CPSC 531: Some more examples –
Time-shared computer and multi-teller bank
Instructor: Anirban Mahanti
Office: ICT 745
Email: [email protected]
Class Location: TRB 101
Lectures: TR 15:30 – 16:45 hours
Class web page:
http://pages.cpsc.ucalgary.ca/~mahanti/teaching/F05/CPSC531/
Notes derived from “Simulation Modeling
and Analysis” by A. Law and W. Kelton,
Third edition, McGraw Hill, 2000.
CPSC 531: Simulation Examples
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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
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Time-Shared Computer Model
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Problem Specification
 Terminals “think” and then issue jobs
 Think times exponentially distributed - 25 s
 Job service times also exponentially distributed - 0.8 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
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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: 1000 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?
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Turning the specifications to a prog.
Job Arrival
CPU
Processing
End
Simulation
Terminals
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Simlib program: events, lists, etc
 Events
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]
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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
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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();
break;
case EVENT_END_SIMULATION:
report();
break;
}
}
} while (next_event_type != EVENT_END_SIMULATION);
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The arrive() function
Function
arrive()
Place job in queue
Start CPU run
Yes
CPU idle?
No
Return
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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();
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The start_CPU_run() function
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The end_CPU_run() function
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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
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Multi-teller Bank
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
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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 nowshorter 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
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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
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Simlib program: events, lists, etc
 Events
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]
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Simlib program: variables, streams
 sampst variable: 1 = delay of customers in
queue(s)
 timest variables: none … use filest for timeaverage number in queues since time-average of
total = total of time averages (details in book)
 Random-number streams:
1 = interarrival times, 2 = service times
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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 */
break;
case EVENT_CLOSE_DOORS:
event_cancel(EVENT_ARRIVAL);
break;
}
}
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The arrive() function
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The depart() function
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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);
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The jockey() function
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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 multiplequeue model with a single-queue multiple-teller
model?
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Job Shop Model
 Five workstations
 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

Initially empty and idle
Stop at time 365  8 hours
Mean service times (2-Erlang
distrib.):
• Type 1: 0.50  0.60  0.85 
0.50
• Type 2: 1.10  0.80  0.75
• Type 3: 1.20  0.25  0.70 
0.90  1.0
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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 = Time-average number of machines that are busy
Number of machines in the group
• Number of machines in the group
 Question: If you could add one machine to the shop,
to which group should it go?
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Simlib program: events, lists, etc
 Events
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)
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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
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Things to do
 Look at the simlib code for this problem
 Next class – continue with Statistical Models
 First assignment will be out this weekend
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