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Simulation Basics ( 模擬基本概念 )

Simulation Basics ( 模擬基本概念 ). By C. L. Hsieh Department of Industrial Management Aletheia University. Questions. What types of simulation are there? ( 模擬類型有些 ?) How is random behavior simulated? ( 隨機行為如何模擬 ?) How does discrete event simulation work? ( 離散事件型模擬之運作過程為何 ?)

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Simulation Basics ( 模擬基本概念 )

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  1. Simulation Basics(模擬基本概念) By C. L. Hsieh Department of Industrial Management Aletheia University

  2. Questions • What types of simulation are there? (模擬類型有些?) • How is random behavior simulated? (隨機行為如何模擬?) • How does discrete event simulation work? (離散事件型模擬之運作過程為何?) • How is simulation software used? (如何使用模擬軟體?) • What is the future of simulation technology? (模擬技術之未來發展?)

  3. Types of Simulation (模擬之類型) • Static v.s. Dynamic Simulation (固定性與動態性模擬) • Static is not based on time: Monte Carlo Simulation (固定性模擬與時間無關，如蒙地卡羅模擬) • Dynamic includes the passage of time. (動態性模擬紀錄時間之變化) • States are changed over time. (系統中之狀態隨時間之改變而變化) • Clock mechanism moves forward in time (系統時鐘紀錄狀態隨時間之改變之任何事件)

  4. Types of Simulation (模擬之類型) • Deterministic (確定性) v.s. Stochastic Simulation (隨機性) One run is enough Several Runs require

  5. Types of Simulation (模擬之類型) • Discrete-Event v.s. Continuous Simulation (離散事件 v.s. 連續型模擬) • A discrete-event simulation is one in which state (狀態) changes at discrete time as triggered by events(離散事件模擬由事件所驅動，紀錄不同時間不同事件之狀態)

  6. Types of Simulation (模擬之類型) • In continuous simulation, state variables changes continuously w.r.t. time (e.g. temperature of a building controlled by a heating system) (連續型模擬中，狀態變數隨時間以連續方式改變，如加熱系統中溫度之變化)

  7. Simulating Random Bahavior (模擬亂數之行為) • Random number Generation (亂數產生方式) • Simulation uses a random number generator (RNG) (模擬過程中使用亂數產生程式). • RNG is a deterministic algorithm used to create uniformly & independently distribution between [0,1] (亂數產生程式RNG昰一種定性演算法，能產生介於[0,1]均勻、獨立的分配) • The most popular RNG is called Linear Congruential Generators (LCGs) (最有名之RNG稱為LCGs)

  8. Examples of LCGs (LCGs範例)

  9. Generating Random Variates (隨機變異值) • “Generating a random variate”: the activity of obtaining an observation of a random variable from desired distribution (產生隨機變異值:昰一種產生某種特殊隨機變數之機率分配的觀察值之方法) • A Random number (from LCGs) is plugged into a transform equation (原理昰將由LCGs程式產生之隨機變數置於一轉置方程式中作運算(See Law, 1991)

  10. DES Simulation (離散事件模擬) • Discrete-event simulation uses process flow by a sequence of events (離散事件模擬藉由一系列之事件產生過程流程) • Scheduled(事先決定DES):determined beforehand by the passage of time • Conditioned (條件式DES):triggered by a condition (e.g. multiple entities waiting for resources when it is available) (由某些條件驅動)

  11. DES Simulation (離散事件模擬) • After events being processed, a clock advances to the next scheduled events & the process continues. (某事件處理後，一個模擬時鐘會移動至下一個排定之事件使整個程序繼續進行) • When a termination event occurs, the simulation ends and statistical reports are generated (終止事件停止所有模擬動作，之後會產生一個統計報表)

  12. Diagram of Discrete-Event Simulation

  13. A Manual Simulation Example (一個人工模擬範例) • Model Assumption (模型假設) • No parts in the system initially (系統起初沒有任何零件) • No operators included in the system (系統無任何作業員) • Move time from queue to the package station is negligible (由等候線至包裝站之移動時間可忽略) • Queue priority rule (等候線以FIFO方式控制) • Package station never fail down (包裝站在模擬過程不會故障)

  14. A Manual Simulation Example(一個人工模擬範例) • 結果計算 • 有幾件事件到達? • 有幾台機器曾在等候線上? • 模擬結束時，仍有幾台在系統中? • 等候線平均等候時間為何? • 系統平均等候時間為何? • 系統平均使用率為何?

  15. 範例模型的模擬流程圖

  16. A Manual Simulation Example (一個人工模擬範例) • Types of Scheduled Events (排定事件之類型) • Arrivals, Package Done & Termination (到達事件，包裝完成事件，模擬終止事件) • Number in Queue (在等候線上之實體數) • 某事件處理完後在等候線上等候之螢幕個數 • Cumulative time in Queue(等候線累計時間) • 等候線上數量乘以下次事件發生的時間減掉本次時間的差,再加上原有累計時間

  17. Commercial Simulation Software (商用模擬軟體)

  18. Simulation Using Promodel (以Promodel 模擬) • Building A Model (建立一個模式) • Entities (實體) (items being processed) • Locations(位址) (the places where processing occurs) • Resources (資源) (agents used to process entities) • Paths (路徑) (pathways along which entities & resources traverse)

  19. Simulation Using Promodel(以Promodel 模擬) • Running the Simulation (執行模擬) • Model database (模式資料庫) • simulation DB (模擬資料庫) • Animation graphics (動畫圖形) • Output Analysis (輸出報告分析) • Summary Reports (總報表) • Time-Series Plots & Histograms (時間序列圖與值方圖)

  20. Future of Simulation (模擬未來發展) • Input data analysis for distribution fitting (資料分析、分配配對) • Graphical User Interface (圖形使用者介面) • Reusable Components (元件回收) • 2-D, 3-D Animation (2-D, 3-D動畫) • Online helps & tutorials (線上教學、求救) • Interactive debugging (互動式偵錯) • Automatic model generation (自動化模式產生) • Output analysis tool (輸出分析工具) • Optimization (最佳化) • Database connectivity (資料庫連結)

  21. Summary (總結) • Most manufacturing & service system are dynamic, stochastic & DES (多數製造與服務系統為動態、隨機、DES型系統) • Random number generator (亂數產生器) • DES based on events & consequent reactions (DES以事件與相關之反應為基礎) • Events are time or conditioned triggered (事件昰被時間或條件所驅動) • Simulation models can be defined by commercial simulation software (e.g. Promodel) (模擬模式可以在商用模擬軟體中定義，如Promodel)

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