personnel level rising as more people are allocated to the project. The allocation rate operates on the difference between actual and planned completion.

This variable of planned completion over time is used in making the personnel allocation decision.

4Mathematically inclined readers may appreciate differential equations to represent the levels. This

represen-tation is notnecessary to understand the model. The following integrals accumulate the inflow and outflow rates over time to calculate a level at any time tusing the standard notation:

level = levelt=0+



(inflow - outflow) dt requirements = requirementst=0–




Figure 1.1. Open system.
Table 1.1. System dynamics model elements (capsule summary)
Figure 1.7. System dynamics representation of simple project feedback.
Figure 1.8. Brooks’s Law model.


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