Lajos Takács

August 21, 1924 – December 4, 2015

Brief Biography

Lajos Takács was born in a small Hungarian town outside Budapest. At fifteen years old, he became interested in mathematics after reading Leonhard Euler’s Elements of Algebra and Manó Beke’s Differential and Integral Calculus. By the time he enrolled at the Technical University of Budapest in 1943, Takács had refined his focus to the study of combinatorics. The Technical University was then one of Europe’s finest institutions of higher education, led by such renowned mathematics and physicists as Charles Jordan, Alfred Rényi, and Zoltán Bay. At age twenty-four, Takács received his first doctoral degree as a probabilist.

Around this time, Takács began working under Bay at the Tungsram Research Laboratory. He eventually took on another research consultancy position at the Hungarian Academy of Sciences. Though his education was interrupted by the Second World War and its aftermath, Takács continued his studies and in 1957 received a habilitation doctorate, a degree that many European universities require for full professorial positions. It was during this period that he developed the theory of point processes and first introduced semi-Markov processes to operations research, culminating in the 1960 publication, Stochastic Processes: Problems and Solutions. Takács began to integrate his work on stochastic probability with queueing theory, applying it to such areas as telecommunications traffic.

Takács was an associate professor at Budapest’s Eötvos Loránd University until 1958 when he took joint appointments at Imperial College in London and London School of Economics. He moved to the United States to accept a professorship at Columbia University before settling at Case Western Reserve University in 1966. While he was at Columbia, Takács held consulting positions at Bell Laboratories, IBM, and Boeing. During his years at Case, he supervised fourteen PhD students and wrote over one hundred monographs and research papers.

In the early 1960s, Takács worked on time-dependent behaviors of various queueing processes, including the so-called "Takács Process". He employed a variety of techniques and methodologies to deal with queue feedbacks, priority queues, and queues with balking. He discovered a generalization of Bertrand’s ballot theorem, making it possible to solve a number of problems in queueing theory and order statistics and probability. In 1967, he published the best-selling book, Combinatorial Methods in the Theory of Stochastic Processes.  

In 1994, The Institute of Management Sciences (TIMS) and the Operations Research Society of America (ORSA) awarded Takács the renowned John von Neumann Theory Prize. The prize celebrated a career spanning over four decades and lauded Takács’ contributions to applied probability in operations research. In 2002, he was elected a Fellow of the Institute for Operations Research and the Management Sciences. 

Other Biographies

Wikipedia Entry for Lajos Takacs

Dshalalow J. H. & Syski R. (1994) Lajos Takacs and His Work. Journal of Applied Mathematics and Stochastic Analysis, 7(3): 215-237. (link)

Haghighi  A. M. & Mohanty S. G. In Honor and Memory of Professor Lajos Takacs, August 21, 1924 - December 4, 2015. Applications and Applied Mathematics, 10(2): 634-666. (link)


Technical University of Budapest, PhD 1948

Technical University of Budapest, Dr Habil 1956 (Mathematics Genealogy)


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS

Application Areas


Cleveland Plain Dealer (2015)  (link) accessed 4/22/2019.

Bingham N. H. (2016)  Lajos Takács, 1924-2015.  J. Royal Stat Soc 179:4 1124-1125 (link)

Awards and Honors

John von Neumann Theory Prize 1994

Institute for Operations Research and the Management Sciences Fellow 2002

Selected Publications

Takács L. (1953) Some investigations concerning recurrent stochastic processes of a certain kind. Magyar Tud. Akad. Alk. Mat. Int. Kozl, 3: 115-128.

Takács L. (1954) Investigations of waiting time problems by reduction to Markov processes. Acta Mathematica Hungarica, 6: 101-129.

Takács L. (1957) On certain sojourn problems in the theory of stochastic process. Acta Mathematica Hungarica, 8: 169-191.

Takács L. (1960) Stochastic Process: Problems and Solutions. Methuen: London.

Takács L. (1962) A generalization of the ballot problem and its application in the theory of queues. Journal of the American Statistical Association, 57(298): 327-337.

Takács L. (1962) Introduction to the Theory of Queues. Oxford University Press: Oxford.

Takács L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley & Sons: New York.

Takács L. (1968) Two queues attended by a single server. Operations Research, 16(3): 639-650.

Takács L. (1978) An increasing continuous singular function. American Mathematical Monthly, 85(1): 35-37.

Takács L. (1991) Conditional limit theorems for branching processes. International Journal of Stochastic Analysis, 4(4): 263-292.