SIMULATION LAB (EX-804) - Unit 2 Short Notes

UNIT 2: SIMULATION MODELING & ANALYSIS

2.1 Fundamentals of Discrete-Event Simulation (DES)

Core Concepts & Terminology

• System: A set of interacting entities pursuing a common objective.

• Model: An abstract, simplified representation of a system.

• Simulation: The process of experimenting with a model over time to understand system behavior.

• Discrete-Event Simulation (DES): A simulation where the state of the system changes at discrete points in time (events). Contrast with Continuous (state changes continuously) and Monte Carlo (static, probabilistic).

• Key DES Components:

  | Component | Description | Example | | :--- | :--- | :--- | | Entity | Dynamic object that moves through the system. | Customer, Job, Part | | Attribute | Characteristic of an entity. | Priority, Type, Size | | Resource | Static object that provides service. | Server, Machine, Agent | | Queue | Holding area for entities waiting for a resource. | Line, Buffer | | Activity | A period of time where an entity occupies a resource. | Service Time | | State Variables | Variables describing the system at an instant. | # in queue, resource state | | Event List | Scheduled future events (time, type). | Arrival at 10:05, Departure at 10:12 |

The Simulation Process Lifecycle

A structured, iterative approach:

1. Problem Definition & Objectives: What is the question? (e.g., "Reduce average wait time by 15%")

2. Data Collection & Input Analysis: Gather data, fit distributions (Exponential, Normal, etc.).

3. Model Conceptualization & Logical Design: Create flowcharts/block diagrams.

   DiagramCANVAS: A simple flowchart with Create -> Queue -> Seize Resource -> Delay -> Release Resource -> Dispose

4. Model Implementation: Build the model in software (coding/module connection).

5. Verification & Validation (V&V): "Did we build the model right?" & "Did we build the right model?"

6. Experimental Design & Output Analysis: Define runs (replications, warm-up), analyze results statistically.

7. Documentation & Presentation: Report findings, recommendations, limitations.

2.2 Simulation Software & Tool Proficiency

Software Architecture (Generic)

• Modules/Blocks: Building blocks (Create, Process, Dispose, Decide, Assign).

• Flowchart View: Visual model construction.

• Data/Spreadsheet View: Define parameters, attributes, resources, schedules.

• Run Controller: Set replication length, warm-up period, number of replications.

• Report/Output Viewer: Built-in statistics and custom reports.

Building Basic Models

• Entity Flow: Create (arrival process) → Process/Seize-Delay-Release → Dispose.

• Resources: Defined in data sheet. Seize (request), Release (free). Can define capacity.

• Queues: Automatically created by Seize if no resource available. Logic: FIFO (default), LIFO, Priority (based on attribute).

• Routing: Decide (probability/condition), Route (assign to specific destination), Branch (split into multiple paths).

• Entity Grouping: BATCH (combine entities), SEPARATE (split batch), MATCH (pair entities).

Input Data Integration

• Statistical Distributions: Fit to real data. Common: Exponential (interarrival), Normal/LogNormal (service), Uniform, Triangular, Empirical (from data file).

• External Data: Import CSV/Excel for arrival schedules, attribute values, or resource schedules.

• Expression Builder: Use for dynamic logic (e.g., IF(Attribute1=1, RouteA, RouteB)).

2.3 Model Verification & Validation (V&V)

2.4 Experimental Design & Output Analysis

Types of Simulation Experiments

• Warm-up Period (Transient Removal): Initial period where system state is not representative (e.g., empty queues). Must be truncated before collecting output data. Determined by batch means method or observing stability of key metrics.

• Replication vs. Single Long Run:

  | Replication (Multiple Short Runs) | Single Long Run | | :--- | :--- | | Use for terminating systems (has natural end). | Use for non-terminating (steady-state) systems. | | Independent runs, different RNG streams. | One very long run. | | Output: Average of replication means. | Output: Time-average over long run. | | Allows calculation of confidence intervals easily. | Requires careful batch means for CI. |

• What-If Scenarios: Compare alternatives (e.g., 2 servers vs. 3 servers) using statistical tests.

Output Data & Statistical Analysis

• Types of Output:

  • Time-Persistent: Single value per replication (e.g., average wait time, max utilization).

  • Time-Series: Value at many time points (e.g., queue length over time).

• Key Performance Indicators (KPIs):

  • Throughput: Entities processed per unit time.

  • Utilization: % time resource is busy. \boxed{\text{Utilization} = \frac{\text{Busy Time}}{\text{Total Time}}}

  • Cycle Time / Sojourn Time: Total time in system.

  • Waiting Time: Time spent in queue only.

  • Bottleneck Identification: Resource with highest utilization or longest queue.

• Statistical Comparison of Alternatives:

  • Calculate mean and standard deviation of the KPI across n replications.

  • For large n (≥30), use t-test for difference in means:

$$t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$

*   Compare |t| to critical t-value. If |t| > t_crit, means are **significantly different** at chosen confidence level (e.g., 95%).

*   **Confidence Interval (CI) for a Mean:**

$$\bar{X} \pm t_{\alpha/2, n-1} \times \frac{s}{\sqrt{n}}$$

> [!TIP] **Exam Tip:** Always state the confidence level (e.g., 95% CI). Non-overlapping CIs for two alternatives suggest a significant difference.

2.5 Advanced Modeling Concepts

Entity Routing & Logic

• Conditional Routing: Based on entity attribute or expression (e.g., IF Type=Express, go to Fast Lane).

• Scheduling: Use Schedule module or Assign with NOW to model time-based events (e.g., shift changes, breaks).

• Submodels/Hierarchical Modeling: Group complex logic into a single submodel block for clarity.

Resource Management

• Schedules/Shifts: Define resource availability over time (e.g., 8am-5pm).

• Failures & Maintenance: Use Downtime or Break modules with scheduled or random failure distributions (MTTF, MTTR).

• Preemptive Resources: Higher-priority entity can interrupt a lower-priority one in service.

Output Reporting & Customization

• Built-in Reports: Standard tables for Entities, Resources, Queues, Processes.

• Custom Reports/Plots: Use expression-based variables to track custom metrics (e.g., Total_Wait_Time).

• VBA/Scripting: For advanced output manipulation, complex logic, or external file writing.

2.6 Case Studies & Application Domains

2.7 Project Workflow & Best Practices

Lab Project Structure

1. Proposal: Problem statement, objectives, conceptual model (flowchart), data sources.

2. Interim Report: Screenshot of working model, verification notes (debugging steps), preliminary output.

3. Final Report: Full model logic, detailed V&V (verification & validation methods used), experimental design (warm-up, replications), results with statistical analysis (tables, CIs, comparisons), conclusions, recommendations, limitations.

Common Pitfalls & Debugging

• Infinite Loops: Entity routing deadlock (e.g., Decide always sends back).

• Entity Starvation: Downstream module blocked, upstream continues creating.

• Misinterpreted Output: Confusing average vs. maximum queue length; not removing warm-up period.

• Debugging Strategy: Use animation at slow speed, add Record modules to log entity paths, check entity counts at module inputs/outputs.

• Best Practice: Animation is critical for validation and communicating model logic to stakeholders.