1. Chapter 2 Modeling Complex Systems (cont’d.)
11/26/2018
Chapter 2 Modeling Complex Systems (cont’d.)
Last time, simlib was introduced for modeling the complex system. Simlib provides list processing, random number generation, and statistics collecting functions such as sampst for discrete time data, timest for continuous-time data, and filest for records in a list. We also use Simlib to simulate M/M/1 queueing system.

2. Use Simlib Determine events, event graph, flow charts,
11/26/2018
Determine events, event graph, flow charts,
Determine what lists are needed, what their attributes are
Determine sampst, timest variables
Determine and assign usage of random-number streams
Declare some global or local variables
write main function and event functions (and maybe other functions),
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

3. 2.5 TIME-SHARED COMPUTER MODEL; 2.5.1 Problem Statement
11/26/2018
Think times of jobs at terminals:
Expon (mean = 25 sec.)
Processing times of jobs at CPU:
Expon (mean = 0.8 sec.)
Fixed number of terminals (and jobs), n
Processing rule: round-robin
Each visit to CPU is  q = 0.1 sec. (a quantum)
If job still needs > q sec., it gets q sec, then kicked out
If job still needs  q sec., it gets what it needs, returns to its terminal
Compromise between extremes of FIFO (q = ) and SJF (q = 0)
Swap time:  = 0.15 sec. Elapse whenever a job enters CPU before processing starts
Response time of ith job Ri = (time ith job returns to terminal) – (time ith job left its terminal)
Each operator at each terminal thinks for an amount of time that is an exponential random variable with mean 25 seconds, and then sends to the CPU a job having service time distributed exponentially with mean 0.8 second. Arriving jobs join a single queue for the CPU but are served in a round-robin manner. The CPU allocates to each job a maximum service quantum of length q = 0.1 second. If a job requires more than q seconds, the CPU will spends q +  seconds on the job, which rejoins at the end of queue with its remaining service time reduced by q seconds. If the (remaining) service time of a job, s seconds, I no more than q, the CPU spends s seconds, plus a fixed swap time of  processing the job, the job returns to its terminal.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

4. 2.5.1 Problem Statement (cont’d.)
11/26/2018
Initially, computer empty and idle, all n jobs in the think state at their terminals
For n = 10, 20, …, 80
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 sec.?
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

5. Event Graph . . . 1 2 n Enter Service End Simulation End CPU run
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Enter
Service
End Simulation 2 .
End CPU
run . . n
Event graph, computer model
If an event node has incoming arcs that are all thin and smooth, this event can be eliminated from the model.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

6. 2.5.2 simlib Program Events simlib lists, attributes:
11/26/2018
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, for now)
(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]
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

7. 2.5.2 simlib Program (cont’d.); 2.5.3 Simulation Output and Discussion
11/26/2018
sampst variable: 1 = response times
timest variables: none (use filest or out_filest)
Random-number streams: 1 = think times, 2 = service times
Program files and Simulation out put
Input file tscomp.in
min_terms max terms incr_terms num_responses_
required mean_think mean_service quantum swap
Figure 2.15 – external definitions (at top of file)
Figure 2.16 – function main
Figure 2.18 – function arrive (flowchart: Figure 2.17)
Figure 2.20 – function start_cpu_run (flowchart: Figure 2.19)
Figure 2.22 – function end_cpu_run (flowchart: Figure 2.21)
Figure 2.23 – function report
Figure 2.24 – output report tscomp.out
Looks like max n is a little under 60 – sure?
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

8. 10 1.324 0.156 0.358 Time-shared computer model
11/26/2018
Time-shared computer model
Number of terminals to 80 by 10
Mean think time seconds
Mean service time seconds
Quantum seconds
Swap time seconds
Number of jobs processed
Number of Average Average Utilization
terminals response time number in queue of CPU
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

