ESI 6529 DIGITAL SIMULATION TECHNIQUES

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ESI 6529 DIGITAL SIMULATION TECHNIQUES

• Lecture 3

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EXAMPLE 3 SINGLE MACHINE WITH INSPECTION Modify
the previous model so that the buffer area can
only hold a maximum of 5 jobs. Excess jobs will
be bulked, counted and deleted from the system.
In addition, change the arrival process so that
the time between arrivals for all jobs is
exponentially distributed with a mean of 4
minutes. Assume that 40 are type 1 jobs and 60
are type 2 jobs. Also, add an inspection station
following the machine. The inspection time
follows a triangular distribution with values
(2,5,6) minutes for type 1 jobs and (1,2,3)
minutes for type 2 jobs. The probability that a
part fails inspection is 10 and is independent
of part type. Count the number of jobs that
balked from the system and the number of jobs
that fail inspection. Collect additional
statistics on the inspection queue length and the
inspection station utilization. Estimate the
stead-state behavior by simulating 8 hours,
clearing the statistics, and then simulating an
additional 100 hours.
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DISCRETE PROBABILITY DISTRIBUTION Allow user to
define discrete empirical distributions. Examples
Value Probability Cumulative 1
0.4 0.4 2 0.6
1.0 DISCRETE(0.4, 1, 1.0, 2) Value Probability
Cumulative 1.4 0.37 0.37 2 0.18 0.55 2.7 0.41
0.96 3.5 0.04 1.00 DISCRETE(0.37, 1.4, 0.55,
2, 0.96, 2.7, 1.0, 3.5).
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THE BRANCH BLOCK BRANCH, MaxTake,
Stream WITH, Probability, Label,
Primary IF, Condition, Label,
Primary ELSE or ALWAYS, Label,
Primary Examples BRANCH, 1 WITH, 0.9,
Orange ELSE, Blue BRANCH, 2 WITH, 0.9,
Orange ALWAYS, Blue BRANCH, 1 IF,
NR(Machine) .EQ. 0, Orange WITH, 0.9,
Blue ELSE, White BRANCH, 2 IF, NR(Machine)
.EQ. 0, Orange WITH, 0.9, Blue ELSE, White
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EXAMPLE 4 REWORK Workpieces enter the system
and wait their turn to be processed on a single
machine. After completing on the machine, they
continue to a second workstation where they are
inspected. At the inspection station, the
workpieces are classified as Good, Repairable, or
Bad. Good parts depart from the system
repairable parts are recycled back to the machine
where they are reworked and bad parts are
discarded. The time between job arrivals is
exponentially distributed with a mean time of 9
minutes. There are two type of jobs randomly
ordered in the arrival stream 30 are Type 1 and
70 are Type 2. The waiting parts are ordered
at both the machine and the inspection station.
The Type 1 jobs have priority over the Type 2
jobs within the queue. The first portion of the
queue contains any Type 1 jobs, ordered according
to their arrival times. The Type 2 jobs follow
the Type 1 jobs, again ordered according to
arrival time. The priority scheme is
non-preemptive, that is, if a Type 2 job is being
processed when a Type 1 job arrives, processing
is not interrupted. The repairable parts
returned to the machines queue have the lowest
priority. These parts wait behind any regular
Type 1 and 2 jobs and are ordered according to
the time at which they re-enter the queue. This
same priority scheme is used for re-inspection of
the reworked parts. Thus, there are three
distinct classes of priority at both machine and
inspector queues Type 1, Type 2, and Repairable.
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The inspection time for each part, regardless of
type or rework status, has a triangular
distribution with a minimum time of 5 minutes, a
most likely time of 8 minutes, and a maximum time
of 10 minutes. Of the jobs inspected, 80 are
classified as Good and depart the system, 10 are
Bad and are discarded, and 10 are repairable and
are returned the machine queue for rework. The
same percentages apply to both types of jobs,
regardless of rework status. Note that a reworked
job classified as Repairable at the inspection
station will be recycled through the machine
station. The combined setup and machine times
for regular and rework Type 1 and 2 jobs are
normally distributed with the means and standard
deviations (given in minutes) provided below.
Regular Rework Mean S. D. Mean S.
D. Type 1 5 2 3 1 Type 2 4
1 2 1
Simulate this system for 480 minutes and to
record the number of parts completed by job type
and the total number of rejected parts sent to
the salvage. Also, obtain the statistics on queue
length and utilization.
