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Abstract

This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had come up with a solution to resolve this paradox. In response, I received an e-mail from Dalma, his wife, that broke down me to tears by the sad news she broke that he passed away on the day I sent my e-mail. I am extremely sorry for the loss of such a great human being, teacher, scholar and a world-leading scientist. He was my teacher, mentor and loving professor Lajos Takács. However, we are consoled by the belief that he is alive and well among the world’s mathematics and science society forever. I am sure he is at peace. He has my prayers. I cannot say more about him than what I had prepared to present in his honor as a Preface to the AAM Vol. 10, Issue 2 (December 2015). I am talking about a humble human being, a mentor, a caring teacher, a brilliant Hungarian mathematician, scientist, probabilist, statistician, a pioneer of queueing theory, honored by many organizations, a winner many prizes, including the John von Neumann Theory prize, and doctoral dissertation guide of 23 students, including Paul Burke and myself. The impact of his 225 original papers and his two books, Introduction to the Theory of Queues and Combinatorial Methods in Theory of Stochastic Processes is tremendous. One could not imagine what the impact of his 1600 unpublished materials on the theory of random fluctuation would be on the theory of probability. While I was writing about his famous Integro-Differential Equation in chapter 5 of my book and reviewing the literature, I noticed that this 1962 formula was applied by Hága et al. (2006) regarding an Efficient and reliable available bandwidth measurement. Another paper I came to notice was by Kim (2014) regarding an available server management in the Internet connected network environments, in which local backup servers are hooked up by LAN and remote backup servers are hooked up by VPN (Virtual Private Network) with high-speed optical network citing Takács (1958), Theory of Telephone Traffic. So, it is not only that his 1962 book has been cited hundreds of times, but even his older papers are also being used these days. The rest of this Preface was presented at the The 8th International Conference on Lattice Path Combinatorics and Applications, on August 18, 2015, at California Polytechnic State University Pomona, California, United States of America, at his 91st birthday, in honor of Professor Lajos Takács. The presentation was made jointly by Professors Aliakbar Montzer Haghighi and Sri Gopal Mohanty.

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