9. 2.6 MULTITELLER BANK W/ JOCKEYING; 2.6.1 Problem Statement
11/26/2018
Service times:
Expon (mean = 4.5 min.)
Interarrival times:
Expon (mean = 1 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 (9 am to 5 pm).
If all tellers are idle at that time, stop immediately
If any tellers are busy, operate until all customers leave service
Customers in the bank before 5 pm will be served.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

10. 2.6.1 Problem Statement (cont’d.)
11/26/2018
Jockeying (line-hopping) 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 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
Estimate
Time-average total number of customers in (all) queues
Average, max delay of customers in queue(s)
Question: What’s the effect of the number of tellers (4-7)?
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

11. simlib Program
11/26/2018
Events
1 = Arrival of a customer to the bank
2 = Departure of a customer from a teller (need to know which 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]
sampst variable: 1 = delay of customers in queue(s)
Now event has one more attribute teller number for event of type 2 so we can manage the queues and jockeying rule correctly.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

12. Event Graph initiate Arrival Departure Close doors
11/26/2018
Arrival
Departure
initiate
Close
doors
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

13. 2.6.2 simlib Program ; 2.6.3 Simulation Output and Discussion
11/26/2018
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
Refer to pp in the book (Figures ) and the file mtbank.c
Input file mtbank.in parameters:
min_tellers max_tellers mean_interarrival mean_service length_doors_open
Figure 2.27 – external definitions (at top of file)
Figure 2.28 – function main
Figure 2.30 – function arrive (flowchart: Figure 2.29)
Figure 2.32 – function depart (flowchart: Figure 2.31)
Figure 2.34 – function jockey (flowchart: Figure 2.33)
Figure 2.35 – function report
Figure 2.36 – output report mtbank.out
Looks like 4 tellers would be a disaster, 6 might be worth it, 7 not (sure?)
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

14. Discussions In arrive () /* Schedule a service completion. */
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In arrive ()
/* Schedule a service completion. */
transfer[3] = teller; /* Define third attribute of type-two event-list record before event_schedule. */
event_schedule(
sim_time + expon(mean_service, STREAM_SERVICE),
EVENT_DEPARTURE);
Event: EVENT_CLOSE_DOORS
Scheduled in the beginning to happen after 8 hours (at 5 pm)
When it occurs, remove the next-arrival event, thus cut off the arrival stream
A simulation ends when the event list is empty.
In arrive () function, when a service completion is schedule, transfer[3] must be define since event_schedule only fills in the first two fields of transfer array.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

15. Discussions
11/26/2018
The avg. of sum of the individual queue lengths = the sum of their avg queue lengths
Is this also true for maximum?
i.e. the maximum total # of customers in the queues = the total of the maximum # of customers in each queue?
In arrive () function, when a service completion is schedule, transfer[3] must be define since event_schedule only fills in the first two fields of transfer array.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

16. Discussions
11/26/2018
From mtbank.out, with four tellers, both the avg number of customers in the queues and the delay in queue are large.
Is this also true for maximum?
i.e. the maximum total # of customers in the queues = the total of the maximum # of customers in each queue?
In arrive () function, when a service completion is schedule, transfer[3] must be define since event_schedule only fills in the first two fields of transfer array.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

17. 2.7 JOB-SHOP MODEL; 2.7.1 Problem Statement
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 (shown at left)
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
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

18. 2.7.1 Problem Statement (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
Why not just average the total delay in queues over all the jobs that show up and get through?
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
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

19. 2.7.2 simlib Program Events simlib lists, attributes:
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)
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

20. 2.7.2 simlib Program (cont’d.)
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
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

21. 2.7.2 simlib Program (cont’d.); 2.7.3 Simulation Output and Discussion
Refer to pp in the book (Figures ) and the file jobshop.c
Figure 2.39 – external definitions (at top of file)
Figure 2.40 – function main
Figure 2.42 – function arrive (flowchart: Figure 2.41)
Note that arrive serves two purposes – new arrival event, “arrival” of an “old” job to its next machine group
Figure 2.44 – function depart (flowchart: Figure 2.43)
Note that depart (and this function) is the event of leaving a particular machine group, which may or may not be the end of the road for a job
Figure 2.45 – function report
Figure 2.46 – output report mtbank.out
Looks like congested machine groups are 1, 2, and 4 (sure?)
Reruns with extra machine at each of these in turn – add machine to 4 (?)
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

