Volume 4 , Issue 1 , PP: 10-27, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Sawsan Rateb almokabaa 1 * , Maissam Ahamad Jdid 2
Doi: https://doi.org/10.54216/PAMDA.040102
The efforts of many researchers and scholars have focused on providing appropriate algorithms for generating random numbers and developing them in a manner that suits the need for them, but these algorithms still have advantages and disadvantages, so they are suitable for a specific study and not suitable for another study. The reason for the interest of researchers and scholars in the process of generating random numbers is that random numbers have many scientific and technical applications, starting with generating a series of semi-random numbers, starting from computer simulation to encryption, games of chance, and random samples for statistics and security. In simulation, which is one of the important methods provided by the new science of operations research, the primary reliance is on generating a series of random numbers that follow the regular distribution in the range [0,1], and then converting these random numbers into random variables that follow the probability distribution according to which the system to be simulated works, as the accuracy of the results we obtain from the simulation process depends on the numbers we generate using one of the algorithms. In other words, the appropriate algorithm for the field of study must be chosen from among the algorithms used, which prompted us to prepare this research, through which we will present a reference study of some of the algorithms used to generate random numbers. Where we will highlight the advantages and disadvantages of these algorithms and the most important areas of their use. Then we will calculate the number of these algorithms and compare them. The algorithms that we will discuss in this research are:
➢Middle Square Method.
➢Middle multi-Method.
➢Fibonacci Methods.
➢Linear congruential Methods.
Random number generation , Center square method , Center product method , Fibonacci series , Linear congruence method , Random number series
[1] A. K. I. Sheet, Introduction to Random Number Generators and Simulation, University of Mosul, 2009.
[2] I. M. Alali, Operations Research, Tishreen University Publications, 2004.
[3] S. Ahmed, Operations Research, Arab Center for Arabization, Translation, Authorship, and Publishing, Damascus, 1998.
[4] A. M. A. R. Bari, Modeling and Simulation, Saudi Arabia, 2002.
[5] D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison-Wesley, 1969.
[6] V. Padanyi and T. Herendi, "Generalized Middle Square Method," 2022.
[7] B. Widynski, "Middle-Square Weyl Sequence RNG," 2022.
[8] H. Rahimov, M. Babaie, and H. Hassanabadi, "Improving Middle Square Method RNG Using Chaotic Map," 2011.
[9] "Pseudo-random numbers/Middle-square method," Rosetta Code, [Online]. Available: https://rosettacode.org/wiki/Pseudo-random_numbers/Middle-square_me. [Accessed: Feb. 2025].
[10] "Fibonacci Series in Java," Javatpoint, [Online]. Available: https://www.javatpoint.com/fibonacci-series-in-java. [Accessed: Feb. 2025].
[11] "Java Program to Implement the Linear Congruential Generator for Pseudo Random Number Generation," GeeksforGeeks, [Online]. Available: https://www.geeksforgeeks.org/java-program-to-implement-the-linear-congruential-generator-for-pseudo-random-number-generation/. [Accessed: Feb. 2025].
[12] D. Johnston, Random Number Generations - Principles and Practices, 2018.
[13] Austrian Academy of Sciences, Random Number Generation and Quasi Monte Carlo Methods, Philadelphia, PA, 1992.
[14] D. E. Knuth, The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd ed., Addison-Wesley, 1997.
[15] J. E. Gentle, Random Number Generation and Monte Carlo Methods, Springer, 2003.
[16] J. Von Neumann, "Various Techniques Used in Connection with Random Digits," Monte Carlo Method, Applied Mathematics Series, vol. 12, National Bureau of Standards, 1949.
[17] S. K. Park and K. W. Miller, "Random Number Generators: Good Ones Are Hard to Find," Communications of the ACM, vol. 31, no. 10, pp. 1192-1201, 1989.