1. Simulation Software

2. Introduction The features that should be programmed in simulation are:
Generating random numbers from the uniform distribution
Generating random variates from any distribution
Advancing simulation time
Determining the next event and passing control to the appropriate block of code
Adding records to, or deleting records from, a list
Collecting output statistics and reporting them
Detecting error conditions
These common features are programmed using general-purpose languages like FORTRAN, C or C++ to develop simulation packages.

3. How to simulate a system with a computer code?
Planning the study
Description of the system
Definitions of the performance measures
Algorithm
Flowchart: Process in the system, collection of statistics to estimate the performance measures, reporting
Algorithm that corresponds to the flowchart
Computer code (Matlab, Java, …)
Data structures (sequential vs linked allocation: in book)
Random number generation
Coding the algorithm

4. Simulating a Multi-Teller Bank
The bank opens its doors at 9 A.M. and closes its doors at 5 P.M., but operates until all customers still in the bank are served. Customer interarrival times are IID and exponential with mean 1 minute and services are IID and exponential with mean 4.5 minutes.
Each teller has a separate queue. An arriving customer joins the shortest queue, choosing the leftmost shortest queue if there is a tie. Let ni be the number of customers in front of teller i. If the completion of service at teller i causes nj > ni + 1 for some other teller j, then the customer from the tail of queue j jockeys to the tail of queue i. If there are two or more such customers, the one from the closest leftmost queue joins.

5. Multiteller Bank with Jockeying

6. Events and state transitions

7. Events and state transitions: arrival to a non-empty system

8. Events and state transitions: arrival to an empty system

9. Events and state transitions: departure from a non-empty system, followed by jockeying

10. Performance measures Expected number in each queue
Expected waiting time of a customer
Expected utilization of each server

11.  a separate flowchart for each event
Events?
 a separate flowchart for each event
Customer arrival
Customer departure
Jockeying
How to combine them?
 main flowchart

12. Arrival Flowchart Yes No Function arrive
Schedule the next arrival event
Is a teller idle?
Yes No
Set a delay of 0 for this customer
Find the number of the leftmost shortest queue (shortest_q)
Make the teller busy
Place the customer at the end of queue number shortest_q
i.e., increase the # in the queue by 1
Schedule the departure of this customer
Record the arrival time of this customer
Return

13. Departure Flowchart Yes No Function depart
Is the queue for this teller empty?
Yes No
Make this teller idle
Remove the first customer from this queue
Compute this customer’s delay and gather statistics
Schedule the departure event for this customer
Call function Jockey
Return

14. Jockeying Flowchart Yes No Yes No Function jockey
Is there a customer to jockey?
Yes
Remove this customer from the tail of his or her current queue No
Is the teller who just completed service now busy?
Yes No
Compute this customer’s delay and gather statistics
Place the jockeying customer at the tail of the queue of the teller who just completed service
Make this teller busy
Schedule the departure event for the jockeying customer
Return

15. Flowchart Combining Departure and Jockeying
Function depart
Flowchart Combining Departure and Jockeying
Is the queue for this teller empty?
Yes No
Is there a customer to jockey?
Remove the first customer from this queue
Yes No
Compute this customer’s delay and gather statistics
Remove this customer from the tail of his or her current queue
Make this teller idle
Schedule the departure event for this customer
Compute this customer’s delay and gather statistics
Is there a customer to jockey?
Yes
Make this teller busy
Place the jockeying customer at the tail of this queue
Schedule the departure event for the jockeying customer No
Return

16. Main flowchart Yes No Start Initialization
Is current_time < finish_time
Yes No
Find the next event
Update current_time: current_time+time_till_next
Report
Call the function corresponding to the event
Stop

17. Flowcharts
Schedule next departure only if you make the server busy with the next customer.
Collect the statistics:
How many customers were waiting between the previous event and the departure now?
The waiting time of the customer who just started service? …

18. How to think to draw a flowchart: Process
Departure function is called, when the minimum of the event times (in this case, time-to-departure and time-to-arrival) corresponds to a departure.
So we know that a customer is leaving the system, which means that the server serving that customer is now idle and has to look for a customer if there is any in the system.
Is there any customer to serve for this server? Check:
The server’s queue
Other queues
Once the server’s state is determined, check for jockeying

19. How to think to draw a flowchart: Process
Which event will happen next?
Events:
Arrival
Potentially departure from queue i, i=1,2,…,5
End of simulation

20. How to think to draw a flowchart: Information gathering
What do you need to know about the queues?
The number of customers in each queue:
State variable: (n1(t),n2(t),..n5(t)), where ni(t) denotes the total number of customers in queue i (including the customer in service).
Server state?
What do we need to know about customers?
For each customer:
The queue that he/she is waiting for (denote by cust_queue)
His/her position in the cust_queue
His/her arrival time

21. How to modify the states?
Let (n1(t),n2(t),..n5(t)) be our state variable where ni(t) denotes the total number of customers in queue i (including the customer in service).
Arrival event:
If there is at least one ni(t-) =0.
Let j be the smallest index of the queue that is empty, then
nj(t)=nj(t-)+1
Else
Find argminj((n1(t),n2(t),..n5(t))
Let j be the smallest index of the queue has the smallest number of customers, then

