Lab 01 Fundamentals SE 405 Discrete Event Simulation

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Lab 01Fundamentals SE 405Discrete Event
Simulation
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Lab Objectives

• Introduction to Simulation
• Needs
• Uses etc.
• Understanding Manual Simulation

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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

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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)

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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

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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

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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, )

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Manual SimulationWhat Well 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

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The SystemA Simple Single server Queuing Model
Machine (Server)
Arriving Blank Parts
Departing Finished Parts
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8
4
6
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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 doesnt know)
• Be reasonable (interpretation, roundoff error)

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Model Specifics

• Initially (time 0) empty and idle
• Time units minutes
• Interarrival times An (n1,2,3) 6.84, 2.4, 2.7,
  
• Service times Sn (n1,2,3) 4.58, 2.96, 5.86,
  
• Stop Criteria
• Stop when customer/part number 10
• Stop when 15 minutes of (simulated) time have
  passed

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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

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Model Specifics
e0 e1
e2 e3

e4
0 t1
t2 c1

c2
A1 A2

A3
S1 S2
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Goals of the StudyOutput 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 gt 1 (why?)
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Goals of the StudyOutput Performance Measures
(contd.)

• 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
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Goals of the StudyOutput Performance Measures
(contd.)

• Utilization of the machine (proportion of time
  busy)
• Many others possible (information overload?)

t
t
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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.)

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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

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Events for Simple Processing System (contd.)

• 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)

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Events for Simple Processing System (contd.)

• 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 calendars top record
  is removed to see what time it is, what to do
• Also must initialize everything

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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)

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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

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Simulation by HandSetup
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Simulation by HandInitialize at t 0.00
3
2
1
t
0
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Simulation by HandArrival of Part 1 at t 0.00
1
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Simulation by HandDeparture of Part 1 at t
4.58
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Simulation by HandArrival of Part 2 at t 6.84
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Simulation by HandArrival of Part 3 at t 9.24
2
3
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Simulation by HandDeparture of Part 2 at t
9.80
3
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Simulation by HandArrival of Part 4 at t 11.94
3
4
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Simulation by HandArrival of Part 5 at t 14.53
3
4
5
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Simulation by HandThe End at t 15.00
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Simulation by HandFinishing Up

• Time-average number in queue
• Server utilization

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Complete Record of the Hand Simulation