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**Lab 01 Fundamentals SE 405 Discrete Event Simulation**

Last update September 7, 1999

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Lab Objectives Introduction to Simulation Needs Uses … etc. Understanding Manual Simulation Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Introduction Background Here the process or facility under consideration is called system Simulation is imitating the (dynamic behavior of) real world system (as compared to static models) using computer programs to study the behavior of the system under study In order to study it there are set of assumptions on how a system works Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Introduction Background These assumptions take the form of mathematical or logical relationships which constitutes simulation model Simulation models are numeric (Not analytic) in order to estimates (presents error or approximation) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Introduction Applications Designing and analyzing manufacturing system Determining ordering policies for an inventory system Evaluating designs for service operations e.g., Banks, post office and hospital customer in-service-out operations Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Introduction Definitions System: Collection of entities interacting to achieve a common objective or logical end State (of a system): collection of variables within a system to describe a system at a particular time. (Number of customer in bank queue) Discrete / Continues systems Model: Representation of actual system Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Introduction Definitions Analytic Solution vs Simulation (Numeric) Static Models vs Dynamic Simulation Deterministic (output determined) vs Stochastic Simulations (output unknown or random) Events (ei= Time of occurrence of the ith event): Any change in system (Part arrival, service complete etc.) Events Lists (e0, e1, e2, …) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Manual Simulation What We’ll Do ...**

Understanding simulation through example Software-independent … Centered around an example of a simple processing system Decompose the problem Terminology Simulation by hand Some basic statistical issues Overview of a simulation study Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**The System: A Simple Single server Queuing Model**

Machine (Server) Arriving Blank Parts Departing Finished Parts 8 7 6 5 4 Queue (FIFO) Part in Process General intent: Estimate expected production Time in queue, queue length, proportion of time machine is busy Time units: arbitrary, but … Be consistent (simulation doesn’t know) Be reasonable (interpretation, roundoff error) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Model Specifics Initially (time 0) empty and idle Time units: minutes Interarrival times An (n=1,2,3…): 6.84, 2.4, 2.7, … Service times Sn (n=1,2,3…): 4.58, 2.96, 5.86, … Stop Criteria: Stop when customer/part number = 10 Stop when 15 minutes of (simulated) time have passed Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Model Specifics Si = time that a server actually spend serving ith customer Di = delay in queue of the ith customer ti = time of arrival of the ith customer t0=?? ci = ti+ Di + Si = time that ith customer completes service and departs Stop Criteria: Stop when customer/part number 10 has Stop when 15 minutes of (simulated) time have passed Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Model Specifics e e e e e4 t t c c2 A A A3 S S2 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Goals of the Study: Output Performance Measures**

*Total production of parts over the run (P) Average waiting time (or delay) of parts in queue: Maximum waiting time of parts in queue: N = no. of parts completing queue wait Di = waiting time in queue of ith part Know: D1 = 0 (why?) N > 1 (why?) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Goals of the Study: Output Performance Measures (cont’d.)**

Time-average number of parts in queue: Maximum number of parts in queue: Average and maximum flowtime of parts (time in system, a.k.a. cycle time): t Q(t) = number of parts in queue at time t t Fi = flowtime of ith part Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Goals of the Study: Output Performance Measures (cont’d.)**

Utilization of the machine (proportion of time busy) Many others possible (information overload?) t t Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation Dynamics: The Event-Scheduling World View**

Identify characteristic events — change state Decide on logic to: effect state changes for each event type, observe statistics Keep a simulation clock, future event calendar Jump from one event to the next, process, observe statistics, update event calendar Stopping rule Usually done with general-purpose programming language (C, FORTRAN, etc.) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Events for Simple Processing System**

Arrival of new part to the system Update time-persistent statistical accumulators (from last event to now) Area under Q(t) Max of Q(t) Area under B(t) “Mark” arriving part with current time (use later) If machine is idle: Start processing (schedule departure), Make machine busy, Tally time in queue (0) Else (machine is busy): Put part at end of queue, Increase queue-length variable Schedule the next arrival event Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Events for Simple Processing System (cont’d.)**

Departure (when a service is completed) Increment number-produced stat accumulator Compute & tally flowtime (now - time of arrival) Update time-persistent statistics If queue is non-empty: Take first part out of queue, compute & tally its time in queue, begin service (schedule departure event) Else (queue is empty): Make the machine idle (Note: there will be no departure event scheduled on the future events calendar) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Events for Simple Processing System (cont’d.)**

The End Update time-persistent statistics (to end of the simulation) Compute final output performance measures using current values of statistical accumulators After each event, the event calendar’s top record is removed to see what time it is, what to do Also must initialize everything Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Specifics for Simple Processing System**

Simulation clock (internal in Arena) Event calendar: List of event records: [Entity No., Event Time, Event Type] Keep ranked in increasing order on Event Time Next event always in top record Initially, schedule first Arrival, The End (Dep.?) State variables: describe current status Server status B(t) = 1 for busy, 0 for idle Number of customers in queue Q(t) Times of arrival of each customer now in queue (a list of random length) Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts**

Simulation by Hand Manually track state variables, statistical accumulators Use “given” interarrival, service times Keep track of event calendar “Lurch” clock from one event to the next Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Setup**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Initialize at t = 0.00**

1 3 2 1 t Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Arrival of Part 1 at t = 0.00**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Departure of Part 1 at t = 4.58**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Arrival of Part 2 at t = 6.84**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Arrival of Part 3 at t = 9.24**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Departure of Part 2 at t = 9.80**

3 t 1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Arrival of Part 4 at t = 11.94**

3 t 1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Arrival of Part 5 at t = 14.53**

1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: The End at t = 15.00**

3 4 5 t 1 t 1 2 3 Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Simulation by Hand: Finishing Up**

Time-average number in queue: Server utilization Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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**Complete Record of the Hand Simulation**

Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

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