CMPE571 Systems Modelling and Simulation 2022-23 Fall Homework 4 Date: Mon., 12/12/2022 Due Date: Mon., 03/01/2023 1. Objective The objective of this homework is to help students understand and enable: (i) Principles of MCG-based Pseudo Random Numbers (PRN) and their generation (ii) Generation of Uniformly Distributed RNs (iii) Understanding of minimal and maximal length sequences. (iv) Limitations of Random Number generators (v) Exhaustive analysis of a simple RN sequence. (vi) Understand the "seed" notion. 2. Problem Given the Linear Congruential Generator (LCG) Method : Xi+1=(aXi+c)modm,c>0,i=0,1,2, Suggested to use X0=27,a=17,c=43, and m=100. Giving: Xi+1=(17Xi+43)mod100,i=0,1,2, 1. You are to investigate and map all the numbers in the range 0 to 99 to the random sequence(s). Note that it is likely that there are more than one sequences in the series. Each sequence should be mapped and non-interleaving sequences found. One (or possibly more) will be maximal length sequence. Others may be locked sequences with limited numbers. 2. Write a "C" program to implement the above LCG. Make sure the "seed" X0, is a parameter to enter to the program. 3. Set seed X0=27 as given above and find the sequence of RIs and RNs that can be generated using modulus m=100. 4. Search and find all the numbers that can be generated with this LCG and state the seeds that must be used in order to get the said sequences. 5. Display these sequences in a table. 3. The Technique - Your programs should be modular and structured (monolithic programs will loose marks). - The preferred technique is to write software with multi-file " C " programs and compiled through the make facility on Cygwin or using the Project facility of the DevC++ IDE. - If you use other platforms, please provide a Readme.txt file and explain how to use the platform. - All possible seed values must be checked and reported (i.e. no gaps must be left in the sequence of numbers possible). 4. Deliverabes Submit a short report for your results. Also include an explanatory README.txt file which should explain how file names (as answers) map to sections (questions/sections), source codes, executables, input and output data files (appropriately named). Please also comment on your results. Submissions with no comments will not receive full marks. 5. Effort Type This homework can be done individually or in a group of 2 students. Students should send e-mail indicating the members of each group. One submission per group is acceptable. Each member's contribution must be mentioned in the Readme.txt file to be provided that must include the names of the team members. 6. References J. Banks, J.S. Carson II, B.L. Nelson, D.M. Nicol, Discrete-Event System Simulation, 5th Ed., Prentice-Hall, 2010, ISBN-10: 0136062121