References
V. E. Beneš, A sufficient set of statistics for a simple telephone exchange model,Bell System Technical Journal,36 (1957), pp. 939–964.
V. E. Beneš, Fluctuations of telephone traffic,Bell System Technical Journal,36 (1957), pp. 965–973.
D. Blackwell, A renewal theorem,Duke Math. Journal.,15 (1948), pp. 145–150.
J. W. Cohen, The full availability group of trunks with an arbitrary distribution of the inter-arrival times and a negative exponential holding time distribution,Simon Stevin Wis-en Natuurkundig Tijdschrift,31 (1957), pp. 169–181.
A. K. Erlang, Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges,Post Office Electrical Engineer's Journal,10 (1918), pp. 189–197.
W. Feller,An introduction to probability theory and its applications (New York, 1950).
R. Fortet, Random functions from a Poisson process,Proc. Second Berkeley Symposium on Math. Stat. and Probability, (1951), pp. 373–385.
R. Fortet, Random distributions with an application to telephone engineering,Proc. Third Berkeley Symposium on Math. Stat. and Probability,2 (1956), pp. 81–88.
F. G. Foster, On the stochastic matrices associated with certain queueing processes,Annals of Math. Stat.,24 (1953), pp. 355–360.
A. Khintchine, Korrelationstheorie der stationären stochastischen Prozesse,Math. Annalen,109 (1934), pp. 604–615.
А. Я. Хинчин, Математические метории массового овслуживаниЯ, ТрудьІ Математического Института им В. А. Стеклова,49 (1955).
Ch. Jordan,Calculus of finite differences (Budapest, 1939).
А. Н. Колмогоров иО.В. Проηоров, О суммах случайного числа слуайньІх, Усп. Мат. Наук,4 (1949), вьІп.4, pp. 168–172.
L. Kosten, On the validity of the Erlang and Engset loss-formulae,Het. P. T. T. Bedrijf,2 (1948–49), pp. 42–45.
L. Kosten, On the accuracy of measurements of probabilities of delay and of expected times of delay in telecommunication systems. I,Applied Scientific Research B,2 (1951), pp. 108–130, and II,2 (1952), pp. 401–415.
L. Kosten, The historical development of the theory of probability in telephone traffic engineering in Europe,Teleteknik,1 (1957), pp. 32–40.
C. Palm, Analysis of the Erlang traffic formulae for busy-signal arrangements,Ericsson Technics, No. 4 (1938), pp. 39–58.
C. Palm, Intensitätsschwankungen im Fernsprechverkehr,Ericsson Technics, No. 44 (1943), pp. 1–189.
F. Pollaczek, Lösung eines geometrischen Wahrscheinlichkeitsproblems,Math. Zeitschrift,35 (1932), pp. 230–278.
F. Pollaczek, Généralisation de la théorie probabiliste des systèmes téléphoniques sans dispositif d'attente,Comptes Rendus Acad. Sci. Paris,236 (1953), pp. 1469–1470.
A. Rényi, On some problems concerning Poisson processes,Publ. Math. Debrecen,2 (1951), pp. 66–73.
C. Ryll-Nardzewski, On the non-homogeneous Poisson processes,Colloquium Math.,3 (1955), pp. 192–195.
Б. А. Севастянов, Эргодическая теорема для марковских пиоцессов и ее приложение к телефонньім с отказами, Теория вероятностей и ее примения,2 (1957), pp. 106–116.
W. L. Smith, Asymptotic renewal theorems,Proc. of the Royal Society of Edinburgh A,64 (1954), pp. 9–49.
W. L. Smith, Regenerative stochastic processes,Proc. of the Royal SocietyA,232 (1955), pp. 6–31.
L. Takács, On secondary processes generated by a Poisson process and their applications in physics,Acta Math. Acad. Sci. Hung,5 (1954), pp. 203–236.
L. Takács, On secondary stochastic processes generated by recurrent processes,Acta Math. Acad. Sci. Hung.,7 (1956), pp. 17–29.
L. Takács, Some investigations concerning recurrent stochastic processes of a certain type (Hungarian, English summary),MTA Alk. Mat. Int. Közl.,5 (1954), pp. 115–128.
L. Takács, On some probability problems concerning the theory of counters,Acta Math. Acad. Sci. Hung.,8 (1957), pp. 127–138.
L. Takács, On certain sojourn time problems in the theory of stochastic processes,Acta Math. Acad. Sci. Hung.,8 (1957), pp. 169–191.
L. Takács, On a sojourn time problem, Teopия верортностеь и ее применения,2 (1957), pp. 61–69.
L. Takács, On the generalization of Erlang's formula,Acta Math. Acad. Sci. Hung. 7 (1956), pp. 419–433.
L. Takács, On a probability problem concerning telephone traffic,Acta Math. Acad. Sci. Hung. 8 (1957), pp. 319–324.
L. Takács, A telefon-forgalom elméletének néhány valószinüségszámitási kérdéséröl,MTA Mat. és Fiz. Oszt. Közl.,8 (1958), pp. 151–210.
L. Takács, On the sequence of events, selected by a counter from a recurrent process of events, Теория вероятностеь и ее nрименения,1, (1956), pp. 90–102.
A. Wald, Sequential tests of statistical hypotheses,Annals of Math. Stat.,16 (1945), pp. 117–186.
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Dedicated to the memory of Conny Palm (1907–1951)on the occasion of the anniversary of his 50th birthday
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Takács, L. On a coincidence problem concerning telephone traffic. Acta Mathematica Academiae Scientiarum Hungaricae 9, 45–81 (1958). https://doi.org/10.1007/BF02023865
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DOI: https://doi.org/10.1007/BF02023865