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THE EXPERIMENT FILE Rework.EXP BEGIN PROJECT,
Rework, CIS 441 ATTRIBUTES JobType Status
Priority VARIABLES Mean(2,2), 5,
3,4,2 Std(2,2), 2,1,1,1 QUEUES MachineQ,
LVF(Priority) InspectQ, LVF(Priority) RESOURC
ES Machine Inspector COUNTERS Type 1 Job
Done Type 2 Job Done Rejects DSTATS NQ(Machine
Q), Machine Queue NQ(InspectQ), Inspector
Queue NR(Machine), Machine Utilization NR(In
spector), Inspector Utilization REPLICATE, 1, 0,
480 END
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THE MODEL FILE Rework.MOD BEGIN CREATE
EXPO(9) ASSIGN JobTypeDISC(0.3, 1, 1.0,
2) Status1 PriorityJobType Merge QUEUE,
MachineQ SIEZE Machine DELAY NORM(Mean(
JobType, Status),
Std(JobType, Status)) RELEASE Machine QUEU
E, InspectQ SIEZE Inspector DELAY TRIA
(5,8,10) RELEASE Inspector BRANCH,
1 WITH, 0.8, Good WITH, 0.1,
Reject WITH, 0.1, Rework Good COUNT JobTy
pe DISPOSE Reject COUNT Rejects DISPOSE
Rework ASSIGN Status2 Priority3
NEXT(Merge) END
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THE SIMULATION RESULTS Rework.OUT Project Rewor
k Analyst CIS 441 Simulation run ended at time
480.0 DISCRETE CHANGE VARIABLES Identifier
Average Variation Minimum Maximum
Final Value Machine Queue 0.4094
2.2953 .00000 5.0000
0.0000 Inspector Queue 2.6506
0.8793 .00000 8.0000
3.0000 Machine Utilization 0.4998
1.0004 .00000 1.0000
1.0000 Inspector Utilization .0.9405
0.2516 .00000 1.0000
1.0000 COUNTERS Identifier Count Limit Type
1 Job Done 23 Infinite Type 2 Job Done
24 Infinite Rejects 7 Infinite
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EXAMPLE 5 A Reataurant Problem Consider a
restaurant where the owner is interested in
studying the flow of customers for dinner (500
PM to 900 PM). Customers arrive in parties of 2,
3, 4, or 5 with respective probabilities of 0.4,
0.3, 0.2, and 0.1, and the time between arrivals
is exponentially distributed with a mean of 1.6
minutes. Customers must arrive at the restaurant
before 900 PM to be seated. The restaurant has
50 tables, each of which can seat two people.
These tables are moved together to accommodate
parties of more than two persons. Each arriving
group gets in line to be seated, but, if there
are already five parties in line, the newest
customers leave and go to another restaurant. The
time it takes to be served is triangularly
distributed with minimum, most likely, and
maximum times of 15, 18, and 20 minutes,
respectively. The time it takes to eat is
normally distributed with a mean of 20 minutes
and a standard deviation of 2 minutes. When the
customers are finished eating, they go to the
cashier and pay the bill. The time it takes the
cashier to process these customers is normally
distributed with a mean of 2.0 minutes and a
standard deviation of 0.5 minute. Simulate this
system for the four-hour dinner period and to
record statistics about the number of customers
served, the number of busy tables, the number of
waiting customers, the number of parties that
departs without eating, and the utilization of
the cashier.
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THE EXPERIMENT FILE Restaurant.MOD BEGIN PROJE
CT, Restaurant, CIS 441 ATTRIBUTES PartySize
VARIABLES Door, 10000 QUEUES TableQ,
CashierQ RESOURSES Table, 50 Cashier COUNTER
S Lost Parties Served Parties DSTATS NR(Table
), Number of busy tables NQ(TableQ),
Number of waiting parties NR(Cashier)100,
Cashier Utilization NQ(CashierQ), Number
of waiting for cashier REPLICATE, 1 END
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THE MODEL FILE Restaurant.EXP BEGIN CREATE E
XPO(1.6), Door BRANCH, 1 IF, TNOW lt 240,
Open ELSE, Closed Closed ASSIGN Door
0 DISPOSE Open ASSIGN PartySizeDISC(.4,2,.7
,3,.9,4,1.0,5) QUEUE, TableQ, 5,
Leave SEIZE Table, (PartySize1)/2 DELAY
TRIA(14,19,24)NORM(24,5) RELEASE Table,
(PartySize1)/2 QUEUE, CashierQ SEIZE Cas
hier DELAY NORM(1.5, .5) RELEASE Cashier
COUNT Served Parties DISPOSE Leave COUNT
Lost Parties DISPOSE END
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THE SIMULATION RESULTS Restaurant.OUT Project
Restaurant Analyst CIS 441 Replication ended
at time 288.294 DISCRETE CHANGE
VARIABLES Identifier Average
Variation Minimum Maximum Final
Value Number of Busy Tables 37.342 .35865
.00000 50.000 0.0000 Number of
Waiting Parties .07187 4.0702
.00000 2.0000 0.0000 Cashier Utilization
76.083 .56068 .00000
100.00 0.0000 Number of Waiting for Cashier
2.3952 1.0425 .00000
10.000 0.0000 COUNTERS Identifier Count
Limit Lost Parties 0 Infinite Served
Parties 148 Infinite
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EXAMPLE 6 An Emergency Room Patients arrive at
an emergency room where they are treated and then
depart. Arrivals are exponentially distributed
with a mean time between arrivals of 0.3 hour.
