Fundamental Simulation Concepts - Banking - Lecture Slides, Slides of Banking and Finance

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Fundamental Simulation

Concepts

Chapter 2

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What We’ll Do ...

• Underlying ideas, methods, and issues in

simulation

• Software-independent (setting up for Arena)
• 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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Model Specifics

• Initially (time 0) empty and idle
• Base time units: minutes
• Input data (assume given for now …), in minutes:

Part Number Arrival Time Interarrival Time Service Time 1 0.00 1.73 2. 2 1.73 1.35 1. 3 3.08 0.71 3. 4 3.79 0.62 4. 5 4.41 14.28 4. 6 18.69 0.70 4. 7 19.39 15.52 2. 8 34.91 3.15 3. 9 38.06 1.76 2. 10 39.82 1.00 5. 11 40...

.... ....

• Stop when 20 minutes of (simulated) time have

passed

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Goals of the Study:

Output Performance Measures

• Total production of parts over the run ( P )
• Average waiting time of parts in queue:
• Maximum waiting time of parts in queue:

N = no. of parts completing queue wait

WQi = waiting time in queue of i th part

Know: WQ 1 = 0 (why?)

N > 1 (why?)

N

WQ

N

i

∑ i

= 1

i i N

max WQ

= 1 ,...,

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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 B t

B t dt

0 if the machine isidle at time

1 if themachine isbusy at time , ( ) 20

20 0

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Analysis Options

• Educated guessing

 Average interarrival time = 4.08 minutes

 Average service time = 3.46 minutes  So (on average) parts are being processed faster than they arrive

• System has a chance of operating in a stable way in the long run, i.e., might not “explode”
• If all interarrivals and service times were exactly at their mean, there would never be a queue
• But the data clearly exhibit variability, so a queue could form  If we’d had average interarrival < average service time, and this persisted, then queue would explode

 Truth — between these extremes

 Guessing has its limits …

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Mechanistic Simulation

• Individual operations (arrivals, service times) will

occur exactly as in reality

• Movements, changes occur at the right “time,” in

the right order

• Different pieces interact
• Install “observers” to get output performance

measures

• Concrete, “brute-force” analysis approach
• Nothing mysterious or subtle

 But a lot of details, bookkeeping

 Simulation software keeps track of things for you Docsity.com

Pieces of a Simulation Model

• Entities

 “Players” that move around, change status, affect and are affected by other entities

 Dynamic objects — get created, move around, leave (maybe)  Usually represent “real” things

• Our model: entities are the parts  Can have “fake” entities for modeling “tricks”
• Breakdown demon, break angel  Usually have multiple realizations floating around

 Can have different types of entities concurrently

 Usually, identifying the types of entities is the first thing to do in building a model

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Pieces of a Simulation Model (cont’d.)

• (Global) Variables

 Reflects a characteristic of the whole model, not of specific entities

 Used for many different kinds of things

• Travel time between all station pairs
• Number of parts in system
• Simulation clock (built-in Arena variable)  Name, value of which there’s only one copy for the whole model

 Not tied to entities

 Entities can access, change variables  Writing on the wall

 Some built-in by Arena, you can define others

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Pieces of a Simulation Model (cont’d.)

• Resources

 What entities compete for

• People
• Equipment
• Space  Entity seizes a resource, uses it, releases it

 Think of a resource being assigned to an entity , rather than an entity “belonging to” a resource  “A” resource can have several units of capacity

• Seats at a table in a restaurant
• Identical ticketing agents at an airline counter  Number of units of resource can be changed during the simulation

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Pieces of a Simulation Model (cont’d.)

• Statistical accumulators

 Variables that “watch” what’s happening

 Depend on output performance measures desired

 “Passive” in model — don’t participate, just watch

 Many are automatic in Arena, but some you may have to set up and maintain during the simulation

 At end of simulation, used to compute final output performance measures

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Pieces of a Simulation Model (cont’d.)

• Statistical accumulators for the simple

processing system

 Number of parts produced so far

 Total of the waiting times spent in queue so far

 No. of parts that have gone through the queue  Max time in queue we’ve seen so far

 Total of times spent in system

 Max time in system we’ve seen so far  Area so far under queue-length curve Q ( t )

 Max of Q ( t ) so far

 Area so far under server-busy curve B ( t )

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Events for the

Simple Processing System

• Arrival of a 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 waiting 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 the

Simple Processing System (cont’d.)

• Departure (when a service is completed)

 Increment number-produced stat accumulator

 Compute & tally time in system (now - time of arrival)

 Update time-persistent statistics (as in arrival event)

 If queue is non-empty:

• Take first part out of queue, compute & tally its waiting 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, which is as desired)

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