Management of the Simulated Clock

1
Management of the Simulated Clock

• Fixed-time Increment
• Variable-time Increment

2
Flowchart for arrival routine, queueing model
3
Flowchart for departure routine, queueing model
4
Distribution of time between arrivals
5
Service Time Distribution
6
Time-between-arrival Determination
7
Service Times Generated
8
Work Sheet
Event Type
Clock Time
Customer Number
Arrival 1
0
. . .
. . .
. . .
9
Findings from the Simulation
10
Findings from the Simulation(cont)
11
Findings from the Simulation(cont)
12
The Able-Baker carhop problem

• The purpose of this example is to indicate the
  simulation procedure when there is more than one
  channel.
• Consider a drive-in restaurant where carhops take
  orders and bring food to the car.
• Cars arrive in the manner shown in the following
  table.

13
The Able-Baker carhop problem(Interarrival
distribution of cars)
14
The Able-Baker carhop problem(continued)

• There are two car hops -- Able and Baker.
• Able is better able to do the job, and works
  somewhat faster than Baker.
• The distribution of service times of Able and
  Baker is following.

15
The Able-Baker carhop problem(Service
Distribution of Able)
16
The Able-Baker carhop problem(Service
Distribution of Baker)
17
The Able-Baker carhop problem(Continued)

• Over the 62-minute period Able is busy 90 of the
  time.
• Baker was busy only 69 of the time. The
  seniority rule keeps Baker less busy.
• Nine of 26 or about 35 of the arrivals had to
  wait. The average waiting time for all customers
  was only about 0.42 minute, or 25 seconds, which
  is very small.

18
The Able-Baker carhop problem(Continued)

• Those 9 who did have to wait only waited an
  average of 1.22 minutes, which is quite low.
• In summary, this system seems well balanced. One
  server cannot handle all the dinners, and three
  servers would probably be too many. Adding an
  additional server would surely reduce the waiting
  time to nearly zero. However, the cost of waiting
  would have to be quite high to justify an
  additional worker.

19
GPSS (Process-Oriented) Diagram
20
GPSS Events

• Current-Event Chain Transaction with BDT lt
  C1
• Future-Event Chain Transaction with BDT gt
  C1

21
GPSS Events(continued)

• Note
• Events must be executed chronologically, so
  chains are maintained in ascending order
• Current-Event Chain performs an additional
  tasks(i.e. maintains by priority)

22
GPSS Execution Trace

• The system. Four transactions enter the system
  at intervals of 3 time units, starting at time
  unit 1.
• They try to seize facility MACH for 4 time units
  and then try to enter storage BUFFE (with
  capacity 2) before releasing MACH.
• After 9 time units in BUFFE, they leave storage
  and terminate. In this model the number of
  transactions must be limited because it has been
  devised to cause catastrophic congestion.

23
GPSS Sample instructions

• BUFFE STORAGE 2
• GENERATE 3,,1,4
• QUEUE WAIT
• SEIZE MACH
• DEPART WAIT
• ADVANCE 4
• ENTER BUFFE
• RELEASE MACH
• ADVANCE 9
• LEAVE BUFFE
• TERMINATE 1
• START 4

24
GPSS (Process-Oriented) Diagram
25
GPSS/H Block Diagram, Queueing Model
26
GPSS/H - Queueing Model

• 1 SIMULATION OF THE M/M/1 QUEUE
• 2
• 3 SIMULATE
• 4 GENERATE RVEXPO(1,1,0) Create
  Arriving Customer
• 5 QUEUE SERVERQ Enter the Queue
• 6 SEIZE SERVER Seize the
  Server
• 7 LVEQ DEPART SERVERQ Leave the Queue
• 8 TEST L NLVEQ,1000,STOP Test for
  Termination
• 9 ADVANCE RVEXPO(2,0.5) Delay for
  service
• 10 STOP RELEASE SERVER Customers Depart
• 11 TERMINATE 1
• 12
• 13 CONTROL STATEMENT
• 14
• 15 START 1000 Make 1
  simulation run
• 16 END

27
GPSS/H standard output report, Queueing Model

• RELATIVE CLOCK 1014.1565 ABSOLUTE
  CLOCK1014.1565
• BLOCK CURRENT TOTAL
• 1 1000
• 2 1000
• 3 1000
• LVEQ 1000
• 5 1000
• 6 999
• STOP 1000
• 8 1000
• -- AVG-UTIL-DURING--
• FACILITY TOTAL AVAIL UNAVL ENTRIES AVG
  CURRENT
• TIME TIME TIME
  TIME/XACT STATUS
• SERVER 0.516
  1000 0.523 AVAIL