22. How to gather statistics
Define the variables:
Cum_delay
Cum_queue
Cum_busy
At each event epoch, update these variables

23. How to think to draw a flowchart: Information gathering
For example: Cum_queue
At each event epoch, update these variables
Inter-arrival times: A1 = 0.4, A2 = 1.2, A3 = 0.5, A4 = 1.7, A5 = 0.2, A6 = 1.6, A7 = 0.2, A8 = 1.4, A9 = 1.9
Processing times: S1 = 2.0, S2 = 0.7, S3 = 0.4, S4 = 1.1, S5 = 3.7, S6 = 0.6 t
Events
Next Event
N1(t)
Cum_queue1
{I1}
I1 (0.4)
0.4
{I2, C1}
I2 (1.6) 1
0+00.4=0
1.6
{I3, C1, C2 }
I3 (2.1) 2
0+0*( )=0
2.1
{I4, C1, C2 }
C2 (2.3) 3
0+0*( )=0
2.3
{I4, C1, C3}
C1(2.4)
0+1*( )=0.2 …

24. Output Report for Multiteller Bank

25. Output Report for Multiteller Bank

26. Comparison of Simulation Packages with Programming Languages
Advantages of simulation packages
They automatically provide most of the features, requiring less programming time and cost.
They provide a natural framework for simulation modeling.
Models are easier to modify and maintain.
They provide better error detection because potential errors are checked for automatically.

27. Comparison of Simulation Packages with Programming Languages
Advantages of general purpose languages
Most modelers already know a language, but this is often not the case with a simulation package.
A simulation model efficiently written in a language may require less execution time.
Programming languages may allow greater programming flexibility.
Software cost is generally lower, but total project cost may not be.

28. Classification of Simulation Software
Earlier times: A combination of general purpose language and simulation concepts such as Simscript, Siman, or SLAM
Recently: Simulation software packages
Easy-to-use
User friendly graphical model building approach involving use of modules and icons selected by the user on screen
Entities represented by icons with a wide range of animation capabilities.

29. Classification of Simulation Software
General-purpose versus application-oriented simulation packages
A general-purpose simulation package can be used for any application, but might have special features for certain ones (like manufacturing, communications, or business process reengineering).
An application-oriented simulation package is designed to be used for a certain class of application (like manufacturing, health- care, or call centers).

30. Classification of Simulation Software
Modeling approach
Event-scheduling approach is based on simulating over time by executing the events selected from the event list in increasing order of their time.
Process approach is based on simulating the time-ordered sequence of processes experienced by a single entity as it flows through the system.

31. Process Approach

32. Prototype customer-process routine for a single-server queueing system

33. Common Modeling Elements
Simulation packages typically include entities, attributes, resources and queues as part of their modeling framework.

34. Desirable Software Features
General capabilities
Modeling flexibility, Ease of use, Hierarchical modeling, Debugging aids, Fast model execution speed, etc.
Hardware and software requirement
Computer platforms (PC’s, UNIX workstations, Apple’s), RAM requirement, Operating system requirement (Windows, UNIX, Mac OS)
Animation and dynamic graphics
Concurrent and post-processed animation, Vector based and pixel based graphics, Two and three dimensional animation, Dynamic graphics and statistics

35. Desirable Software Features
Statistical capabilities
Good random number generation, Theoretical discrete and continuous distributions, Empirical distributions, Independent replications or runs, Performance estimation, Confidence interval determination, Warmup period, Optimization via simulation
Customer support and documentation
Public and customized training
Technical support
Good documentation
Output reports and graphics
Standart and customized reports
Descriptive statistics (histograms, time plots, bar chart, pie chart, etc.)

36. General-Purpose Simulation Packages
Arena
This is the package we will be using in this course. Modeling is done using modules arranged into a number of templates:
Basic Process template has modules used in many models for modeling arrivals (create), services (process) and departures (dispose).
Advanced Process template contains modules to perform very specific logical functions such as choosing a queue when several are available or coordinating the advancement of multiple entities in different areas
Advanced Transfer template contains modules (like conveyors and transporters) that are used to describe the transfer of entities from one part of the system to another.

37. Arena
A model is constructed by dragging and dropping modules into the model window, connecting them to indicate the flow of entities through the simulated system, and then detailing the modules using dialog boxes of Arena’s built-in spreadsheet.

38. Arena

39. Arena

40. Arena

41. Arena

42. Arena

43. Other General-Purpose Simulation Packages
·       Extend ·       AweSim
·       GPSS/H ·       Micro Saint
·       MODSIM III ·       SES/workbench
·       SIMPLE++ ·       SIMUL8
·       SLX ·       Taylor Enterprise Dynamics

44. Application-Oriented Simulation Packages
Manufacturing: AutoMod, AutoSched AP, Extend + Manufacturing, Arena Packaging Edition, ProModel, QUEST, Taylor Enterprise Dynamics, WITNESS
Communication Networks: COMNET, IT DecisionGuru, OPNET Modeler
Process Reengineering and Services: Arena Business Edition, Extend + BPR, ProcessModel, ServiceModel, SIMPROCESS
Health Care: MedModel
Call Centers: Arena Call Center Edition
Animation: Proof Animation