22. 2.8 EFFICIENT EVENT-LIST MANIPULATION
Have seen two different ways to store, handle the event list
Sequential by event type – search for smallest entry for next event
Must always look at the whole event list
Ranked in increasing order by event time – insert correctly, take next event from top
Event insertion might not require looking at the whole list
In large simulations with many events, event-list processing can consume much of the total computing time (e.g., 40%)
Generally worth it to try hard to manage the event list efficiently
Better methods – binary search, storing event list as a tree or heap
Exploit special structure of model to speed up event-list processing
e.g., if time a record stays on event list is approximately the same for all events, insert a new event via a bottom-to-top search
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

23. Example of Process-Oriented Simulation
Approaches to modeling and simulation (Chapter 1)
Event-scheduling – as described above, coded in general-purpose language
Process – focuses on entities and their “experience,” usually requires special-purpose simulation software, also called process-oriented
Process-oriented simulation of MM1 mm1posim.c using CSIM library from Mesquite Software Inc.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

24. Simlin function list_file
In list_file(int option, int list) , “Cut” versus “Copy” transfer array
Cut – transfer is allocated new memory
(*row).value = transfer;
/* Make room for new transfer. */
transfer = (float *) calloc(maxatr + 1, sizeof(float));
Copy – transfer is unchanged, values is copied to the list.
(*row).value = (float *) calloc(maxatr + 1, sizeof(float));
for (item = 0; item <= maxatr; ++item)
(*row).value[item] = transfer[item];
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

25. Stopping Rule M/M/1: # of customers left the waiting queue (Ch 1 & 2)
M/M/1: simulation time (Ch 1)
Time Shared Computer Model: # of jobs completed (Ch 2)
Multiteller Bank Model: closing time, allowing existing customers to finish (Ch 2)
Job Shop Model: simulation time (Ch 2)
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

26. Stats Collection Average, maximum, minimum delay in queue(s)
Length of queue, total length of queues
Server or servers utilization
Average, maximum, minimum response time
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

27. Chapter 3 Simulation Software

28. CONTENTS 3.1 Introduction
3.2 Comparison of Simulation Packages with Programming Languages
3.3 Classification of Simulation Software
3.4 Desirable Software Features
3.5 General-Purpose Simulation Packages
3.6 Object-Oriented Simulation
3.7 Examples of Application-Oriented Simulation Packages
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

29. 3.1 INTRODUCTION Activities common to most simulations:
Random-number generation … draws from U(0, 1) distribution
Random-variate generation … draws from probability distributions specified as part of the inputs to the model
Advancing simulated time
Determining the next event from the event list, and passing control to the appropriate event logic
Adding records to lists, deleting records from lists
Collecting output statistics and reporting results
Detecting error conditions
Simulation software packages are designed to do these things (and more) for you
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

30. 3.2 COMPARISON OF SIMULATION PACKAGES WITH PROGRAMMING LANGUAGES
Advantages of simulation packages
Provide most modeling features, so “programming” effort, cost is reduced, often significantly
Natural framework for simulation modeling
Usually make it easier to modify models
Better error detection for simulation-specific errors
Advantages of general-purpose programming languages
More widely known, available
Usually executes faster … if well written
May allow more modeling flexibility
Software cost is usually lower
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

31. 3.3 CLASSIFICATION OF SIMULATION SOFTWARE
General-purpose vs. application-oriented packages
Traditionally: simulation languages and simulators
Languages were flexible but required programming, simulators were easy to use but not very flexible
Now, almost all simulation software uses graphical interface so is relatively easy to use, learn
Distinction now is between general-purpose simulation software and applications-oriented package
Specific applications include manufacturing, call centers, telecommunications, etc.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

