Lajos Takács
Encyclopedia
Lajos Takács is a Hungarian mathematician
, known for his contributions to probability theory
and in particular, queueing theory
. He wrote over two hundred scientific papers and six books.
He studied at the Technical University of Budapest (1943-1948), taking courses with Charles Jordan
and received a Ph.D.
for his dissertation On a Probability-theoretical Investigation of Brownian Motion (1948). From 1945-48 he was a student assistant to Professor Zoltan Bay and participated in his famous experiment of receiving microwave echoes from the Moon (1946). In 1957 he received the Academic Doctor's Degree in Mathematics for his thesis entitled "Stochastic processes arising in the theory of particle counters" (1957).
He worked as a mathematician at the Tungsram Research Laboratory (1948-55), the Research Institute for Mathematics of the Hungarian Academy of Sciences (1950-58) and was an associate professor in the Department of Mathematics of the L. Eotvos University (1953-58). He became one of the first to introduce semi-Markov process
es in queueing theory (1952).
He took a lecturing appointment at Imperial College in London
and London School of Economics
(1958), before moving to Columbia University
in New York City
(1959-66) and Case Western Reserve University
in Cleveland (1966-87), advising over twenty Ph.D.-theses. He also held visiting appointments at Bell Labs
and IBM Research
, had sabbaticals at Stanford University
(1966). At present he is Professor Emeritus at Case Western Reserve University.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his contributions to probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and in particular, queueing theory
Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
. He wrote over two hundred scientific papers and six books.
He studied at the Technical University of Budapest (1943-1948), taking courses with Charles Jordan
Charles Jordan
Charles Thorton Jordan was an American magician.-Early life:Charles Jordan was born in Berkeley, California to Charles Renalt Jordan, a wholesale supply manager and chicken farmer, and Mary Louise Jordan; he had a younger sister, Margaret Louise...
and received a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
for his dissertation On a Probability-theoretical Investigation of Brownian Motion (1948). From 1945-48 he was a student assistant to Professor Zoltan Bay and participated in his famous experiment of receiving microwave echoes from the Moon (1946). In 1957 he received the Academic Doctor's Degree in Mathematics for his thesis entitled "Stochastic processes arising in the theory of particle counters" (1957).
He worked as a mathematician at the Tungsram Research Laboratory (1948-55), the Research Institute for Mathematics of the Hungarian Academy of Sciences (1950-58) and was an associate professor in the Department of Mathematics of the L. Eotvos University (1953-58). He became one of the first to introduce semi-Markov process
Semi-Markov process
A continuous-time stochastic process is called a semi-Markov process or 'Markov renewal process' if the embedded jump chain is a Markov chain, and where the holding times are random variables with any distribution, whose distribution function may depend on the two states between which the move is...
es in queueing theory (1952).
He took a lecturing appointment at Imperial College in London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
and London School of Economics
London School of Economics
The London School of Economics and Political Science is a public research university specialised in the social sciences located in London, United Kingdom, and a constituent college of the federal University of London...
(1958), before moving to Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
(1959-66) and Case Western Reserve University
Case Western Reserve University
Case Western Reserve University is a private research university located in Cleveland, Ohio, USA...
in Cleveland (1966-87), advising over twenty Ph.D.-theses. He also held visiting appointments at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
and IBM Research
IBM Research
IBM Research, a division of IBM, is a research and advanced development organization and currently consists of eight locations throughout the world and hundreds of projects....
, had sabbaticals at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
(1966). At present he is Professor Emeritus at Case Western Reserve University.
Publications
The following is a partial list of publications- Some Investigations Concerning Recurrent Stochastic Processes of a Certain Kind, Magyar Tud. Akad. Alk. Mat.Int. Kozl. vol.3, pp.115-128, 1954.
- Investigations of Waiting Time Problems by Reduction to Markov Processes, Acta Math. Acad. Sci. Hung. vol.6, pp. 101-129, 1955.
- Sojourn times for the Brownian motion, Journal of Applied Mathematics and Stochastic Analysis, vol. 11, no. 3, pp. 231–246, 1998
- In memoriam: Pál Erdős (1913-1996), Journal of Applied Mathematics and Stochastic Analysis, vol. 9, no. 4, pp. 563–564, 1996
- Sojourn times, Journal of Applied Mathematics and Stochastic Analysis, vol. 9, no. 4, pp. 415–426, 1996
- Brownian local times, Journal of Applied Mathematics and Stochastic Analysis, vol. 8, no. 3, pp. 209–232, 1995
- Limit distributions for queues and random rooted trees, Journal of Applied Mathematics and Stochastic Analysis, vol. 6, no. 3, pp. 189–216, 1993
- On a probability problem connected with railway traffic, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 1, pp. 1–27, 1991
- Conditional limit theorems for branching processes, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 4, pp. 263–292, 1991
- On the distribution of the number of vertices in layers of random trees, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 3, pp. 175–186, 1991
- Queues, random graphs and branching processes, Journal of Applied Mathematics and Stochastic Analysis, vol. 1, no. 3, pp. 223–243, 1988
- On the distribution of the supremum for stochastic processes, Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, 6(3):237-247, 1970
- On the Total Heights of Random Rooted Binary Trees, J. Comb. Theory, Ser. B 61(2): 155-166 (1994)
- Counting forests, Discrete MathematicsDiscrete Mathematics (journal)Discrete Mathematics is a journal in the broad area of discrete mathematics, combinatorics, graph theory and their applications, published by Elsevier. It publishes both short notes, full length contributions, as well as survey articles. In addition, DM publishes a number of special issues each...
84(3): 323-326 (1990) - On Cayley's formula for counting forests, J. Comb. Theory, Ser. A 53(2): 321-323 (1990)
- A generalization of an inequality of Stepanov, J. Comb. Theory, Ser. B 48(2): 289-293 (1990)
- On the Number of Distinct Forests, SIAM Journal on Discrete MathematicsSIAM Journal on Discrete MathematicsSIAM Journal on Discrete Mathematics is a peer-reviewed mathematics journal published quarterly by SIAM.The journal includes articles on pure and applied discrete mathematics....
3(4): 574-581 (1990) - On the "problème des ménages", Discrete Mathematics 36(3): 289-297 (1981)
- On a Combinatorial Theorem Related to a Theorem of G. Szegö, J. Comb. Theory, Ser. A 30(3): 345-348 (1981)
- An Identity for Ordered Partial Sums, J. Comb. Theory, Ser. A 23(3): 364-365 (1977)
Books
- Stochastic Processes. Problems and Solutions (Methuen, 1960)
- Introduction to the Theory of Queues, (Oxford University PressOxford University PressOxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
, 1962) - Combinatorial Methods in the Theory of Stochastic Processes, (John Wiley, 1967)
Awards
- 1993 Foreign Membership Magyar Tud. Akad.
- 1994 John von Neumann Theory PrizeJohn von Neumann Theory PrizeThe John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciencesis awarded annually to an individual who has made fundamental and sustained contributions to theory in operations research and the management sciences.The Prize named after mathematician John von...
- 2002 Fellows Award. Inst. for Operations Research and Management Sciences
Literature
- Jewgeni H. Dshalalow and Ryszard SyskiRyszard SyskiRyszard Syski was a Polish-American mathematician whose research was in queueing theory....
, Lajos Takács and his work, in Jrn. of Applied Math. and Stochastic Analysis, 7(3):215-237, 1994. - Studies in Applied Probability, Papers in Honour of Lajos Takacs. by J. Galambos, J. Gani, The Journal of the Operational Research Society, 46(11):1397-98, 1995