1) Random numbers are used as inputs to simulation models and are generated using pseudo-random number generators like the linear congruential method. 2) Conceptual modeling involves describing the problem, inputs, outputs, components and their interactions of the system being modeled in a non-software specific way. 3) Data collection and simplification are important parts of conceptual modeling to develop the simulation model in a faster and more accurate manner.

1. Modeling Variability Main ingredient of Simulation models are Random Numbers. Random numbers refer to a sequence of numbers that appear in random order. Random numbers follow the properties of uniformity and independence. Random numbers are represented as real numbers from 0 to 1 and are converted to random integers

2. Generating Random Numbers Tables of Random Numbers RAND function in Excel Random Numbers are rarely stored due to inefficient use of computer memory Random Number are generated when required Pseudo Random Numbers are created to represent random numbers

3. Linear Congruential Method A pseudo random number generator Where: X i = stream of pseudo random numbers integers from the interval (0, m-1) a = multiplier constant c = additive constant m = modulus or remainder of m

4. Using Random Numbers to generate events Example: Service Frequency Data If RN = 47, then Service Time = 3 minutes 95 – 00 1 .05 6 90 – 94 .95 .05 5 75 – 89 .90 .15 4 35 – 74 .75 .40 3 10 – 34 .35 .25 2 00 – 09 .1 .10 1 Random Digit Assignment Cumulative Frequency Observed Frequency Service Time (minutes)

5. Random Variates Random variates are randomly sampled information which will be used as inputs to the simulation model. Random numbers are together with empirical or statistical distributions to generate random variates.

6. Example of a random variate generator

7. Conceptual Modeling

8. Conceptual Modeling Most critical part of the simulation modeling process. Model design can impact the following: Data requirements Speed and ease of model development Validity of the model Speed of experimentation Level of confidence on the simulation results

9. Conceptual Modeling It expects the modeler to have a thorough understanding of the operations of the system being modeled. Often the least understood and removed from the modeling process It is considered as an art due to the lack of defined methods and procedures

10. What is conceptual modeling? A non-software specific description of the simulation model that is to be developed (Robinson, 2004) It describes the input, output, content, assumptions, and simplifications of the model in relation to the system problem and objectives

11. Elements of Conceptual Modeling Problem and Objectives – purpose of the model and the simulation project Inputs – elements that can be altered to create an improvement (experimental factors) Outputs – results of the simulation model Content – components in the model and their interactions

12. Elements of Conceptual Modeling Assumptions – uncertainties or beliefs about the real world being modeled Simplifications – ways of reducing the complexity of the model

13. Representing the Conceptual Model System Component List – Description of the components in the model Ex. Supermarket Payment System Entities = Customer – Inter-arrival time Attribute = Paying customers Activity = Coding of purchased items, payment, and packing Etc.

14. Representing the Conceptual Model Process Flow Diagram – process map of the flow of the entities across processes Customers (inter arrival time) Queue Capacity Service (Service time distribution)

15. Representing the Conceptual Model Logic Flow Diagram – process map involving logical decisions across the process flow. Customer Arrives Space in Queue? Queue for Service Customer Served Customer Leaves Server Available? No No Yes Yes

16. Framework for Conceptual Modeling Source: Simulation by Robinson, 2004 Inputs Experimental Factors Simulation Model Outputs Responses Model Objectives Problem Situation

17. Methods of Model Simplification Model simplification – Way of handling the complexity of the model. Done by: Removing of components and interconnections that have little effect on model accuracy Representing more simply the components and interconnections while maintaining a satisfactory level of model accuracy

18. Simplification Approaches Aggregation of components Black box modeling Grouping of entities Excluding component details Replacing components with random variables Excluding infrequent events Reducing set rules Splitting models

19. Guidelines for simplification Use judgment whether simplification will have a significant effect on model accuracy. Get agreement with client. Aim is faster development time Do a comparison between with and without simplification and compare performance. Better certainty on the simplification, but longer development time. Simplification should not compromise transparency and result to a loss of confidence by the client or decision maker

20. Data Collection Uses of Data in the simulation modeling process: Preliminary or contextual data Qualitative information leading to understanding of the problem and its situation Model realization data Quantitative data for developing and running the model Model validation data Quantitative and qualitative data of the real world system for comparison to the output of the simulation model

21. Types of Data Data that is readily available Layout, throughput, staffing levels, schedules, service times Data that is NOT available but collectible Arrival patterns, machine failure rates, repair times, nature of decision making Data that is NOT available and NOT collectible Rare failure times, availability of personnel for data collection, machine failures, lost transactions

22. Dealing with Unobtainable Data Data may estimated from other sources. Use surrogate data from similar systems. Example: predetermined time and motion information, standard times, etc Consider data as an experimental factor. Example: if machine failure is not available, what should the acceptable machine failure to achieve desired throughput?

23. Other Data Issues Data Accuracy – historical data is not necessarily a good indicator of future patterns. Example: historical breakdown patterns and arrival patterns may not occur in the future Data Format – contextual meaning of the data should be explicit. Example: time between failures (TBF) Time TBF1 Machine down time TBF2

24. Data Representing Unpredictable Variability (Random) Traces – Stream of data based actual sequence of events of the real world system Empirical Distributions – Summarize Trace data converted into a frequency distribution Statistical Distributions – known probability density functions Bootstrapping – re-sampling from a small data set

25. Verification and Validation Verification – process of ensuring that the conceptual model has been successfully transformed into a computer model Validation – process of ensuring that the model is sufficiently accurate to represent the real world system being modeled.

26. Case