32. 3.3 Classification of Simulation Software (cont’d.)
Modeling approaches
Event-scheduling approach – as in Chaps. 1 and 2
Can uses general programming languages, or some simulation languages
During processing of an event, no simulated time passes
Process-interaction approach
Now used by most simulation software
Instead of identifying events, identify entities (a.k.a. processes) that are created, flow around or through the system, maybe leave
May have multiple realizations of an entity/process
May have different kinds of entities/processes
“Program” consists of a description of what happens to the different kinds of processes (including their entry and exit)
Usually expressed graphically, like a flowchart
During processing of an entity/process, simulated time usually passes
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

33. 3.3 Classification of Simulation Software (cont’d.)
Common modeling elements
Entities – represent customers, parts, messages, paperwork, airplane, etc.
Attributes – Information stored with each entity
Usually, every individual entity has the same set of attributes, but the values differ to distinguish the entities
Some attributes are automatic, others are user-defined and user-maintained
Resources – servers, machines, workers, nodes, links, runways, gates, agents, clerks, etc.
Queues – where entities wait if resources are not available
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

34. 3.4 DESIRABLE SOFTWARE FEATURES
General capabilities
Modeling flexibility – ability to drill down to lower levels of programming, create custom modeling constructs
Ease of use
Hierarchical modeling – submodels containing submodels, etc.
Fast execution speed
Ability to create user-friendly front/back ends for template creation
Run-time version for wide distribution of model
Import/export data from/to other applications
Automatic execution of models for different input-parameter combinations
Combined discrete/continuous modeling
Ability to initialize in other than empty & idle state
Save state at end to re-start later
Affordable
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

35. 3.4 Desirable Software Features (cont’d.)
Hardware and software requirements
Matches platform/OS – Windows, UNIX, MacOS
Animation and dynamic graphics
Concurrent vs. postprocessing
2D vs. 3D
Import CAD drawings
Display statistics, graphs dynamically during execution
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

36. 3.4 Desirable Software Features (cont’d.)
Statistical capabilities
Adequate random-number generator for basic U(0, 1) variates
Statistical properties, cycle length, adequate streams and substreams
RNG seeds should have good defaults, be fixed – not dependent on clock
Comprehensive list of input probability distributions
Continuous, discrete, empirical
Ability to make independent replications
Confidence-interval formation for output performance measures
Warmup
Experimental design
Optimum-seeking
Customer support and documentation
Output reports and graphics
Standard defaults, customizable – stored in database for postprocessing
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

37. 3.5 GENERAL-PURPOSE SIMULATION PACKAGES
Two popular general-purpose simulation packages
Arena and Extend
Both GUI, drag/drop/connect/detail the modules (blocks)
Some additional general-purpose simulation packages
AweSim, Micro Saint, GPSS/SLX, SIMPLE++, SIMUL8, Taylor Enterprise Dynamics
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

38. 3.6 OBJECT-ORIENTED SIMULATION
OO programming and OO simulation originated in the same product – SIMULA, from the 1960s
OO simulation has objects that interact as simulation progresses through simulated time
Objects contain data, methods
Also have encapsulation, inheritance, etc.
Recent software product for OO simulation – MODSIM III
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

39. 3.7 EXAMPLES OF APPLICATION-ORIENTED SIMULATION PACKAGES
Oriented toward specific classes of applications
Manufacturing
Communications
Process reengineering and service systems
Health care
Call centers
Standalone animation – links to multiple simulation-modeling packages
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems

40. Homework 2
11/26/2018
Download simlib from and use new  simlib.c, which  copies the attributes of the record and leaves them intact in the transfer array for subsequent use when a record is placed into a list
Solve the problem 2.4 (d) in the textbook with additional output measurements such as the maximum number of customers waiting in the queues and the utilization defined in 2.4 (c)
Submit a write up for the problem with the explanation of the code you add and modify, the C code, the output file.
Due February 2 in class.
Simulation Modeling and Analysis – Chapter 2 – Modeling Complex Systems