28
GPSS/H standard output report, Queueing
Model(Continued)

• QUEUE MAXIMUM AVERAGE TOTAL ZERO
  PERCENT
• CONTENTS CONTENTS ENTRIES
  ENTRIES ZEROS
• SERVERQ 8 0.605
  1000 454 45.4
• QUEUE AVERAGE AVERAGE QTABLE
  CURRENT
• TIME/UNIT TIME/UNIT NUMBER
  CONTENTS
• SERVERQ 0.614 1.124
  0
• RANDOM ANTITHETIC INITIAL CURRENT SAMPLE
  CHI-SQUARE
• STREAM VARIATES POS.
  POS. COUNT UNIFORMITY
• 1 OFF 100000
  101001 1001 0.71
• 2 OFF 200000
  200999 999 0.69

29
SIMSCRIPT II.5 Preamble,Queueing Model

• 1 PREAMBLE
• 2 PROCESSES INCLUDE ARRIVAL.GENERATOR,
• 3 CUSTOMER, AND REPORT
• 4 RESOURCES INCLUDE SERVER
• 5 DEFINE DELAY.IN.QUEUE, MEAN.INTERARRIVAL.TIME
  ,
• 6 AND MEAN.SERVICE.TIME AS REAL
  VARIABLES
• 7 DEFINE TOT.DELAYS AS AN INTEGER VARIABLE
• 8 DEFINE MINUTES TO MEAN UNITS
• 9 TALLY AVG.DELAY.IN.QUEUE AS THE AVERAGE AND
• 10 NUM.DELAYS AS THE NUMBER OF
  DELAY.IN.QUEUE
• 11 ACCUMULATE AVG.NUMBER.IN.QUEUE AS THE
• 12 AVERAGE OF N.Q.SERVER
• 13 ACCUMULATE UTIL.SERVER AS THE AVERAGE OF
• 14 N.X.SERVER
• 15 END

30
SIMSCRIPT II.5 Main programQueueing Model

• 1 MAIN
• 2
• 3 READ MEAN.INTERARRIVAL.TIME,
• 4 MEAN.SERVICE.TIME, AND
  TOT.DELAYS
• 5
• 6 CREATE EVERY SERVER(1)
• 7 LET U.SERVER(1) 1
• 8
• 9 ACTIVATE AN ARRIVAL.GENERATOR NOW
• 10
• 11 START SIMULATION
• 12
• 13 END

31
SIMSCRIPT II.5 Process routineARRIVAL.GENERATOR

• 1 PROCESS ARRIVAL.GENERATOR
• 2
• 3 WHILE TIME.V gt 0.0
• 4 DO
• 5 WAIT EXPONENTIAL.F(MEAN.INTERARR
  IVAL.TIME,
• 6
  1) MINUTES
• 7 ACTIVATE A CUSTOMER NOW
• 8 LOOP
• 9
• 10 END

32
SIMSCRIPT II.5 Process routineCUSTOMER

• 1 PROCESS CUSTOMER
• 2
• 3 DEFINE TIME.OF.ARRIVAL AS A REAL VARIABLE
• 4 LET TIME.OF.ARRIVAL TIME.V
• 5 REQUEST 1 SERVER(1)
• 6 LET DELAY.IN.QUEUE TIME.V -
  TIME.OF.ARRIVAL
• 7 IF NUM.DELAYS TOT.DELAYS
• 8 ACTIVATE A REPORT NOW
• 9 ALWAYS
• 10 WORK EXPONENTIAL.F (MEAN.SERVICE.TIME, 2)
• 11
  MINUTES
• 12 RELINQUISH 1 SERVER(1)
• 13
• 14 END

33
SIMSCRIPT II.5 Process routineREPORT

• 1 PROCESS REPORT
• 2
• 3 PRINT 5 LINES THUS
• SIMULATION OF THE M/M/1 QUEUE
• 9 PRINT 8 LINES WITH MEAN.INTERARRIVAL.TIME,
• 10 SERVICE.TIME, AND TOT.DELAYS THUS
• MEAN INTERARRIVAL TIME .
• MEAN SERVICE TIME .
• NUMBER OF CUSTOMERS

34
SIMSCRIPT II.5 Process routineREPORT(Continued)

• 19 PRINT 8 LINES WITH AVG.DELAY.IN.QUEUE,
• 20 AVG.NUMBER.IN.QUEUE(1),
  ANDUTIL.SERVER(1)
• 21 THUS
• AVERAGE DELAY IN QUEUE .
• AVERAGE NUMBER IN QUEUE .
• SERVER UTILIZATION .
• 29 STOP
• 30
• 31 END

35
SIMSCRIPT II.5 Output ReportQueueing Model

• SIMULATION OF THE M/M/1 QUEUE
• MEAN INTERARRIVAL TIME 1.00
• MEAN SERVICE TIME .50
• NUMBER OF CUSTOMERS 1000
• AVERAGE DELAY IN QUEUE .43
• AVERAGE NUMBER IN QUEUE .43
• SERVER UTILIZATION .50

