1. CPSC 531: Some more examples – Time-shared computer and multi-teller bank
Instructor: Anirban Mahanti
Office: ICT 745
Class Location: TRB 101
Lectures: TR 15:30 – 16:45 hours
Class web page:
Notes derived from “Simulation Modeling and Analysis” by A. Law and W. Kelton, Third edition, McGraw Hill, 2000.
CPSC 531: Simulation Examples

2. Objective Under simulation fundamentals via examples
Time-shared computer model
Multi-teller bank with jockeying
Job shop model
Get a grip of “simlib”
CPSC 531: Simulation Examples

3. Time-Shared Computer Model
CPSC 531: Simulation Examples

4. Problem Specification
Terminals “think” and then issue jobs
Think times exponentially distributed - 25 s
Job service times also exponentially distributed s
Job processing rule: round-robin
Each visit to CPU is  q = 0.1 sec. (a quantum)
If remaining processing requirement > q sec., it gets q sec, then kicked out
If remaining processing requirement  q sec., it gets what it needs, returns to its terminal
Other job processing possibilities: FIFO, SJF, LIFO etc.
Swap time:  = 0.15 sec. Elapse whenever a job enters CPU before processing starts
CPSC 531: Simulation Examples

5. Problem Specification
Response time of a job = (time job returns to terminal) – (time it left its terminal)
Initially, computer empty and idle, all n jobs in the think state at their terminals
Stopping rule: response times collected
Output:
Average of the response times
Time-average number of jobs in queue for the CPU
CPU utilization
Question: how many terminals (n) can be loaded on and hold average response time to under 30 s?
CPSC 531: Simulation Examples

6. Turning the specifications to a prog.
Job Arrival
CPU
Processing
End
Simulation
Terminals
CPSC 531: Simulation Examples

7. Simlib program: events, lists, etc
1 = Arrival of a job to the computer (at end of a think time)
2 = A job leaves the CPU (done or kicked out)
3 = End simulation (scheduled at time 1000th job gets done)
(Also, have “utility” non-event function start_CPU_run to remove first job from queue, put it into the CPU)
simlib lists, attributes:
1 = queue, attributes = [time of arrival of job to computer, remaining service time]
2 = CPU, attributes = [time of arrival of job to computer, remaining service time]
In CPU, if remaining service time > 0 then job has this much CPU time needed after current CPU pass; if remaining service time  0, job will be done after this pass
25 = event list, attributes = [event time, event type]
CPSC 531: Simulation Examples

8. Simlib program: variables, random streams
sampst variable:
1 = response times
timest variables:
none (use filest on the lists)
Random-number streams:
1 = think times, 2 = service times
CPSC 531: Simulation Examples

9. Overview of function main()
/* ……… code fragment from main() ……….. */
for (num_terms = min_terms; num_terms <= max_terms; num_terms += incr_terms) {
init_simlib(); /* Initialize simlib */
maxatr = 4; /* NEVER SET maxatr TO BE SMALLER THAN 4. */
num_responses = 0; /* Initialize the non-simlib statistical counter. */
for (term = 1; term <= num_terms; ++term) /* Schedule the first arrival to the CPU from each terminal. */
event_schedule(expon(mean_think, STREAM_THINK), EVENT_ARRIVAL);
do {
timing(); /* Determine the next event. */
/* Invoke the appropriate event function. */
switch (next_event_type) {
case EVENT_ARRIVAL:
arrive();
break;
case EVENT_END_CPU_RUN:
end_CPU_run();
case EVENT_END_SIMULATION:
report(); }
} while (next_event_type != EVENT_END_SIMULATION);
CPSC 531: Simulation Examples

10. The arrive() function Function arrive() Place job in queue CPU idle?
Yes No
Return
Start CPU run
CPSC 531: Simulation Examples

11. The arrive() function
void arrive(void) /* Event function for arrival of job at CPU after think
time. */ {
/* Place the arriving job at the end of the CPU queue.
Note that the following attributes are stored for each job record:
1. Time of arrival to the computer.
2. The (remaining) CPU service time required (here equal to the
total service time since the job is just arriving). */
transfer[1] = sim_time;
transfer[2] = expon(mean_service, STREAM_SERVICE);
list_file(LAST, LIST_QUEUE);
/* If the CPU is idle, start a CPU run. */
if (list_size[LIST_CPU] == 0)
start_CPU_run(); }
CPSC 531: Simulation Examples

12. The start_CPU_run() function
CPSC 531: Simulation Examples

13. The end_CPU_run() function
CPSC 531: Simulation Examples

14. Things to do
Look at the simlib code for the time shared computer model
Try problem 2.3 from the LK00 text book
Our next stop will be
Multi-teller Bank with Jockeying
CPSC 531: Simulation Examples

15. Multi-teller Bank New arrivals: Initially empty and idle
Interarrival times:
Expon (mean = 1 min.)
Service times:
Expon (mean = 4.5 min.)
New arrivals:
If there’s an idle teller, choose leftmost (idle) teller
If all tellers are busy, choose shortest queue (ties – leftmost)
Initially empty and idle
Termination: close doors at time 480 min.
If all tellers are idle at that time, stop immediately
If any tellers are busy, operate until all customers leave service
CPSC 531: Simulation Examples

16. Jockeying Rules
Suppose teller i (i fixed) finishes service — e.g., i = 3 above
Then either teller i becomes idle, or queue i becomes one shorter
Maybe a customer at the end of some other queue j ( i) moves to teller i (if now idle) or the end of the now-shorter queue i
For each teller/queue k, let nk = number of customers facing (in queue + in service) teller k just after teller i finishes service
Procedure:
If nj > ni + 1 for some j  i, then a jockey will occur
If nj > ni + 1 for several values of j  i, pick the closest j (min |j – i|)
If nj > ni + 1 for two equally closest (left and right) values of j  i, pick the left (smaller) value of j
CPSC 531: Simulation Examples

