1. COMPUTER 2430 Object Oriented Programming and Data Structures I

2. Prog 4: Simulation From Webster
a: the imitative representation of the functioning of one system or process by means of the functioning of another
 a computer simulation of an industrial process

3. Queuing Systems Single Line Single Server
Jobs
Waiting to be served
One server services jobs Jobs wait in line (queue) if the server is busy (example: Mongolian Grill)

4. Performance of Queuing Systems
Some properties of interest
Max line length
Average line length
Server utilization
Jobs served immediately
Average time in line (with or without “no-waits”)
Max waiting time (with or without “still waiting”)
. . .

5. Performance of Queuing Systems
How to get the statistics?
Actual observation/recording
Simulation
Prog4
Not real
But close to real

6. Simulation
Server
Job_Processed: null
curTime
Jobs

7. Time Unit Discrete time unit Integer starting with 0
Pick the right unit so that at most one arrival per time unit
Job is just a time stamp

8. Simulation Server Job_Processed: null When does the first job come?
Initialization
Job1: 4
. . .
When does the first job come?
Pre-Scheduled
curTime
Jobs

9. Simulation Server Job_Processed: null Jobs: Pre-Scheduled!
Initialization
Job1: 4
. . .
curTime
Jobs: Pre-Scheduled!

10. Simulation Server Job_Processed: null Jobs: Pre-Scheduled!
Initialization
Job1: 4 4 9
Job1: 4
Job2: 5
curTime
Jobs: Pre-Scheduled!

11. Simulation Server Job_Processed: Job1 Next event? Completing at 8.
When completed?
Pre-Scheduled: 4
Next event?
Completing at 8.
Initialization 4 8 9
Job1: 4
Job2: 5
curTime
Jobs: Pre-Scheduled!

12. Simulation Server Job_Processed: Job1 Jobs: Pre-Scheduled!
Initialization 4 8 9
Job1: 4
Job2: 5
curTime
Jobs: Pre-Scheduled!

13. Simulation Server Job_Processed: null Next event? Arrival at 9.
Initialization 4 8 9
Job1: 4
Job2: 5
curTime
Jobs: Pre-Scheduled!

14. Simulation Server Job_Processed: null Jobs: Pre-Scheduled!
Initialization 4 8 9 13
Job1: 4
Job2: 5
Job3: 4
curTime
Jobs: Pre-Scheduled!

15. Simulation Server Job_Processed: Job2 Next event? Arrival at 13.
Pre-Scheduled: 6
Next event?
Arrival at 13.
Initialization 4 8 9 13 15
Job1: 4
Job2: 5
Job3: 4
curTime
Jobs: Pre-Scheduled!

16. Simulation Server Job_Processed: Job2 Jobs: Pre-Scheduled!
Initialization 4 8 9 13 15 20
Job1: 4
Job2: 5
Job3: 4
Job4: 7
curTime
Jobs: Pre-Scheduled!

17. Simulation Server Job_Processed: Job2 Next event? Completing at 15.
Pre-Scheduled: 6
Job3
Next event?
Completing at 15.
Initialization 4 8 9 13 15 20
Job1: 4
Job2: 5
Job3: 4
Job4: 7
curTime
Jobs: Pre-Scheduled!

18. Simulation Server Job_Processed: Job2 Jobs: Pre-Scheduled! Job3
Initialization 4 8 9 13 15 20
Job1: 4
Job2: 5
Job3: 4
Job4: 7
curTime
Jobs: Pre-Scheduled!

19. Simulation Server Job_Processed: Job3 Jobs: Pre-Scheduled!
Completing at 20
Initialization 4 8 9 13 15 20
Job1: 4
Job2: 5
Job3: 4
Job4: 7
curTime
Jobs: Pre-Scheduled!

20. Simulation Server Job_Processed: Job3 Next event?
Pre-Scheduled: 5
Completing at 20
Next event?
Arrival & Completing:20
Initialization 20 4 8 9 13 15
Job1: 4
Job2: 5
Job3: 4
Job4: 7
curTime
Jobs: Pre-Scheduled!

21. Pseudo Code
Initialize simulation While not done update curTime to nextEventTime If curTime == Service Completion Time then Do Service Completion If curTime == Arrival Time then Do Arrival If curTime == Stop Time then Set done to true Dump statistics Multiple events can happen at the same time! Not If - Else The order to handle the events!

22. Class java.util.Random
import java.util.*; Random randInt = new Random(2345); // seed 2345 int rand = randInt.nextInt(x); // returns an integer between 0 and (x – 1) // randInt.nextInt(6): 0 to 5 // To generate a random number in [5, 10] // 5 + randInt.nextInt(6) // To generate a random number in [a, b] // a + randInt.nextInt(b – a + 1)

23. Pre-Scheduling Jobs
Random randArrival = new Random(2345); // seed 2345 // Arrival: [arr_min, arr_max] nextArrivalTime = arr_min + randArrival.nextInt(arr_max – arr_min + 1); nextArrivalTime = curTime + nextArrivalTime;

24. Pre-Scheduling Job-Completion
Random randCompl = new Random(5432); // Different seed! . . .

25. Constructor Set values for arr_min, arr_max, sc_min, sc_max, stop_time
Class Simulation
Constructor Set values for arr_min, arr_max, sc_min, sc_max, stop_time

26. Initialize Simulation
Job reset server  idle Initialize stats to be collected if stop time is 0 then done  true else done  false Create a queue Schedule the first Arrival Time

27. Next Event Time When the server is idle When the server is busy
the minimum of the arrival time and Stop time
When the server is busy
the minimum of the arrival time, Service Completion time, and Stop time

28. Arrival Event (without statistics gathering)
Create a Job Schedule the next Arrival Time If server is busy then Enter the queue Else Schedule Service Completion Time Set server to busy

29. Server Completion (without statistics gathering)
If the queue is empty then Set server to idle Else Remove a job from the queue Schedule Service Completion Time

30. Pseudo Code
Initialize simulation While not done update curTime to nextEventTime If curTime == Service Completion Time then Do Service Completion If curTime == Arrival Time then Do Arrival If curTime == Stop Time then Set done to true Dump statistics

31. Simulation Output
Current Job: J:19/T:190 Num Arrived: 20 Num Waiting: 1 Num Served Immed: 3 Max Waiting Time: 15

32. Multiple Line Single Server
Jobs

33. Multiple Line Multiple Server
Jobs
Server2

34. Single Line Multiple Server
Jobs
Server2

35. Schedule Prog4 Groups Signup 5 PM, Wednesday, 11-8 Quiz 4
Friday, 11-10
Prog4 Work Plan
5 PM, Friday, 11-10
Lab8 and Lab9: Job and Queue
11 PM, Wednesday, 11-15
Test 2:
Friday, 11-17
Prog4:
Tuesday, 11-21