36
SLAM II network forsingle-server queue simulation
37
SLAM II Model of Single-Server Queue

• GEN, BANKS CARSON, NELSON SINGLE SERVER QUEUE
  EXAMPLE, 1/20/95
• LIMITS,1,0,30 MODEL CAN USE 1 FILE, MAX NO. OF
  SIMULTANEOUS ENTRIES 30
• NETWORK BEGINNING OF MODEL
• CREATE, EXPON(4.5) CUSTOMERS ARRIVE AT CHECKOUT
• QUEUE(1) CUSTOMERS WAIT FOR SERVICE IN
• QUEUE FILE ONE (1)
• ACTIVITY(1)/1,RNORM(3.2,.6) CHECKOUT SERVICE
  TIME IS N(3.2,0.6)
• TERMINATE, 1000 SIMULATE UNTIL 1000 CUSTOMERS
• ARE CHECKED OUT
• ENDNETWORK END OF MODEL
• END OF SIMULATION

38
CSIM Sample Code(1)

• / simulate an M/M/1 queue
• (an open queue with exponential service times
  and interarrival intervals)
• /
• include "lib/csim.h"
• define SVTM 1.0 /mean of service time
  distribution /
• define IATM 2.0 /mean of inter-arrival time
  distribution /
• define NARS 5000 /number of arrivals to be
  simulated/
• FACILITY f /pointer for facility /
• EVENT done /pointer for counter /
• TABLE tbl /pointer for table /
• QTABLE qtbl /pointer for qhistogram /
• int cnt /number of active tasks/

39
CSIM Sample Code(2)

• sim() /1st process - named sim /
• int i
• set_model_name("M/M/1 Queue")
• create("sim") /required create statement/
• f facility("facility") /declare facility/
• done event("done") /declare event/
• tbl table("resp tms") /declare table /
• qtbl qhistogram("num in sys", 10) /declare
  qhistogram/
• cnt NARS /initialize cnt/
• for(i 1 i lt NARS i)
• hold(expntl(IATM)) / hold interarrival/
• cust() /initiate process cust/
• wait(done) /wait until all done/
• report() /print report/
• theory() /print theoretical res/

40
CSIM Sample Code(3)

• cust() /process customer/
• float t1
• create("cust") /required create statement/
• t1 clock /time of request /
• note_entry(qtbl) /note arrival /
• reserve(f) /reserve facility f/
• hold(expntl(SVTM)) /hold service time/
• release(f) /release facility f/
• record(clock-t1, tbl) /record response
  time/
• note_exit(qtbl) /note departure /
• cnt-- /decrement cnt/
• if(cnt 0)
• set(done) /if last arrival, signal/

41
CSIM Sample Code(4)

• theory() /print theoretical results/
• float rho, nbar, rtime, tput
• printf("\n\n\n\t\t\tM/M/1 Theoretical
  Results\n")
• tput 1.0/IATM
• rho tputSVTM
• nbar rho/(1.0 - rho)
• rtime SVTM/(1.0 - rho)
• printf("\n\n")
• printf("\t\tInter-arrival time
  10.3f\n",IATM)
• printf("\t\tService time
  10.3f\n",SVTM)
• printf("\t\tUtilization 10.3f\n",rho)
• printf("\t\tThroughput rate
  10.3f\n",tput)
• printf("\t\tMn nbr at queue
  10.3f\n",nbar)
• printf("\t\tMn queue length
  10.3f\n",nbar-rho)
• printf("\t\tResponse time
  10.3f\n",rtime)
• printf("\t\tTime in queue 10.3f\n",rtime
  - SVTM)

42
CSIM Results(1)

• Tue Dec 1 092518 1987 CSIM Simulation Report
  Version 12
• Model M/M/1 Queue
• Time 10041.661
• Interval 10041.661
• CPU Time 32.183 (seconds)
• Facility Usage Statistics
• -------------------------------------means------
  -------------counts----
• facility srv disp serv_tm util tput
  qlen resp cmp pre
• facility 0.992 0.494 0.5
  0.991 1.989 5000 0

43
CSIM Results(2)

• Table 1
• Table Name resp tms
• mean 1.989 min 0.000
• variance 3.813 max 14.273
• Number of entries 5000
• QTable 2
• QTable Name num in sys
• Mean queue length 0.991 Max queue length
  13
• Mean time in queue 1.989 Number of entries
  5000

44
CSIM Results(3)

• Queue Table Histogram
• Length of Elapsed Time Cumulative Count Mean
  Time
• 0 0.506 0.506 2516
  2.020
• 1 0.242 0.748 3694
  0.657
• 2 0.123 0.871 1845
  0.671
• 3 0.067 0.938 1014
  0.659
• 4 0.035 0.972 510
  0.686
• 5 0.015 0.988 234
  0.652
• 6 0.007 0.995 99
  0.700
• 7 0.002 0.997 40
  0.627
• 8 0.001 0.998 21
  0.469
• 9 0.001 0.999 13
  0.823
• 10 0.000 0.999 6
  0.519
• over 0.001 1.000 8
  0.807

45
CSIM Results(4)

• M/M/1 Theoretical Results
• Inter-arrival time 2.000
• Service time 1.000
• Utilization 0.500
• Throughput rate 0.500
• Mn nbr at queue 1.000
• Mn queue length 0.500
• Response time 2.000
• Time in queue 1.000