17. Performance Metrics Estimate
Time-average total number of customers in (all) queues
Average, max delay of customers in queue(s)
What’s the effect of the number of tellers?
CPSC 531: Simulation Examples

18. Simlib program: events, lists, etc
1 = Arrival of a customer to the bank
2 = Departure of a customer from a teller (need to know teller #)
3 = Close doors at time 480 min. (may or may not be The End)
(Also, have “utility” non-event function jockey to see if anyone wants to jockey, and, if so, carry it out)
simlib lists, attributes (n = number of tellers):
1, …, n = queues, attributes = [time of arrival to queue]
n + 1, …, 2n = tellers, no attributes = (dummy lists for utilizations)
25 = event list, attributes = [event time, event type, teller number if event type = 2]
CPSC 531: Simulation Examples

19. Simlib program: variables, streams
sampst variable: 1 = delay of customers in queue(s)
timest variables: none … use filest for time-average number in queues since time-average of total = total of time averages (details in book)
Random-number streams: 1 = interarrival times, 2 = service times
CPSC 531: Simulation Examples

20. The main() function // code fragment // … see text for the rest
event_schedule(expon(mean_interarrival, STREAM_INTERARRIVAL), EVENT_ARRIVAL); /* Schedule the first arrival. */
/* Schedule the bank closing. (Note need for consistency of units.) */
event_schedule(60 * length_doors_open, EVENT_CLOSE_DOORS);
/* Run the simulation while the event list is not empty. */
while (list_size[LIST_EVENT] != 0) {
/* Determine the next event. */
timing();
/* Invoke the appropriate event function. */
switch (next_event_type) {
case EVENT_ARRIVAL:
arrive();
break;
case EVENT_DEPARTURE:
depart((int) transfer[3]); /* transfer[3] is teller number */
case EVENT_CLOSE_DOORS:
event_cancel(EVENT_ARRIVAL); }
CPSC 531: Simulation Examples

21. The arrive() function
CPSC 531: Simulation Examples

22. The depart() function
CPSC 531: Simulation Examples

23. The depart() function …
void depart(int teller) /* Departure event function. */ {
/* Check to see whether the queue for teller "teller" is empty. */
if (list_size[teller] == 0)
/* The queue is empty, so make the teller idle. */
list_remove(FIRST, num_tellers + teller);
else {
/* The queue is not empty, so start service on a customer. */
list_remove(FIRST, teller);
sampst(sim_time - transfer[1], SAMPST_DELAYS);
transfer[3] = teller; /* Define before event_schedule. */
event_schedule(sim_time + expon(mean_service, STREAM_SERVICE),
EVENT_DEPARTURE); }
/* Let a customer from the end of another queue jockey to the end of this
queue, if possible. */
jockey(teller);
CPSC 531: Simulation Examples

24. The jockey() function
CPSC 531: Simulation Examples

25. Things to do Look at the simlib code for the multi-teller bank model
Try problem 2.4 from the LK00 text book
Some food for thought
How about replacing this multiple-teller multiple-queue model with a single-queue multiple-teller model?
CPSC 531: Simulation Examples

26. Job Shop Model Five workstations Three types of jobs
Number of identical machines at each workstation as shown
Network of multiserver queues
Three types of jobs
Interarrival times (all job types combined) expon (mean = 0.25 hour)
Job type determined just after arrival
Type 1, 2, 3 w.p. 0.3, 0.5, 0.2
Workstation routes for job types:
Type 1: 3  1  2  5 (see fig.)
Type 2: 4  1  3
Type 3: 2  5  1  4  3
Mean service times (2-Erlang distrib.):
Type 1:  0.60  0.85  0.50
Type 2:  0.80  0.75
Type 3:  0.25  0.70  0.90  1.0
Initially empty and idle
Stop at time 365  8 hours
CPSC 531: Simulation Examples

27. Job Shop Model (cont’d.)
Estimate
Average total delay in queues for each job type separately
Overall average total delay in queues over all job types, weighted by their (known) probabilities of occurrence
For each machine group separately:
Average delay in queue there (all job types lumped together)
Time-average number of jobs in queue (all job types together)
Group utilization =
Number of machines in the group
Question: If you could add one machine to the shop, to which group should it go?
Time-average number of machines that are busy
Number of machines in the group
CPSC 531: Simulation Examples

28. Simlib program: events, lists, etc
1 = Arrival of a job to the system
2 = Departure of a job from a particular station
3 = End of the simulation
simlib lists, attributes:
1, …, 5 = queues, attributes = [time of arrival to station, job type, task number]
25 = event list, attributes = [event time, event type, job type (if event type = 2), task number (if event type = 2)]
(Task number of a job is how far along it is on its route, measured in stations, so starts at 1, then is incremented by 1 for each station)
CPSC 531: Simulation Examples

29. Simlib program: variables
sampst variables:
1, …, 5, = delay in queue at machine group 1, …, 5
6, 7, 8 = total delay in queues for job type 1, 2, 3
timest variables:
1, …, 5 = number of machines busy at machine group 1, …, 5
(We’ll keep our own, non-simlib variable num_machines_busy[j] to track the number of machines busy in group j)
Random-number streams: 1 = interarrival times, 2 = job-type coin flip, 3 = service times
CPSC 531: Simulation Examples

30. Things to do Look at the simlib code for this problem
Next class – continue with Statistical Models
First assignment will be out this weekend
CPSC 531: Simulation Examples