Public Transportation Systems

"This unique book explains how to think systematically about public transportation through the lens of physics models. The book includes aspects of system design, resource management, operations and control. It presents both, basic theories that reveal fundamental issues, and practical recipes that can be readily used for real-world applications. The principles conveyed in this book cover not only traditional transit modes such as subways, buses and taxis but also the newer mobility services that are being enabled by advances in telematics and robotics. Although the book is rigorous, it includes numerous exercises and a presentation style suitable for senior undergraduate or entry-level graduate students in engineering. The book can also serve as a reference for transportation professionals and researchers keen in this field."--Publisher's description

6.2.2. Optimization and Solution Properties

Intro; Contents; Preface; About the Authors; Chapter 1. Transit Basics; 1.1. Need for Public Transportation; 1.2. Expectations and Challenges; 1.2.1. Stakeholders and Expectations; 1.2.2. Challenges; 1.3. Basic Typology of Transit Systems; 1.3.1. ROW; 1.3.2. Infrastructure; 1.3.3. Vehicles; 1.3.4. Type of Service; 1.4. Cost and Performance; 1.4.1. Costs; 1.4.2. Performance; References; Homework; Chapter 2. Analysis Tools; 2.1. The Time-Space Diagram; 2.1.1. A Single Vehicle; 2.1.2. Multiple Vehicles; 2.1.3. Application to Modeling and Analysis; 2.2. The Queueing Diagram; 2.2.1. Basics

2.2.2. Interpreting Data: Smoothing, Averages and Little's Formula2.2.3. Predicting Delay and Queue Evolution; 2.3. Optimization; 2.3.1. Unconstrained Optimization; 2.3.2. Constrained Optimization; 2.4. Dimensional Analysis; 2.4.1. Formula Verification; 2.4.2. Fundamental Ideas: Reformulation with Dimensionless Groups; 2.4.3. Application; References; Homework; Appendix 2.A. How to Identify Maximal Sets; Chapter 3. Planning -- General Ideas; 3.1. Planning Decisions; 3.1.1. Temporal Horizon; 3.1.2. Scope of the Solution Domain; 3.1.3. Modeling Philosophy

3.1.4. The Two-Step Method: Integer vs. Contin…