Upon arrival, patients are assigned a rating of 1
to 5, depending on the severity of their
ailments. Patients in Category 1 are the most
severe, and they are sent to a bed where they
await medical attention. All other patients must
first wait in the receiving room until a basic
registration form and medical record are
completed. They then proceed to a bed.
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The emergency room has three beds, one
registration nurse, and two doctors. In all cases
the priority for allocating these resources is
based on the severity of the ailment. The
registration time for patients in Categories 2
through 5 is 0.15 hour. The treatment time for
all patients is triangularly distributed with the
parameters differing according to the patients
category. The distribution of patients by
category and the corresponding parameters for
treatment times are summarized below.
Category 1 2 3 4 5 Percent
6 8 18 33 35 Minimum .8
.7 .4 .2 .1 Most likely 1.2
.95 .6 .45 .35 Maximum 1.6 1.1 .75 .6 .45 The
problem is to simulate this system over a 30-day
period and record statistics about the
utilization of the resources and the time that
the patients spend in the system, categorized by
ailment.
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THE EXPERIMRNT FILE Emergency.EXP BEGIN PROJECT
, EmergencyRoom, CIS 441 ATTRIBUTES Category
TimeIn VARIABLES Minimum(5), .8,.7,.4,.2,.1
Mode(5), 1.2,.95,.60,.45,.35 Maximum(5),
1.6,1.1,.75,.6,.45 QUEUES BedQ,
LVF(Category) DoctorQ, LVF(Category) NurseQ,
LVF(Category) RESOURCES Bed, 3 Doctor, 2
Nurse, 1 TALLIES Open Wounds Closed
Injuries Multiple Trauma Viscerel Complaints
Chronic Complaints Overall Flow Time,
Time.dat DSATS NR(Bed), Number of Busy Beds
NR(Doctor), Number of Busy Doctors NR(Nurse),
Number of Busy Nurses NQ(BedQ), Bed Queue
Length NQ(DoctorQ), Doctor Queue
Length NQ(NurseQ), Nurse Queue
Length REPLICATE, 1, 0, 720 END
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THE MODEL FILE Emergency.MOD BEGIN CREATE EX
PO(.3) MARK(TimeIn) ASSIGN Category(.06,1,.14
,2,.32,3,.65,4,1,5) BRANCH, 1 IF, Category
.EQ. 1, ToBed ESLE, Records Records QUEUE,
NurseQ SEIZE Nurse DELAY UNIF(.1,.2)
RELEASE Nurse ToBed QUEUE, BedQ SEIZE B
ed QUEUE, DoctorQ SEIZE Doctor DELAY
TRIA(Minimum(Category),
Mode(Category), Maximum(Category))
RELEASE Doctor Bed TALLY Category,
INT(TimeIn) TALLY Overall Flow Time,
INT(TimeIn) DISPOSE END
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THE SIMULATION RESULTS Emergency.OUT Project E
mergencyRoom Analyst CIS 441 Replication ended
at time 720.0 TALLY VARIABLES Identifier
Average Variation Minimum Maximum
Observations Open Wounds 1.4186
.20885 .83392 2.5421 141 Closed Injuries
1.3333 .22874 .88326 3.1810
174 Multiple Trauma 1.0677
.34556 .53932 4.0369 406 Visceral
Complaints 1.0421 .66916 .34407
6.3397 825 Chronic Complaints 1.6258
1.1206 .23144 13.772 833 Overall Flow
Time 1.2945 .92551 .23144
13.772 2379
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THE SIMULATION RESULTS Emergency.OUT
(Cont.) DISCRETE CHANGE VARIABLES Identifier
Average Variation
Minimum Maximum Final Value Number of
Busy Beds 2.1297 .49040 .00000
3.0000 3.0000 Number of Busy Doctors
1.6103 .41021 .00000
2.0000 2.0000 Number of Busy Nurses
.46372 1.0754 .00000
1.0000 1.0000 Bed Queue Length
1.5029 1.8094 .00000 17.000
3.0000 Doctor Queue Length .51926
.96199 .00000 1.0000 1.0000 Nurse
Queue Length .19719 2.7098 .00000
5.0000 2.0000